Assessing the feasibility of near-ambient conditions superconductivity in the Lu-N-H system

communica ions ma e ialsA icle h ps://doi.o g/10.1038/s43246-024-00500-9 Assessing he easibili y o nea -ambien condi ions supe conduc i i y in he Lu-N- Hsys em Check o upda es Yue-Wen Fang 1,2 ,Đo đeDangić1,2 & Ion E ea 1,2,3 The epo o nea -ambien supe conduc i i y in ni ogen-doped lu e ium hyd ides (Lu-N-H) has gene a ed a g ea in e es . Howe e , conflic ing esul s aised doub s ega ding supe conduc i i y. He e, we combine high- h oughpu c ys al s uc u e p edic ions wi h a as p edic o o supe conduc ing c i ical empe a u e (T c ) based on elec on localiza ion unc ion o shed ligh on he p ope ies o Lu-N-H a 1 GPa. None o he p edic ed s uc u es suppo s high- empe a u e supe conduc i i y and he inclusion o ni ogen in he c ys al s uc u e p edic ions leads o mo e insula ing s uc u es han me allic ones in quan i y. Despi e he lack o nea -ambien supe conduc i i y, we conside al e na i e me as able empla es and s udy hei T c and dynamical s abili y including quan um anha monic e ec s. Lu 4 H 11 N exhibi s a T c o 100 K a only 20 GPa, a la ge inc ease compa ed o 30 K o i s pa en LuH 3 . In e es ingly, i has a simila X- ay pa e n o he expe imen al one. The LaH 10 -like LuH 10 and CaH 6 -like LuH 6 become high- empe a u e supe conduc o s a 175 GPa and 100 GPa, wi h T c o 286 K and 246 K, espec i ely. Ou findings sugges ha high- empe a u e supe conduc i i y is no possible in s able phases a nea -ambien p essu e. Howe e , a a sligh ly enhanced p essu e o 20 GPa, high-T c supe conduc i i y eme ges in Lu-H-N, and me as able oom- empe a u e supe conduc ing empla es pe sis a high p essu es. Supe conduc i i y is one o he mos ascina ing physical p ope ies o ma e . E e since i s disco e y in me cu y below 4.2 K in 1911, humani y has emba ked on a es less ques o oom- empe a u e supe conduc i i y a ambien condi ions, ceaselessly mo ing he field o wa d. Ashc o sug- ges ed ha he chemical p ecomp ession exe ed by he hos a oms could boos he supe conduc ing c i ical empe a u es (T c ) o hyd ogen- ich compounds a lowe p essu es han pu e me allic hyd ogen1.Thisideawas u he p opelled by ab ini io c ys al s uc u e p edic ion echniques a high p essu e, which could p edic he modynamically s able high-T c c ys al s uc u es2–8. The main b eak h ough a i ed in 2015 when D ozdo e al.9 obse ed supe conduc i i y a 203 K in H 3 S a 155 GPa, a compound ha had been an icipa ed heo e ically by Duan e al.10. Since hen, expe imen s ha e epo ed supe conduc i i y abo e 200 K in se e al bina y sys ems such as LaH 10 (~250 K a 150 GPa11,12), CaH 6 (~215 K a 172 GPa13), YH 9 (~243 K a 201 GPa14), and YH 6 (~224 K a 166 GPa14,15). Rema kably, ab ini io calcula ions suppo o ha e e en an icipa ed all hese disco e ies7,8,10,15–18. Conside ing ha s anda d ab ini io c ys al s uc u e sea ches o bina y hyd ides ha e been exhaus ed, he a en ion is shi ing owa ds e na y hyd ides, which o e mo e possibili ies due o he inc eased complexi y o he phase space6,19. This ecen e o has led o he p edic ion o e na y supe hyd ides wi h high T c s a mode a e (below 100 GPa) and e en ambien p essu es, a which bina y supe hyd ides do no seem o sus ain a c i ical empe a u e la ge han 100 K20–28. In pa icula , Dasenb ock-Gammon e al. ha e ecen ly epo ed expe imen al e idence o supe conduc i i y in ni ogen-doped lu e ium hyd ide (Lu-N-H) samples wi h a oom- empe a u e T c o 294 K a nea ly ambien p essu e (1 GPa)29. This las claim has d i en a su ge o in e es and exci emen , bu a li ely discussion and polemic oo. Nume ous expe imen al and heo e ical e o s ha e been made la ely ying o eplica e o explain he findings unco e ed by Dasenb ock-Gammon e al. Howe e , eme ging e idence challenges he claim o oom- empe a u e supe conduc i i y. The imp essi e colo change wi h p essu e in hei s udy is sugges ed o a ise om Fm  3mLuH 2 due o he p esence o an undamped in e band plasmon ha en e s he isible ange 1Fisika Aplika ua Saila, Gipuzkoako Ingenia i za Eskola, Uni e si y o he Basque Coun y (UPV/EHU), Eu opa Plaza 1, 20018Donos ia/San Sebas ián, Spain. 2Cen o de Física de Ma e iales (CSIC-UPV/EHU), Manuel de La dizabal Pasealekua 5, 20018 Donos ia/San Sebas ián, Spain. 3Donos ia In e na ional Physics Cen e (DIPC), Manuel de La dizabal Pasealekua 4, 20018 Donos ia/San Sebas ián, Spain. e-mail: yuewen. [email protected];do [email protected];ion.e [email protected] Communica ions Ma e ials | (2024) 5:61 1 1234567890():,; 1234567890():,; wi h inc easing p essu e and, hus, does no ha e any impac on supe conduc i i y30, con a y o he o iginal claim29. Fu he expe imen al and heo e ical s udies31–35 suppo ha he colo change can be explained alone by LuH 2 , a compound ha is known since a long ime in which Lu a oms o m a ace-cen e ed cubic ( cc) la ice and H a oms occupy in e - s i ial e ahed al si es36. In addi ion, se e al expe imen al and heo e ical in es iga ions o he X- ay powde di ac ion (XRD) poin ou ha he majo peaks in Dasenb ock-Gammon e al.’s s udy should mos ly come om Fm  3mLuH 2 31,32,34,37–39. These s udies ha e indica ed ha he pa en phase o he Lu-N-H is mo e likely o be Fm  3mLuH 2 , a he han he Fm  3m LuH 3 as claimed by Dasenb ock-Gammon e al. Howe e , all he exis ing expe imen al and heo e ical s udies30,35,39–41 ha e shown ha LuH 2 is no supe conduc ing o only shows heo e ical T c on he o de o 0.01 K a 0~1 GPa. Ab ini io c ys al s uc u e p edic ions explo ing di e en s oi- chiome ies o ni ogen-doped lu e ium hyd ides do no p edic any phase wi h nea -ambien supe conduc i i y39,42,43. Fu he mo e, Ming e al.32 and Cai e al.44 ha e success ully ob ained ni ogen-doped lu e ium hyd ides, and asse ed ha he c ys al s uc u es o hei samples we e he same as hose syn hesized by Dasenb ock-Gammon e al.29.Specifically, he la ice cons an s o wo ace-cen e ed-cubic phases (5.03 Åand 4.755 Å)inCai e al.’s s udy a e in excellen ag eemen wi h Dasenb ock-Gammon e al.’s sample A (5.0289 Å) and sample B (4.7529 Å). Howe e , despi e his close ag eemen in la ice cons an s, nei he o he wo s udies obse ed supe - conduc i i y, e en a p essu es up o 40 GPa and empe a u es as low as 2 K. In addi ion, Ming e al. ha e p oposed he sample is mo e app op ia ely ep esen ed as LuH 2±x N y a he han LuH 3−δ N ϵ , sugges ing ha LuH 2 is mo e likely o be he pa en phase. I should be no ed ha he c ys al s uc u e o Fm  3mLuH 3 is iden ical o Fm  3mLuH 2 wi h an ex a hyd ogen a om loca ed a he oc ahed al in e s i ial si e30. The con o e sial esul s equi e a comp ehensi e unde s anding o he p ope ies o Lu-N-H sys em. He ein, we epo high- h oughpu c ys al s uc u e calcula ions in he Lu-H and Lu-N-H sys ems and sc een he po en ial T c o he p edic ed compounds wi h a simple desc ip o based on elec onic p ope ies45.SinceLuH 2 and LuH 3 ha e been sugges ed o be he po en ial pa en phases o he nea -ambien supe conduc ing Lu-N-H, we ocus he s uc u al sea ch on de i a ions o bo h o hem wi h and wi hou ni ogen. By sc eening mo e han 15,000 s uc u es a 1 GPa, ou p edic ion has esul ed in he disco e y o 638 phases loca ed wi hin 0.24 eV pe a om abo e he con ex hull, a easonable limi o he syn hesizabili y o me a- s able phases, wi h 214 o hem me allic. Ou esul s sugges ha hese 1- GPa-phases a e imp obable o mani es high- empe a u e supe - conduc i i y, as deduced by p edic ing hei T c s wi h he ne wo king alue model45.Ou findings sugges ha , when seeking o de elop me allic lu e- ium hyd ides a 1 GPa, doping wi h ni ogen should be a oided as i s la ge elec onega i i y emo es elec ons om hyd ogen si es and p omo es insula ing phases. Mo eo e , we iden i y ens o s able me allic phases ha exhibi XRD ea u es s ongly esembling he expe imen al XRD, sugges ing ha many o he p edic ed s uc u es ha e a Lu a angemen no a om he cc la ice and ha H o N a oms occupy in e s i ial si es. Conside ing ha XRD is no capable o dis inguishing hem, one should app oach XRD s uc u al assignmen s in he Lu-H-N sys em wi h ca e. As a esul o he absence o high- empe a u e supe conduc i i y a 1 GPa, we s udy he dynamical s abili y and supe conduc ing p ope ies o high-symme y lu e ium hyd ides wi h and wi hou ni ogen a highe p essu es in c ys al s uc u es ha a o high T c s. We find ha quan um anha monic e ec s os e dynamical s abili y a lowe p essu es in all cases and s ongly impac he phonon spec a. Specifically, cubic Lu 4 H 11 N exhibi s a high T c o 100 K a a mode a e p essu e o 20 GPa. Upon inc easing p essu e, CaH 6 -like Im  3mLuH 6 and LaH 10 -like Fm  3mLuH 10 a e ound o main ain high T c so 246 K and 289 K, espec i ely, a 100 GPa and 175 GPa. Resul s and discussions Phase diag am The phase diag am o he Lu-N-H sys em a 1 GPa is cons uc ed by he con ex hull in Fig. 1a. The ci cles ep esen he modynamically s able phases o ming he hull and he squa es show he me as able phases up o 0.24 eV⋅a om−1abo e he con ex hull (abb e ia ed as H hull ≤0.24 eV⋅a om−1). Fo each s oichiome y, only he lowes -en halpy s a e is shown in he phase diag am. The en halpy calcula ions a e pe - o med wi hou conside ing he ze o-poin ionic ene gy, i.e., conside ing jus he Bo n-Oppenheime ene gy. The phase diag am includes he known s able bina y phases P  3c1LuH 3 ,Fm  3mLuN, Fm  3mLuH 2 , and mul iple a ificially cons uc ed s uc u es (e.g. Lu 2 H 5 )basedonFm  3mLuH 2 and LuH 3 by adding/ emo ing H a oms a e agonal/oc ahed al si es. In addi ion, he phase diag am comp ises 638 phases p edic ed h ough high- h oughpu c ys al s uc u e sc eening o e a ound 15,000 c ys al s uc- u es. Among he 638 p edic ed s uc u es wi hin his en halpy cu o , he e a e 214 me allic and 424 insula ing phases. The P2 1 /mLuH 2 N, wi h s uc u e ID in ou da abase o 2 u_LuH2N_389, is iden ified as he lowes -en halpy s a e among he e na y Lu-H-N compounds a 1 GPa. The elaxed s uc u e a 1 GPa is a ailable in “Da a a ailabili y”sec ion, and is schema ically shown in he inse o Supplemen a y Fig. S1. Dynamical s abili y in he ha monic app oxima ion o he P2 1 /mLuH 2 N is examined by pe o ming fini e dis- placemen DFT calcula ions o 2 × 2 × 2 supe cells. The phonon spec a and phonon densi y o s a es (DOS), as depic ed in Supplemen a y Fig. S1, demons a e he absence o any imagina y modes, he eby subs an ia ing he dynamic s abili y o he sys em. Seeing ha he P2 1 /mLuH 2 Nis ound o be he modynamically me as able nea he con ex hull, i is likely o be syn hesized unde p ope expe imen al condi ions. Howe e , he elec onic DOS o he P2 1 /mLuH 2 N as shown in Supplemen a y Fig. S2 exhibi s a band gap o ~2 eV, undoub edly excluding i o be a supe conduc ing phase. Because P2 1 /mLuH 2 N is he lowes -en halpy s a e and is dynamically s able, he phase diag am wi h espec o s able P  3c1LuH 3 and me as able LuH 2 N is explici ly shown in Fig. 1b, in which he s uc u es up o H hull o 0.3 eV⋅a om−1a e displayed. Figu e 1c shows he phase diag am wi h espec o elemen s, in which he bina y hyd ides wi h H hull ≤0.8 eV⋅a om−1a e included. The Fm  3m phase o LuH 3 , which has been p oposed by Dasenb ock-Gammon e al.29 as he pa en compound o he oom- empe a u e supe conduc o , is howe e ound o be loca ed abo e he con ex hull by a ound 82 meV⋅a om−1.This en halpy di e ence a his p essu e is no expec ed o be o e come by ionic ze o-poin ene gy e en i quan um anha monic e ec s a e conside ed18. To iden i y po en ial hos s o supe conduc i i y, we ha e ocused ou a en ion on he s abili y o he 214 me allic phases wi h H hull ≤0.24 eV⋅a om−1 ha ha e been ound in ou high- h oughpu c ys al s uc u e p edic ions. In o de o assess he phonon s abili y o he 214 me allic phases in he ha monic app oxima ion, we ha e pe - o med high- h oughpu DFT calcula ions o e 165,000 supe cells gene a ed by he fini e displacemen me hod (see “Me hods”sec ion). These calcula ions iden i y 57 dynamically s able me allic phases including 20 Lu 4 H 7 ,19Lu 4 H 9 ,11Lu 4 H 7 N, 2 Lu 4 H 9 N, 2 Lu 4 H 8 N, 2 Lu 3 H 8 N, and 1 Lu 4 H 11 N. The ha monic phonon spec a o 20 Lu 4 H 7 and 19 Lu 4 H 9 a e displayed in Supplemen a y Figs. S3 and S4, espec i ely. Addi ionally, he phonon spec a o he 18 e na y Lu-N-H phases a e p esen ed in Supplemen a y Fig. S5. The dynamical s abili y o hese 57 phases is well e idenced by he depic ed phonon spec a, which do no show imagina y phonon modes. The a io o he con ibu ion o hyd ogen o he o al elec onic densi y o s a es (DOS) a he Fe mi le el is widely sugges ed o be an impo an desc ip o o supe conduc i i y in supe hyd ides7,45,46. The e o e, he hyd ogen ac ion o he o al DOS a he Fe mi le el, a.k.a. H DOS ,a e compu ed o he 214 me allic phases. Table 1lis s H DOS ,spaceg oup symbols, and he en halpy dis ances abo e he con ex hull (H hull )o he 57 s able me allic phases a 1 GPa. A comple e lis o he 214 me allic phases ega dless o he dynamical s abili y is a ailable in Supplemen a y Table S1. As shown in Table 1,55ou o he57s ableme allicphasesshow e ylow H DOS anging om 0.02 o 0.05 (o 2%–5%), and only he Lu 4 H 9 N(ID: 1 u_Lu4H9N_136) and Lu 3 H 8 N (ID: 1 u_Lu3H8N_216) wi h he same space g oup P3m1showla geH DOS exceeding 20%. The low H DOS widely h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 2 obse ed in he p edic ed s uc u es signals he low c i ical empe a u e o e en he absence o supe conduc i i y o he p edic ed phases. To gain mo e insigh in o he possible onse o supe conduc i i y among he me allic phases, an unde s anding beyond H DOS is necessa y. Howe e , pe o ming elec on–phonon coupling calcula ions o all hese low-symme y sys ems is no easible. As an al e na i e, Belli e al. ha e p oposed ha a physical quan i y e med he ne wo king alue (ϕ), which is he elec on localiza ion unc ion alue ha c ea es an isosu - ace spanning h oughou he whole c ys al, can be used o p edic easily T c .In ac ,ϕexhibi s a s onge co ela ion wi h he ac ual T c o hyd ogen-based supe conduc o s han any o he desc ip o used so a , and can be used o p edic T c wi h an accu acy o abou 60 K wi h he o mula Tc¼ð750ϕH HDOS385ÞK, whe e H is he hyd ogen ac ion in he compound45. The esul s o ϕand he es ima ed T c o he dynamically s able phases and all he 214 me allic s a es i espec i e o he s abili y a e included in Table 1and Supplemen a y Table S1, espec i ely (an Excel file is also a ailable in “Da a a ailabili y”sec ion). Ou esul s indica e ha he uppe limi o he p edic ed T c among he 214 me allic s a es is only 13.94 ± 60 K. These esul s collec i ely indica e ha he me allic phases p edic ed om he high- h oughpu c ys al s uc u e p edic ion a e unlikely o hos high- empe a u e supe - conduc i i y a 1 GPa. The in e a omic dis ances and Bade cha ge analysis In Fig. 2a, we show he sho es N-H and H-H dis ances o he 638 Lu-H and Lu-N-H compounds wi hin an en halpy o 0.24 eV⋅a om−1abo e he con ex hull (i.e. H hull ≤0.24 eV⋅a om−1) i espec i e o hei dynamical s abili y. Fo he 124 bina y Lu-H sys ems whe e N is absen , he sho es Fig. 1 | The phase diag am o he Lu-N-H sys em a 1 GPa. a The phase diag am o Lu-N-H wi h espec o elemen s. Only he lowes -lying en halpy s a e is shown o each s oichiome y. bThe phase diag am ela i e o s able P  3c1 LuH 3 and me as able P2 1 /mLuH 2 N, in which H hull ≤0.3 eV⋅a om−1.cThe phase diag am o Lu-H wi h espec o elemen s, in which H hull ≤0.8 eV⋅a om−1. The black ci cles in all panels ep esen he he modynamically s able phases. Squa e ma ke s e e o phases loca ed abo e he con ex hull, wi h colo coding hei ene gy dis- ance om he con ex hull. The line be ween LuH 3 and LuH 2 in (c) is se o dash because i is no a con ex hull as hose in o he panels. h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 3 Table 1 | The 57 dynamically s able me allic s a es a 1 GPa ID H hull (eV⋅a om−1) Space g oup H DOS ϕT c (±60 K) XRD simila i y (%) 1 u_Lu3H8N_216 0.24 P  3m1 0.26 0.31 13.94 75.03 1 u_Lu4H7_495 0.17 R3m0.04 0.42 –64.48 2 u_Lu4H7_242 0.17 Cmc2 1 0.04 0.40 –12.78 2 u_Lu4H9_373 0.05 Pba2 0.03 0.39 –93.61 2 u_Lu4H9_34 0.02 Cm 0.04 0.33 –98.53 1 u_Lu4H9_213 0.01 Cmmm 0.04 0.34 –99.07 2 u_Lu4H9_231 0.01 P2 1 /m0.04 0.34 –99.48 1 u_Lu4H9_190 0.11 R3m0.05 0.30 –62.05 2 u_Lu4H9_12 0.15 Cm 0.03 0.32 –94.71 2 u_Lu4H7_51 0.19 P4/mmm 0.02 0.43 –68.09 2 u_Lu4H9_233 0.01 Cmmm 0.04 0.30 –98.97 1 u_Lu4H9_139 0.06 Pmmm 0.03 0.32 –98.66 1 u_Lu4H9_175 0.01 Pm  3m0.03 0.32 –99.12 2 u_Lu4H7_391 0.04 Pc 0.03 0.35 –97.01 2 u_Lu4H7_62 0.08 Fmm2 0.03 0.35 –98.19 1 u_Lu4H9_182 0.01 Pmmm 0.03 0.31 –98.91 2 u_Lu4H7_149 0.09 P2 1 /m0.03 0.33 –98.41 2 u_Lu4H7_66 0.03 Cmcm 0.03 0.34 –97.52 1 u_Lu4H7_318 0.12 Amm2 0.03 0.34 –97.97 1 u_Lu4H7_478 0.04 Amm2 0.03 0.34 –99.15 1 u_Lu4H7_417 0.03 P  43m0.02 0.35 –97.87 2 u_Lu4H7_375 0.09 Cmc2 1 0.03 0.33 –95.62 1 u_Lu4H7_64 0.07 Cm 0.03 0.31 –97.45 1 u_Lu4H7_288 0.16 Amm2 0.02 0.35 –65.62 1 u_Lu4H7_467 0.23 P  4m2 0.02 0.39 –59.39 2 u_Lu4H9_401 0.02 P4/mmm 0.04 0.26 –99.12 2 u_Lu4H7_63 0.17 Cmc2 1 0.03 0.32 –62.64 1 u_Lu4H7_29 0.16 P1 0.02 0.33 –68.36 1 u_Lu4H7N_358 0.10 R3m0.02 0.36 –68.35 2 u_Lu4H9_225 0.20 P1 0.03 0.26 –97.85 2 u_Lu4H9_184 0.10 I4mm 0.02 0.28 –22.18 1 u_Lu4H7_367 0.19 P1 0.03 0.28 –48.26 1 u_Lu4H7_81 0.17 Cm 0.02 0.31 –57.65 1 u_Lu4H9_167 0.01 I4/mmm 0.03 0.25 –98.97 1 u_Lu4H8N_5 0.07 R  3m0.03 0.27 –51.47 1 u_Lu4H7N_471 0.15 Pmm2 0.03 0.28 –67.44 1 u_Lu4H7_44 0.19 C2 0.02 0.30 –58.91 2 u_Lu4H9_111 0.10 Cc 0.03 0.24 –91.48 1 u_Lu4H7N_166 0.15 P1 0.04 0.26 –27.14 1 u_Lu4H9N_10 0.21 P3m1 0.04 0.24 –37.17 1 u_Lu4H9_6 0.16 P1 0.04 0.22 –64.86 2 u_Lu3H8N_116 0.20 P1 0.03 0.24 –49.77 1 u_Lu4H9N_136 0.04 P3m1 0.31 0.11 –13.12 1 u_Lu4H11N_251 0.19 Cm 0.05 0.19 –66.42 1 u_Lu4H7_378 0.14 Cmm2 0.02 0.27 –79.79 1 u_Lu4H7N_11 0.11 Cm 0.03 0.24 –91.97 1 u_Lu4H7_379 0.20 Pm 0.02 0.22 –88.22 1 u_Lu4H8N_105 0.07 Pm 0.03 0.21 –74.46 1 u_Lu4H7N_377 0.15 Cm 0.03 0.20 –21.50 1 u_Lu4H7N_491 0.14 P1 0.03 0.21 –84.14 1 u_Lu4H9_129 0.15 Imm2 0.03 0.17 –14.80 h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 4 N-H is a ificially se o 0.0 Å. As we can see, all he bina y hyd ides a e me allic and show an H-H dis ance om 1.75 o 2.5 Å. A he same p essu e, he H-H dis ance in he he modynamically s able Fm  3mLuH 2 ,whe eallH a oms occupy he e ahed al si e (H e ahed al )is2.48Å. In his c ys al, he dis ance be ween a e ahed al and an oc ahed al si e is 2.15 Å. This sugges s ha he hyd ogen a oms in mos o he bina y p edic ed hyd ides a e close o a e ahed al o oc ahed al a angemen in an cc la ice. The majo i y o he 90 e na y me allic Lu-N-H compounds, 64 ou o 90, also exhibi H-H dis ances la ge han 1.75 Å. Obse ing all he p e iously documen ed supe hyd ides compiled in e . 45, i can be seen ha none o hem exhibi T c > 50 K when hei sho es H-H dis ance exceeds 1.75 Å. This analysis u he indica es ha nei he he bina y no e na y me allic phases p edic ed om ou high- h oughpu c ys al s uc u e p edic ion is likely o hos high- empe a u e supe conduc i i y. Based on he sho es N-H dis ance, hese 638 compounds can be classified in o h ee dis inc clus e s, which a e indica ed by double-headed a ows in Fig. 2. Clus e 1, which only con ains bina y Lu-H compounds, consis s o 124 phases ha a e all me allic. Clus e 2 comp ises 352 insu- la ing phases and 32 me allic phases, cha ac e ized by N-H dis ances <2 Å and ≥1Å. Clus e 3 is composed o a o al o 130 compounds whose sho es N-H dis ances a e all la ge han 2 Å, wi h 72 o hem being insula ing and 58 o hem being me allic. The his og am in Fig. 2b, in which he e ical axis uses a loga i hmic scale, explici ly displays he dis ibu ion o he numbe o compounds based on hei sho es N-H dis ance. In con as o clus e 1 Table 1 (con inued) | The 57 dynamically s able me allic s a es a 1 GPa ID H hull (eV⋅a om−1) Space g oup H DOS ϕT c (±60 K) XRD simila i y (%) 1 u_Lu4H7N_172 0.17 P1 0.03 0.21 –83.10 2 u_Lu4H9_67 0.14 P4 2 /nmc 0.02 0.20 –40.45 1 u_Lu4H7N_488 0.17 Cm 0.02 0.22 –67.76 1 u_Lu4H7N_372 0.15 P4mm 0.03 0.19 –52.78 2 u_Lu4H9_420 0.04 Cmcm 0.03 0.15 –93.12 1 u_Lu4H7N_494 0.15 Cm 0.02 0.16 –63.68 1 u_Lu4H7N_67 0.02 R  3m0.03 0.06 –53.46 The supe conduc ing ansi ion empe a u es (T c ) a e es ima ed by using he ne wo king alue model in e . 45. I he p edic ed T c is no g ea e han ze o, he esul is displayed as ‘–’. Only s uc u es below 0.24 eV⋅a om−1abo e he con ex hull a e conside ed. H hull ep esen s he en halpy dis ance abo e con ex hull. ID e e s o he unique iden ifie o a s uc u e en y in ou da abase. H DOS is he hyd ogen ac ion o he o al densi y o s a es a he Fe mi le el, ϕ e e s o he ne wo king alue. XRD simila i y e e s o he deg ee o simila i y in he simula ed X- ay di ac ion (XRD) pa e ns be ween he s uc u e being analyzed and he e e ence s uc u e (i.e. Fm  3mLuH 2 ). Fig. 2 | The analysis o sho es N-H and H-H dis ances. a The compa ison be ween minimal dis ances o N-H and H-H o 124 bina y Lu-H sys ems and 514 e na y Lu-N-H sys ems. The do s and squa es e e o insula ing and me allic s a es, espec i ely. The colo ba shows he en halpy dis- ance abo e he con ex hull om 0 o 0.24 eV⋅a om−1.bThe numbe o compounds dis- ibu ed wi h he sho es N-H dis ance. The inse shows he elec on localiza ion unc ions o 5 ep esen a i e compounds. The isosu ace alues o 2 u_Lu4H7_51, 1 u_Lu4H11N_251, 1 u_LuH2N_366, 1 u_Lu4H7N_372, and 1 u_Lu2H5N_42 a e se o 0.52, 0.75, 0.75, 0.52, and 0.75, espec i ely. The blue (o ange) ba s/iso alues indica e he me allic (insula ing) na u e. h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 5 comp ising 124 bina y Lu-H compounds, which exhibi exclusi ely me allic beha io in he absence o N, he e na y compounds in clus e 2 and clus e 3 con aining N exhibi al e ed cha ac e is ics ac oss a o al o 514 com- pounds. The p esence o N is ound o lead o a significan p opo ion o 424 insula ing phases, which accoun s o app oxima ely 82.5% o all e na y compounds. This no able p opo ion unde sco es N’s c ucial ole in a o ing he o ma ion o mo e insula ing s uc u es han me allic s uc u es in quan i y. In clus e 1 consis ing o 124 Lu-H compounds, i is obse ed ha all he sho es H-H dis ances span he ange o 1.75–2.80 Å. The p esence o ela i ely la ge H-H dis ances p e en s he o ma ion o H 2 molecules o H-H chains which ypically con ibu e o o ming insula ing s a es42,47 al hough he e a e se e al excep ions such as MgH 4 48 and ScH 9 49.The obse a ion o ela i ely la ge H-H dis ances p o ides a clea explana ion o he exclusi ely me allic beha io o he bina y compounds in clus e 1. Howe e , as no ed in Table 1and Supplemen a y Table S1, he con ibu ion o hyd ogen o he elec ons a he Fe mi le el is mino in mos o hese compounds, whe e Lu ds a es domina e a he Fe mi le el. Fo example, in he case o 2 u_Lu4H7_51 s uc u e, he p ojec ed densi y o s a es in Supplemen a y Fig. S6 p o ides compelling e idence o he p ominen con ibu ion o Lu do bi als a he Fe mi le el. Fu he mo e, in Fig. 2b, we ha e included an inse displaying he elec on localiza ion unc ion o 2 u_Lu4H7_51 s uc u e a an isosu ace o 0.52. This inse illus a es he ionic bonding ea u e be ween Lu and H. In his bina y Lu 4 H 7 ,adis inc sepa a ion exis s be ween he hyd ogen a oms, cha ac e ized by he sho es H-H dis ance o 2.18 Å. Among he 514 e na y compounds in clus e s 2 and 3, clus e 2 accoun s o app oxima ely 74.7% (384 compounds) o all e na y Lu-N-H sys ems. The compounds in clus e 2 a e dis inguished by hei small N-H dis ances and a no iceable p opensi y owa ds insula ing cha ac e . I is ound ha 99.5% o he compounds in clus e 2, including 352 insula ing en ies and 30 me allic en ies, ea u e a sho es N-H dis ance o app oxima ely ~1.1 Å. This pa icula ly sho N-H dis ance co esponds o he s ong co alen bonding be ween N and H, which is e idenced by he elec on localiza ion unc ions o me allic 1 u_LuH2N_366 and insula ing 1 u_Lu4H11N_251 belonging o clus e 2 in Fig. 2b. Only wo phases in his clus e ha e a sho es N-H dis ance la ge han 1.1 Å, and bo h o hem a e me allic. I should be no ed ha he N-H bond leng h o NH 3 molecule is gene ally be ween 1.0 and 1.1 Å, and pu ely ammonia is pe ec ly insula ing. Fu he mo e, by su eying all he compounds exclusi ely composed o N and H in Ma e ials P ojec 50 ha a e loca ed wi hin 0.2 eV⋅a om−1abo e he con ex hull, hese N-H compounds all show insula ing p ope ies and he sho es N-H bond leng hs a e all in he ange o 1.0~1.1 Å.Thus,ou finding sugges s ha he p esence o N s ongly a o s insula ing phases due o he o ma ion o s ongly co alen bonds be ween N and H a oms. The s ong co alen N-H bonds esul bo h in NH o NH2 uni s in mos Lu-N-H s uc u es p edic ed in ou wo k. Compa ed o he small magni ude o he a e age sho es N-H dis ance in clus e 2, he sho es N-H dis ance o clus e 3 is mo e han wice he o me , spanning om 2.0 o 3.05 Å. The e a e 72 insula o s and 58 me als in clus e 3. In addi ion, Fig. 2a demons a es a s ong co ela ion be ween he elec onic p ope ies and he sho es H-H dis ance. Among he 71 compounds wi h sho es H-H dis ances la ge han 1.75 Åbelonging o clus e 3, 52 compounds (73.2%) a e me allic and 19 compounds a e insula ing. Analogous o he bina y Lu-H compounds in clus e 1, long H-H dis ances a o he p esence o me allic s a es domina ed by elec ons coming om Lu. The example s uc u e wi h ID 1 u_Lu4H7N_372, hos ing he sho es N-H dis ance o 2.59 Åand he sho es H-H dis ance o 2.28 Å, shows ionic ea u es o N and H ions. On he con a y, he e a e 53 insu- la o s and 6 me als whose sho es H-H dis ances a e smalle han 1.75 Åin his clus e . In pa icula , 52 o hese 53 insula ing compounds ha e he sho es H-H dis ances below 1.1 Å, indica ing ha he o ma ion o H-H molecules plays a c ucial ole in de e mining hei insula ing cha ac e . To exempli y his, he elec on localiza ion isosu ace wi h he alue o 0.75 o he 1 u_Lu2H5N_42 s uc u e is shown in Fig. 2b, which unambiguously displays he p esence o an H-H molecule wi h an H-H dis ance o 0.78 Å. These analyses o he in e a omic dis ances in Clus e s 2 and 3 imply ha me allic phases a e a o ed when he sho es H-H dis ance exceeds 1.75 Å and he sho es N-H dis ance su passes 2.0 Å. Howe e , he e na y Lu-N- H compounds, un o una ely, do no sa is y he a o emen ioned condi ions in mos cases, he eby esul ing in he p omo ion o insula ing cha ac e . To be e unde s and he elec onic p ope ies o he 638 Lu-H and Lu- N-H compounds wi h H hull ≤0.24 eV⋅a om−1, we ha e pe o med a Bade cha ge analysis o all hese compounds. The a e age Bade cha ges o H and N o each compound a e explici ly shown in Supplemen a y Fig. S7 e sus he sho es N-H dis ance and sho es H-H dis ance. Among he 514 e na y compounds, he a e age Bade cha ge o N in me allic phases and insula ing phases is −1.70eand −1.64e, espec i ely. I implies ha N in me allic phases ob ains a sligh ly g ea e numbe o elec ons han in insula ing cases. Howe e , his di e ence is no significan , which can also be seen in panels (a) and (c) o Supplemen a y Fig. S7. In con as o he small fluc ua ion o he a e age Bade cha ge o N, he a e age Bade cha ge o Hinme allicphasesisa ound−0.59e, which is nea ly wice he alue o insula ing phases (−0.32e). This di e ence e eals ha gaining mo e elec- ons a he hyd ogen si e is c ucial o en e ing he me allic s a e. The Bade cha ge o hyd ogen e sus he sho es N-H dis ance, as exemplifiedin panel (b) in Supplemen a y Fig. S7, demons a es ha longe N-H dis ances can be ad an ageous o hyd ogen a oms o gain addi ional elec ons. In o he wo ds, he p esence o ni ogen does no enhance he abili y o hyd ogen o acqui e elec ons. Thus, i is comp ehensible why all he 124 bina y Lu-H cases wi hou N, in which he a e age Bade cha ge o H is −0.71e,mani es me allic s a es. The e o e, he cha ge a ound H a oms plays a mo e sig- nifican ole han a ound ni ogen in de e mining elec onic p ope ies. Panels (b) and (d) in Supplemen a y Fig. S7 demons a e ha , among all me allic compounds, a g ea e acquisi ion o elec ons occu s p ima ily in compounds whe e he sho es N-H dis ance is a ound 2.5 Å,while simul aneously ensu ing ha he sho es H-H dis ance is g ea e han 1.75 Å. This u he sugges s ha , when aiming o de elop me allic s a es in lu e ium hyd ides, i is ad isable o a oid o keep ni ogen away om he hyd ogen si e. This allows H o acqui e mo e elec ons om Lu, p omo ing he o ma ion o me allic s a es. Based on s a is ical da a on all p e iously epo ed supe conduc ing hyd ides in e . 45, i is ound ha all supe - conduc ing c i ical empe a u es in he li e a u e a e lowe han 50 K i hei sho es H-H dis ances ≥1.75 Å. In ou case, by examining all 214 me allic s a es, 188 o hem show he sho es H-H dis ances ≥1.75 Å.Thisalso implies ha i is unlikely o find high- empe a u e supe conduc i i y in he s uc u es om he high- h oughpu s uc u e sc eening a 1 GPa. XRD compa ison a 1 GPa Among he bina y lu e ium hyd ides ha ha e been s udied expe imen ally, Fm  3mLuH 2 has been sugges ed by Xie e al.51 and Ming e al.32 o ha e he mos simila XRD pa e n as he one measu ed by Dasenb ock-Gammon e al.29.We huscompa e heXRDo LuH 2 wi h all 638 p edic ed phases om ou high- h oughpu sc eening wi h H hull ≤0.24 eV⋅a om−1a 1 GPa. In o de o compa e he XRDs o di e en s uc u es quan i a i ely, he simila i y be ween wo XRDs is compu ed acco ding o he co ela ion unc ion implemen ed in PyX al52. Fo simple compa ison, he XRD o Fm  3mLuH 2 is se as he e e ence and i s simula ed XRD is shown in Fig. 3 as a compa ison wi h he expe imen al XRD epo ed by Dasenb ock- Gammon e al.29. The XRD simila i y pe cen ages (%) o he 57 dynami- cally s able me allic s uc u es a e shown in Table 1, while a comp ehensi e lis o he 214 me allic s a es, i espec i e o hei dynamical s abili y, is a ailable in Supplemen a y Table S1. By analyzing he 214 me allic phases, we find ha 48 o hem show s ong XRD simila i y pe cen ages la ge han 90%. In con as o he me allic phases, we do no find any s uc u e among he 424 insula ing phases showing XRD simila i y pe cen ages ≥90%. Ou o hese 48 me allic phases showing s ong simila i y in XRD, 24 o hem a e dynamically s able, including 9 Lu 4 H 7 (mean XRD simila i y ~97.68%), 14 Lu 4 H 9 (mean XRD simila i y ~97.26%), and 1 Lu 4 H 7 N 11 (XRD simila i y ~91.97%). In Fig. 3, hedynamicallys ablebina yhyd ideswi hXRD h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 6 simila i y pe cen ages la ge han 99% a e p esen ed, oge he wi h he dynamically s able Cm Lu 4 H 7 N(ID:1 u_Lu4H7N_11) displaying XRD simila i y highe han 90%. In addi ion, he c ys al s uc u es a e also shown in he inse o Fig. 3. Obse ing he space g oups and he c ys al s uc u es in Fig. 3, al hough all six me allic phases show e y high XRD simila i y, he c ys al s uc u e a ies om cubic la ice wi h high symme y o Pm  3m o he monoclinic la ice wi h low symme y o Cm. The high XRD simila i y can e en occu in he iclinic s uc u es. Fo ins ance, he 2 u_Lu4H11N_570 s uc u e, included in Supplemen a y Table S1, shows a la ge XRD simila i y o 93.23% despi e i s space g oup is P1. The p onounced simila i y in XRD can be a ibu ed o he Lu sub- la ice, which does no di e significan ly om he cc one e en i he symme y educ ion is conside able. In Supplemen a y Figs. S3–S5 which show he phonon spec a and XRD simila i y o he 57 dynamically s able me allic phases, we find ha 20 s uc u es exhibi ing high XRD simila i y g ea e han 95% sha e a common ea u e ha hei dis ibu ion o phonons in equencies esemble ha o Fm  3mLuH 2 a 1 GPa displayed in Sup- plemen a y Fig. S8a. The specific cha ac e is ic is ha mos phonon b an- ches a e sepa a ed in o wo dis inc equency egions, in which some phonons a e dis ibu ed below 6 THz, which ha e mainly a Lu cha ac e , and o he b anches a e loca ed a ound 32 THz. By compa ing hese spec a wi h he one o LuH 2 displayed in Supplemen a y Fig. S8b, we find ha all equencies a ound 32 THz in hese compounds a e associa ed o ib a ions o H a oms a ound e ahed al in e s i ial si es. This means ha , despi e he no able a ia ions in space g oups among he 20 me allic s a es in Table 1, he high XRD simila i y and sha ed cha ac e is ics in he phonon spec a imply ha hese s uc u es a e simila . The e o e, we ha e pe o med an in- dep h analysis o he occupa ion o H a oms and he configu a ion o Lu subla ices o he 20 me allic s uc u es. Supplemen a y Fig. S9 illus a es he numbe o H a oms ha a e si ua ed a e ahed al and oc ahed al si es in di e en configu a ions o Lu subla ice. In bina y Lu 4 H 7 compounds, all hyd ogen a oms occupy e ahed al si es as expec ed, and he Lu subla ice o ms he cc s uc u e excep o 1 u_Lu4H7_64, exhibi ing a body- cen e ed e agonal subla ice displayed in Supplemen a y Fig. S10a. When i comes o Lu 4 H 9 , he e a e always eigh H a oms loca ed a e ahed al si es and one H a om posi ioned a an oc ahed al si e. The cc Lu subla ice is also obse ed in hese Lu 4 H 9 compoundsal hough2 u_Lu4H9_225hasa de ec i e cc Lu subla ice (see Supplemen a y Fig. S10b) ha is significan ly dis o edcompa ed o he ccLusubla iceinFm  3mLuH 2 . Ou analysis sugges s ha he majo i y o me allic s able phases wi h high XRD simila i y a e de i ed om he cubic LuH 2 , in which in e s i ial e ahed al hyd ogen a oms can be widely obse ed in cc Lu subla ices. Al hough Dasenb ock-Gammon e al.29 claimed hei samples we e likely composed o Fm  3mand Immm phases based on hei XRD mea- su emen s, ou analysis o XRD simila i y and he a angemen s o Lu subla ices sugges ha XRD echnique migh pose challenges in iden i ying he c ys al s uc u e o lu e ium hyd ides. As e idenced abo e, we ha e iden ified ens o dynamically s able me allic phases ha possess simila XRD ea u es, e en hough some o hem ha e a conside ably lowe sym- me y. I is impo an o no e ha he alidi y o his a gumen is con ingen on he pa ame e s u ilized in he XRD simila i y calcula ion, pa icula ly he pa ame e go e ning he maximum pe missible ime delay in he c oss- co ela ion unc ion. Po en ial hos s o high- empe a u e supe conduc i i y abo e 1 GPa Failing o find any candida e wi h H hull <0.24eV⋅a om−1 ha can hos high- empe a u e supe conduc i i y in he Lu-H-N sys em a 1 GPa, we s udy high-symme y c ys al s uc u es wi h po en ial high elec on–phonon in e ac ion ha may be me as able e en i a he abo e he con ex hull: Pm  3mLu 4 H 11 N, Im  3mLuH 6 ,andFm  3mLuH 10 .AsshowninFig.1b, Pm  3mLu 4 H 11 N is loca ed 0.27 eV⋅a om−1abo e he con ex hull (s uc u e ID: 1 u_Lu4H11N_137) a 1 GPa. This s uc u e can be de i ed om LuH 3 by gene a ing he con en ional cell o Fm  3mLuH 3 and subs i u ing one o he oc ahed al H a oms wi h N. In he ha monic app oxima ion, his Lu 4 H 11 N, whose space g oup is Pm  3m,isuns ablea 1GPa.Theo he wo high-symme y bina y s uc u es conside ed a e LuH 6 and LuH 10 ,which a e a ificially cons uc ed based on he al eady known high- empe a u e hyd ogen-based supe conduc o s Im  3mCaH 6 13 and Fm  3mLaH 10 18.I is no ed ha he c ys al s uc u e o Im  3mLuH 6 has been heo e ically epo ed in e . 53. A 1 GPa, he phase diag am in Fig. 1cshows ha Im  3m LuH 6 and Fm  3mLuH 10 a e loca ed a ound 0.64 and 0.77 eV⋅a om−1abo e he con ex hull, implying a highly uns able na u e a 1 GPa and 0 K. They a e also bo h dynamically uns able a his p essu e a he ha monic le el. The ze o-poin ene gy is no enough o make any o hese s uc u es ene ge i- cally compe i i e a 1 GPa. In o de o in es iga e he impac o quan um anha monic e ec s on he dynamical s abili y o hese high-symme y s uc u es, we elax hem wi hin he s ochas ic sel -consis en ha monic app oxima ion (SSCHA)54–57 a 300 K a di e en p essu es. This comple es hep io s udype o medon he dynamical s abili y o he po en ial pa en Fm  3mLuH 2 and Fm  3mLuH 3 phases30. In o de o assess he dynamical s abili y o hese phases we cal- cula e he phonons de i ed om he Hessian o he SSCHA ee ene gy and check o he p esence o imagina y phonon modes56. Ou SSCHA analysis in Fig. 4ashows ha Pm  3mLu 4 H 11 Nbecomes dynamically s able a a ound 20 GPa and 300 K, which is compa able o he s abili y ange o LuH 3 (6 GPa and 300 K)30,58. The phonon band s uc u e shows fi e dis inc i e egions: Lu-domina ed modes below 5 THz, N-domina ed modes be ween 8 and 11 THz, and h ee egions o H-domina ed modes abo e 11 THz. The highes phonon equency o his sys em(43.7THz)issligh lyla ge hanin hecaseo LuH 3 (40 THz a 20 GPa and 300 K). Using elec on–phonon coupling calcula ions based on he c ys al s uc u e o Lu 4 H 11 N om SSCHA, he Eliashbe g spec al unc ions, and cumula i e elec on–phonon coupling cons an we e com- pu ed and shown in Fig. 5a. Addi ionally, u ilizing he iso opic Migdal- Eliashbe g equa ions, we es ima e he supe conduc ing c i ical empe a u e Fig. 3 | XRD analysis and c ys al s uc u es. The simula ed XRD o p edic ed s uc u es a e compa ed wi h he e e ence s a e Fm  3mLuH 2 and he expe imen al XRD in e . 29. S uc u e ID, space g oup, and XRD simila i y wi h espec o Fm  3m LuH 2 a e displayed, along wi h c ys al s uc u e maps. h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 7 in his ma e ial o be 100 K a 20 GPa. This is a significan imp o emen compa ed o he po en ial pa en compound LuH 3 a he same p essu e, T c = 30 K. The elemen p ojec ed Eliashbe g spec al unc ions in Supple- men a y Fig. S11 shows ha mos o he elec on–phonon coupling comes om H-domina ed modes, wi h e y small con ibu ions om Lu and N. The majo e ec o N doping in his sys em hus comes om b eaking he symme y o e ahed al si es occupied by H, leading o a d i o H a oms away om hese posi ions. This in u n has a la ge impac on he phonon equencies and he alue o he elec onic densi y o s a es a he Fe mi le el in his sys em and consequen ly he elec on–phonon coupling. In Sup- plemen a y Table S2, he c ys al s uc u e pa ame e s and he Wycko posi ions o he a oms o Pm  3mLu 4 H 11 N a e compa ed wi h hose o Fm  3m LuH 3 . I is clea ha he H a oms, which a e o iginally loca ed a he high- symme y Wycko si es (0.25, 0.25, 0.25) in LuH 3 a e shi ed o lowe symme y Wycko si es (0.23835, 0.23835, 0.23835). In Supplemen a y Fig. S12, o -cen e ing displacemen s o he hyd ogen a oms a he e a- hed al si es a e schema ically shown o demons a e he e ec o N. Because he ni ogen a om eplaces he hyd ogen a om loca ed a he oc ahed al si e, he la ge a omic adius pushes he hyd ogen a oms a he e ahed al si es ou wa ds. The bina y compound Im  3mLuH 6 has been p edic ed as a high- empe a u e supe conduc o a 100 GPa wi hou he inclusion o ionic quan um and anha monic e ec s53. We ully elax his compound a di - e en p essu es wi hin he SSCHA o de e mine he phase diag am. Al hough we find i uns able a 100 GPa in he ha monic app oxima ion, i is s abilized wi h anha monic and quan um e ec s a 300 K, which is e i- denced by he phonon spec a in Fig. 4b. The ins abili y in he ha monic app oxima ion is localized a a singula qpoin , which in e . 53 is also showing significan so ening. The qpoin ha showssignifican so ening in e . 53 appea s in an 8 × 8 × 8 g id, which could explain why he ins abili y is no p esen in he p e ious s udy ha uses ins ead a 6 × 6 × 6 g id. The calcula ed elec on–phonon coupling cons an is huge, which explains he so ening o his phonon mode. Due o he la ge elec on–phonon coupling cons an s (see Fig. 5b), we find nea ly oom- empe a u e supe conduc i i y a 100 GPa wi h T c o 246 K in his s uc u e, simila o he alue epo ed in e . 53,whe eaT c o 273 K was p edic ed a 100 GPa a he ha monic le el. The Fm  3m LuH 10 s uc u eis heoneadop edby hehigh- empe a u e supe conduc o LaH 10 .Wefind ha he ee ene gy Hessian displayed in Fig. 4c does no show imagina y equencies abo e 175 GPa and 300 K indica ing a me as able s a e. We calcula e he elec on–phonon coupling o his s uc u e and ound ha he onse o supe conduc i i y happens p ac ically a oom empe a u e, T c = 289 K (~16 °C). The co e- sponding Eliashbe g spec al unc ionisshowninFig.5c. In compa ison o ano he polymo ph o LuH 10 wi h a space g oup P63/mmc, which can also be s abilized a 200 GPa in he ha monic app oxima ion and has a heo- e ically epo ed T c o 134–152 K59,Fm  3mLuH 10 phase in ou s udy no only e eshes he eco d o highes T c o LuH 10 bu i can also be s abilized dynamically a a educed p essu e. In o de o confi m he capaci y o he ne wo king alue model o p edic T c s used in he high- h oughpu calcula ions, we also es ima e T c o hese high-symme y s uc u es wi h i o he SSCHA s uc u es. We ound ha he T c o Fm  3mLuH 3 and Pm  3mLu 4 H 11 N a 20 GPa a e 47.46 ± 65 K and 99.67 ± 65 K, espec i ely. Fu he mo e, he ne wo king alue model p edic s ha LuH 6 a 100 GPa and LuH 10 a 175 GPa a e supe conduc o s wi h a T c o 296.85 ± 65 K and 389.50 ± 65 K, espec i ely. The es ima ed T c alues a e e y close o hose om accu a e ab ini io elec on–phonon coupling calcula ions, especially o LuH 3 and Lu 4 H 11 N. This implies ha he ne wo king alue model can be applicable o he es ima ion o T c o supe hyd ides, e en o hose ha ha e ne e been epo ed. Consequen ly, i jus ifies he use o he ne wo king alue model as a apid es ima o o he T c o he s uc u es ob ained in he high- h oughpu sc eening (i.e. he esul s in Table 1). In o de o es ima e whe he hese high-symme y s uc u es may be iden ified by di ac ion expe imen s, we compu e he XRD simila i y o 015 30 45 60 F equency (THz) 0.0 0.5 1.0 1.5 2.0 2 F() Lu 4 H 11 N T c = 100 K 20 GPa 015 30 45 60 F equency (THz) 0.0 0.5 1.0 1.5 2.0 2 F() LuH 6 T c = 246 K 100 GPa 015 30 45 60 75 F equency (THz) 0.0 0.5 1.0 1.5 2.0 2 F() LuH 10 T c = 289 K 175 GPa 0 1 2 3 0 1 2 3 0 1 2 3 abc Fig. 5 | Elec on–phonon coupling. Iso opic Eliashbe g spec al unc ion α2F(ω) and in eg a ed elec on–phonon coupling cons an λin aLu 4 H 11 N, bLuH 6 , and cLuH 10 . X M R X|R M -15 0 15 30 45 60 F equency (THz) 20 GPa SSCHA DFPT DOS Lu 4 H 11 N H N P H|P N 100 GPa SSCHA DFPT DOS LuH 6 X U|K L W X 175 GPa SSCHA DFPT DOS LuH 10 abc Fig. 4 | Dynamical s abili y. Ha monic and anha monic SSCHA ee ene gy Hes- sian phonon spec a o aLu 4 H 11 N a 20 GPa, bLuH 6 a 100 GPa, and cLuH 10 a 175 GPa. The blue and ed lines e e o he ha monic and anha monic phonon spec a calcula ed by DFPT and SSCHA, espec i ely. The absence o imagina y modes in he SSCHA phonon spec a indica es dynamical s abili y in all cases. h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 8 Pm  3mLu 4 H 11 N, Im  3mLuH 6 ,andFm  3mLuH 10 a 1 GPa wi h e e ence o he cubic LuH 2 . The esul s show ha while Im  3mLuH 6 and Fm  3mLuH 10 a e e y di e en , wi h a simila i y o 35% and 58%, espec i ely, Pm  3m Lu 4 H 11 N has a simila i y o 95%, which ema ks ha i may be indis- inguishable in di ac ion expe imen s om Fm  3mLuH 2 and may be consis en wi h he obse ed XRD pa e n in e . 29. Because Pm  3nLu 4 H 23 has been syn hesized ecen ly in he expe imen wi h T c o 71 K a 218 GPa and T c o 65 K a 181 GPa60,weha e ied o es ima e i s T c om ab ini o s udy. Howe e , he p imi i e cell o Pm  3n Lu 4 H 23 has 54 a oms in he p imi i e cell (see Supplemen a y Fig. S13), which is no p ac ical o pe o m elec on–phonon coupling calcula ions wi h DFPT me hod o Quan um Esp esso. Thus, we used he ne wo king alue model o es ima e he T c o he c ys al s uc u e in which cell pa a- me e s we e fixed o hose ob ained om XRD a 185 GPa and he in e nal coo dina es we e ully elaxed. The T c was calcula ed o be 136.93 ± 65 K which is no a om he expe imen ally obse ed alues wi hin he accu acy e o . Conclusions In conclusion, we ha e pe o med a comp ehensi e s udy by combining a high- h oughpu s uc u e sc eening, a apid es ima o o T c ,and elec on–phonon coupling calcula ions including quan um anha monic e ec s o explo e he easibili y o nea -ambien supe conduc i i y in he Lu- N-H sys ems. Ou s udy sugges s ha he p esence o ni ogen leads o mo e insula ing s uc u es han me allic ones in quan i y, and des abilizes he lu e ium hyd ide sys ems by significan ly shi ing hem away om he con ex hull. As a esul , he majo i y o iden ified dynamically s able me allic phases in ou in es iga ion a e bina y hyd ides, which a e no a om he pa en Fm  3mLuH 2 . Fu he mo e, we did no obse e high- empe a u e supe conduc i i y in all o he s udied s uc u es a 1 GPa wi hin a easonable h eshold o me as abili y. We, he e o e, p opose ha in o de o ha e me allic and supe conduc ing s a es in lu e ium hyd ides i is be e o a oid ni ogen doping. Despi e he absence o nea -ambien supe conduc i i y, he combined e ec o p essu e and quan um anha - monici y kindles he hope o high- empe a u e supe conduc i i y in he Lu- N-H sys ems by ealizing a T c o 100 K a a sligh ly enhanced p essu e o only 20 GPa in Pm  3mLu 4 NH 11 . This s uc u e is simila o Fm  3mLuH 3 , bu wi h one ou o ou H a oms in oc ahed al si es subs i u ed by a ni ogen a om. This cubic Lu 4 NH 11 is a he modynamically me as able phase a 20 GPa, and i is p ac ically indis inguishable om he pa en Fm  3mLuH 2 compound in di ac ion expe imen s. Thus, his s uc u e o a ia ions o i p o ide, i any, he only possible high-T c s uc u e a low p essu es in he Lu- H-N sys em. A highe p essu es, abo e 100 GPa, CaH 6 -like LuH 6 and LaH 10 -like LuH 10 a e supe conduc o s wi h c i ical empe a u es a ound oom empe a u e, bu wi h an XRD pa e n incompa ible wi h expe imen s. Me hods High- h oughpu c ys al s uc u e p edic ion S a e-o - he-a c ys al s uc u e p edic ion me hods, i.e., he e olu iona y algo i hm implemen ed in C ySPY61 and he pa icle swa m algo i hm implemen ed in CALYPSO62,63, we e combined o p edic c ys al s uc u es. We ha e sc eened o e 15,000 c ys al s uc u es o he Lu-N-H sys em. The specific s oichiome y ha we ha e conside ed du ing he c ys al s uc u e p edic ion a e LuH 2 N, Lu 4 H 7 N, Lu 4 H 8 N, Lu 4 H 9 N, Lu 4 H 11 N, Lu 2 H 5 N, Lu 3 H 8 N, Lu 4 H 7 ,andLu 4 H 9 . Fo he c ys al s uc u e p edic ion o a fixed s oichiome y, we ha e pe o med se e al pa allel c ys al s uc u e sea ches wi h fixed composi ion by a ying he numbe o o mula uni s. The size o he uni cell s uc u es is cons ained up o 32 a oms. C ys al s uc u e p edic ions we e pe o med wi hin fi s -p inciples densi y unc ional heo y (DFT) calcula ions using he Vienna Ab ini io Simula ion Package (VASP)64,65. The gene alized g adien app oxima ion wi hin he pa a- me iza ion o Pe dew e al. 66 was used wi h a Hubba d Uco ec ion in he Duda e ’s o m 67 o imp o e he accu acy o he ene gies o he Lu -s a es. An accep able alue o U= 5.5 eV, commonly used o accoun o he localized -s a es o he lan hanide sys ems29,68,wasused.The es calcula- ions in Supplemen a y Fig. S14 e idenced ha he Hubba d co ec ion only a ec s Lu 4 o bi als which lie p e y a away om he Fe mi le el. The plane wa e ene gy cu o was se o 450 eV du ing c ys al s uc u e p edic ions. The k-poin g id is gene a ed based on he specific s uc u e by Pyma gen69 wi h a ela i ely high g id densi y o 60 poin s pe Å−3o ecip ocal cell olume. To add ess he elec onic p ope ies o he s uc u es, he ene gy cu o was imp o ed o 550 eV wi h an imp o ed k-poin g id densi y o 80 poin s pe Å−3. To calcula e he hyd ogen ac ion o he o al DOS H DOS a he Fe mi le el, we used Sumo70 o ex ac he hyd ogen DOS and he o al DOS. In he high- h oughpu DFT calcula ions o he DOS, we used Gaussian smea ing me hod implemen ed in VASP. To gua an ee he accu acy o he DOS calcula ion, we used a ela i ely small wid h o he smea ing o 0.05 eV oge he wi h a e y high k-poin g id densi y o 120 poin s pe Å−3ob ained by he k-poin gene a ion scheme o Pyma gen. The TcESTIME code has been used o es ima e he supe conduc ing T c based on he ne wo king alue model45. The XRD simula ion and compa ison o he XRD simila i y we e pe o med by PyX al52. In he PyX al simula ions o XRD, we used he wa eleng ho 1.5406 Å in line wi h he expe imen al s udy29. Addi ional pa ame e s we e assigned de aul alues in PyX al, such as FWHM = 0.1 and wid h = 1.0. In he phonon calcula ions o he c ys al s uc u es p edic ed om high- h oughpu s uc u e sc eening, he VASP DFT calcula ions we e combined wi h he supe cell and fini e displacemen me hods implemen ed in Phonopy71. Ini ially, he uni cells om he c ys al s uc u e p edic ions we e u he op imized wi h a cu o ene gy o 550 eV and a k-poin g id densi y o 130 pe Å−3o ecip ocal cell olume un il he ene gy con e gence eaches 10−8eV and o ces o each a om we e less han 10−3eV⋅Å−1.Sub- sequen ly, he op imized cells we e expanded o supe cells o o ce calcu- la ions in DFT. Howe e , conside ing he e we e many s uc u es o be examined, i has become in easible o conside pa icula ly la ge supe cells. I is no ed ha a omic in e ac ions in mos cases we e significan ly dec eased wi h inc eased in e a omic dis ances, and hus a cu o dis ance o 7.2 Åwas conside ed o be p ope in se ing up he supe cells. Specifically, i he la ice pa ame e (a,b,o c) o he uni cell was smalle han 7.2 Å,i wasexpanded wice, o he wise, i emained unchanged. Wi h his cons ain , he 214 me allic phases wi h H hull ≤0.24 eV⋅a om−1 om he high- h oughpu c ys al s uc u e p edic ions esul ed in mo e han 165,000 supe cells o DFT calcula ions. Elec on–phonon coupling calcula ions We elaxed he Pm  3mLu 4 H 11 N, Im  3mLuH 6 and Fm  3mLuH 10 using he s ochas ic sel -consis en ha monic app oxima ion me hod54–57 on 2 × 2 × 2 supe cells. The numbe o configu a ions used in he minimiza ion o he ee ene gy was 400 o Lu 4 H 11 N, and 200 o LuH 6 and LuH 10 .The calcula ion o he ee ene gy Hessian phonons needed o confi m he dynamical s abili y o final s uc u es was pe o med wi h 5000 configu a- ions o each s uc u e. To calcula e supe conduc ing c i ical empe a u e o hese com- pounds we pe o med elec on–phonon calcula ions o he s uc u es ob ained h ough he SSCHA minimiza ion o o al ee ene gy using densi y unc ional pe u ba ion heo y (DFPT) me hod as implemen ed in Quan um Esp esso72,73. Elec on–phonon coupling cons an s we e calcu- la ed on a 4 × 4 × 4qpoin g id o Lu 4 H 11 N,andan8×8×8g id o LuH 6 and LuH 10 . The a e age o he elec on–phonon ma ix elemen s o e he Fe mi su ace was done on 24 × 24 × 24kpoin g id and 0.012 Ry smea ing o Lu 4 H 11 N and 42 × 42 × 42kpoin g id and 0.008 Ry smea ing o LuH 6 and LuH 10 . Un o una ely, la ge elec on–phonon coupling makes he ull con e gence o esul s in he LuH 6 compound e y challenging. Howe e , he es ima ion o c i ical empe a u e is qui e obus and does no change mo e han 20 K be ween he wo highes k-poin g ids (363and 423) and wo lowes smea ing alues (0.008 and 0.012 Ry). The Eliashbe g spec al unc ion was calcula ed using phonon equencies ob ained om ee ene gy Hessian. The solu ion o he iso opic Migal-Eliashbe g equa ion was h ps://doi.o g/10.1038/s43246-024-00500-9 A icle Communica ions Ma e ials | (2024) 5:61 9