Dataset and article "Tracking polarons in real space by STM/AFM"

 View Online  Export Citation PERSPECTIVE | OCTOBER 09 2025 Tracking polarons in real space by STM/AFM Sreehari Sreekumar ; Pavel Kocán ; Martin Setvin  Appl. Phys. Lett. 127, 140502 (2025) https://doi.org/10.1063/5.0288242 Articles You May Be Interested In Photoinduced phase separation in the lead halides is a polaronic effect J. Chem. Phys. (June 2020) Hiding in plain sight: The prevalence and impact of trions and Fermi polarons in transient absorption spectroscopy experiments of 2D semiconductors J. Chem. Phys. (November 2024) Self-trapping in bismuth-based semiconductors: Opportunities and challenges from optoelectronic devices to quantum technologies Appl. Phys. Lett. (December 2021) 09 October 2025 13:30:45 Tracking polarons in real space by STM/AFM Cite as: Appl. Phys. Lett. 127, 140502 (2025); doi: 10.1063/5.0288242 Submitted: 30 June 2025 .Accepted: 18 September 2025 . Published Online: 9 October 2025 Sreehari Sreekumar, Pavel Koc an, and Martin Setvin a) AFFILIATIONS Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University, 180 00 Prague, Czech Republic a) Author to whom correspondence should be addressed: [email protected] ABSTRACT While the concept of polaron was formulated almost a century ago, this topic has been gradually emerging in many fields in physics, chemistry, and materials science. Polarons, i.e., charge carriers that are spatially confined by electron–phonon coupling, affect various properties of materials and devices. While we mostly deduce their properties indirectly from macroscopic characteristics of materials, it is appealing to observe these localized charge carriers in real space. Such experimental inputs could directly answer fundamental questions, as well as provide precise quantitative information about the polaron physics. In this perspective, we discuss seminal works focused on realspace imaging of polarons by scanning tunneling microscopy and atomic force microscopy, summarize the opportunities emerging from such experiments, highlight both the technical and fundamental challenges that remain, and provide an outlook on future directions and open questions in the field. V C2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/5.0288242 Polarons 1 are quasiparticles that form when excess charges are introduced into a semiconductor. An excess electron in the conduction band (or hole in the valence band) would ideally behave as a delocalized carrier, but electron–phonon coupling always tends to confine the charge in space. Such localization is associated with distortions of the surrounding lattice, creating an effective potential that self-traps the charge carrier. 2 The degree of localization is closely related to polaron properties: polarons can be categorized as small and large, where small means that the excess charge is localized approximately within a single unit cell of the material. Small polarons are typically associated with lattice distortions on the order of 10 pm, their apparent electronic energy is on the order of 1 eV below the conduction band (or above the valence band for holes), and they normally require certain activation energy for migration to a different site. Large polarons spatially extend over many unit cells, the associated lattice distortions are on the order of 1pm, their apparent electronic energies are tens of meV, and they can typically move through the material without any activation, i.e., coherently with their phonon cloud. 1 It has been reported since the early days that polarons play a major role in electrical transport 3–5 and optical properties of ionic crystals. 6–8 The topic later gained increasing attention in electrical conductivity and luminescence of polymers, 9–12 microelectronics, where polaron formation in gate oxide contributes to the noise, 13,14 or surface reactivity of metal oxides. 15–17 Polarons also turned out to be responsible for exotic material properties such as colossal magnetoresistance, 18,19 high-Tc superconductivity, 20–23 or recently attracted attention as a source of electronic friction. 24,25 Regardless of their technological importance, our understanding of polarons remains limited, with many open questions. On the theory side, the main challenge 1,26 stems from the difficulties related to modeling electron–phonon coupling, leading to an inability to accurately predict their excited and transition states that are essential for understanding polaron migration. 3 A correct description of coupling between multiple polarons and nontrivial coupling to defects also remains a challenge. On the experimental side, our knowledge about polarons is mainly derived from measurements of macroscopic material properties and area-averaged spectroscopies. This includes transport measurements, 27,28 various photoemission experiments 29,30 including angle-resolved photoemission, 31 resonance photoelectron diffraction, 32 time-resolved 33–38 and two-photon photoemission spectroscopies, 39 optical probes such as Raman scattering 40 and infrared absorption. 6 Relying on such indirect experimental evidence appears suboptimal, since polarons are by definition localized quasiparticles. In this respect, scanning probe microscopies (SPMs) have been attracting attention for many years, trying to visualize single polarons in real space. Pioneering experiments used scanning tunneling microscopy (STM) and focused mostly on oxides such as TiO 241–43 and CeO 2 . 44 These experiments brought partial success but also pointed out the limitations of this method. Figure 1 shows a prototypical example of Appl. Phys. Lett. 127, 140502 (2025); doi: 10.1063/5.0288242 127, 140502-1 V CAuthor(s) 2025 Applied Physics Letters PERSPECTIVE pubs.aip.org/aip/apl 09 October 2025 13:30:45 polarons measured in TiO 2 . In the rutile polymorph, oxygen vacancies donate electrons that form small polarons at the surrounding lattice sites. STM images of the material show two distinct pieces of knowledge: Empty-state images are typically used to map the surface topography [see Fig. 1(a)], highlighting individual oxygen vacancies (red arrows). Occupied state images [Fig. 1(b)] detect in-gap electronic states that appear unexpectedly spread across all surface titanium sites. This seemingly contradicts the localized nature of small polarons, but the apparent “delocalization”arises from rapid polaron hopping among equivalent sites, faster than STM can resolve. The image thus represents a time-averaged snapshot of all possible polaron positions, creating the illusion of a delocalized electronic state. A nice experiment addressing this issue was reported in Ref. 42, where a single isolated oxygen vacancy was prepared by tip-induced manipulations [see Figs. 1(c)–1(e)]. The vacancy [marked with red arrows in Fig. 1(c)] donates two excess electrons, and their spatial distribution is shown at different temperatures in Figs. 1(d) and 1(e). At lower temperatures, polarons appear closer to the positively charged vacancy, while at higher temperatures, they tend to spread over a larger area. This experiment touches the limitation of STM: The tunneling currents are on the order of 1 pA, which corresponds to 10 7 electrons per second. The technique requires sufficient electron mobility to generate detectable currents, which limits experiments to regimes where polarons remain highly mobile and can rapidly reform after being extracted by the tunneling tip. Attempts to distinguish small polarons from large ones based on STM images carry certain pitfalls: A single large polaron contains many atomic orbitals with fractional occupancy, which are imaged as neighboring localized spots [Fig. 1(h)]. Small polarons are mostly imaged in the regime where they hop quickly among many adjacent sites, creating a similar pattern [Figs. 1(b),1(d),and1(e)]. STM does not discern this time-averaged smearing of small polarons from real delocalization present in large polarons. However, valuable information can be obtained from scanning tunneling spectroscopy (STS), as shown in Fig. 1(c).TheSTSofTiO 2 rutile shows a deep in-gap state, peaking at 0.7 eV below the Fermi level, a clear signature of a small polaron. An STS spectrum measured on the anatase TiO 2 (101) surface is included for comparison; the anatase polymorph supports large polarons, which are characterized by a sharp state approximately 40 meV below the Fermi level. The spatial distribution of the polaronic states [Fig. 1(d)] shows that the occupied density of states is mostly accumulated around defects that were attributed to subsurface donors. While the STM experiments in Fig. 1 show that this technique can provide useful information, it seems clear that the main goal cannot be achieved this way: The target is to isolate a single polaron and watch its trajectory in real time; the advantages of this approach are explained later in the section on Opportunities. To achieve this, we need to measure in the regime when the polarons are frozen and the sample is insulating; therefore, use atomic force microscopy (AFM). Pioneering experiments that demonstrated the capability to inject and manipulate charges in an insulator were performed already in the 1990s; 45,47–59 see Fig. 2(a) for a pioneering experiment by Sch€ onenberger and Alvarado. 45 Here, excess electrons were injected into silicon nitride (Si 3 N 4 )films,andthespatial FIG. 1. STM imaging of polarons in TiO 2 . STM images of the TiO 2 rutile (110) surface showing surface topography in empty states (a) and polaronic states in filled states (b). Red arrows mark oxygen vacancies. (c)–(e) Single oxygen vacancy prepared by the STM tip, donating electron polarons to the surface. (c) Empty-state STM image at 78 K. (d) and (e) Filled-state images at 78 and 16 K, respectively. The filled-state images show the spatial distribution of polaronic states. Image resolution: (2.8 2.8) nm 2 . (f) STS spectra measured above the TiO 2 rutile (110) surface, showing signatures of small polarons, and the TiO 2 anatase (101) surface, showing signatures of large polarons. STM images of the anatase TiO 2 (101) surface, showing empty-state images with topography (g) and filled-state distribution of the large-polaron states (h). (a), (b), and (f)–(h) Reproduced with permission from Setvin et al., Phys. Rev. Lett. 113, 086402 (2014). 41 Copyright 2014 American Physical Society. (c)–(e) Reproduced with permission from Yim et al., Phys. Rev. Lett. 117, 116402 (2016). 42 Copyright 2016 Authors, licensed under a Creative Commons Attribution License. Applied Physics Letters PERSPECTIVE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 140502 (2025); doi: 10.1063/5.0288242 127, 140502-2 V CAuthor(s) 2025 09 October 2025 13:30:45 decay of the cloud was monitored as a function of time, using a microscopic AFM tip. Already these early studies pointed out the possibility of detecting charges with single-electron precision, and the detection sensitivity further improved with dynamic cantilever systems. 49,60 However, localizing single-electron charges and imaging their positions were not achievable at the time. Further advances, already indicating single-polaron precision using AFM, were performed in 2008 by Valdre et al. 46 They employed contact mode AFM to deposit and erase charges underneath the surface of a sandwich structure of silicon oxide/silicon nitride/silicon oxide grown on a GaAs/AlGaAs heterostructure. Kelvin Probe Force Microscopy (KPFM) was performed to electrically characterize the surface potential [Figs. 2(b)–2(d)]. A milestone experiment in manipulating single charges by noncontact AFM 60 was performed by Gross et al. in 2009, using a system of single Au adatoms adsorbed on a thin NaCl film. 61 The NaCl film provided electrical decoupling of the adatoms from the surroundings, and the Au adatoms serve as a trap for charges (these charges are not polarons; they classify as trapped electrons). Here, the gold (Au) adatom could be repeatedly switched between its neutral (Au) and negatively charged (Au  ) states, see Figs. 3(a)–3(d). This was accomplished by positioning the tip directly above the Au adatom and applying a voltage pulse between the tip and the sample. When this experiment was initially performed by STM, 61 the switching event was identified by a sharp decrease in tunneling current [Fig. 3(d)]. Later the application of q-Plus AFM to the same system allowed for a precise characterization of the adatom charge states using KPFM [see Fig. 3(e)]. Here, the Kelvin parabolas measured above differently charged Au atoms have their maxima shifted due to the localized charge [Fig. 3(e)]. Thepossibilitytomanipulateandmeasurethechargestates of atoms adsorbed at insulators quickly led to many follow-up studies and attracted attention mainly for organic molecules. 63–67 The principles and rules of manipulating such electrons confined at trap states are well-established nowadays. Recently, there were attempts to transfer this technique to the field of polarons. The main additional degree of difficulty is that polarons can be selftrapped at any lattice position and they can migrate between such equivalent sites. Studies on creating and imaging single polarons using conventional STM methods have been reported recently; 69,70 here Liu used STM to form polarons in a 2D semiconductor, CoCl 2 ,grownon graphite. A competing approach has been reported by Redondo, where AFM was used to study polaron dynamics at the hematite Fe 2 O 3 (1–102) surface. 68 Hematite supports the formation of stable small polarons for both excess electrons and holes. 71 The combined AFM/STM approach seems to provide a major advantage due to its wider applicability to insulating systems (where polaron motion is frozen) and also the absence of tunneling current that can excite polarons. The achievements are briefly summarized in Fig. 4;the authors have built on the experimental advances reported in earlier works (Figs. 2 and 3) and injected clouds of holes and electrons into a hematite sample [see AFM topography image in Fig. 4(a)] cooled down below 5 K. The thermal motion of these charges was activated through annealing, and the underlying mechanisms were explained using polaron physics and simulated with kinetic Monte Carlo models. An important achievement of this work is a demonstration of single-polaron resolution in both space and time. While applying a suitable bias between the tip and sample, the time evolution of the measured force [or frequency shift, see Fig. 4(b)] allowed the identification of injections of single polarons and also indicated how the already injected polarons reorganize during the process. Then, the creation and stability of single-hole polarons was demonstrated, see Fig. 4(c). OPPORTUNITIES The imaging of a single polaron in real space is a key milestone that opens many further possibilities. Once we can freeze and image the polaron, it becomes principally possible to study its dynamics: Thermally activated motion, excitations by external stimuli such as light, electric fields, or other perturbations. The trajectory of a (quasi)particle during such excitation carries complete information about this entity. By statistical processing, one can extract quantitative information about the activation energies for hopping, determine the frequency prefactors, and understand interaction with lattice defects, as well as the polaron–polaron coupling. Also, the exact migration mechanism can be identified this way, thereby distinguishing between the nearest-neighbor hopping, FIG. 2. Injecting clouds of charges into insulating samples. (a) The physical concept. (b) KPFM map of a surface of silicon oxide/silicon nitride/silicon oxide grown on a GaAs/ AlGaAs heterostructure with charges injected in lines, using various sample biases for the injection. (c) Surface potential map measured 15 h after the charge injection, showing lateral migration of the charges. (d) Line profiles along the lines marked in (b) and (c). (a) Reproduced with permission from Sch€ onenberger and Alvarado, Phys. Rev. Lett. 65(25), 3162 (1990). 45 Copyright 1990 American Physical Society. (b) and (c) Reproduced with permission from Valdre et al., Nanotechnology 19(4), 045304 (2008). 46 Copyright 2008 IOPscience. Applied Physics Letters PERSPECTIVE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 140502 (2025); doi: 10.1063/5.0288242 127, 140502-3 V CAuthor(s) 2025 09 October 2025 13:30:45 random flight of polarons, contributions from tunneling, etc. From the technical side, the situation with polarons is very similar to the diffusion of atoms at surfaces. This topic was prominent in the 1990s and later and enabled the fundamental understanding of processes occurring during the growth of thin films and surface diffusion. 72–76 Experimental data from STM experiments served as a benchmark for the development of theoretical methods. A similar opportunity now opens in the field of polarons. It is principally possible to provide precise data about phenomena that are currently at the forefront of interest in theory: The excited/transition states of polarons that play a key role in charge transport, or nontrivial interactions among multiple polarons that occur through the cloud of lattice distortions. In addition, SPM has recently been combined with multiple powerful experimental techniques that allow additional characterization of matter at the atomic scale. This includes, for example, tip-enhanced Raman spectroscopy, which nowadays achieves subnanometer resolution 77,78 and can provide critical information about the phonon cloud that is coupled to a single polaron. The combination of light and SPM can currently achieve subpicosecond time resolution, 79,80 while maintaining the spatial resolution of SPM. Such enhancement in time resolution is interesting for polarons, since the highly mobile polarons are particularly interesting for applications. Another interesting aspect is the spin of a polaron, which can be principally addressed by techniques such as EPR-STM (electron paramagnetic resonanceSTM). 81 This would allow us to use the spin of a polaron for its detection instead of its Coulomb interactions, as well as provide detailed information about the polaron’s coupling to the surrounding environment. CHALLENGES A key technical challenge in the investigation of polarons is their (in)stability. These quasiparticles carry electric charge, which makes them easy to manipulate by electric fields, while the activation energies for migration are typically on the order of tens of meV. Since their detection via AFM relies on their electrostatic signature, the force used for their detection is also applied to the polaron. The AFM therefore needs to reach a sensitivity on the order of single piconewtons, which is possible, yet the signal-to-noise considerations 60 limit the time resolution. A conceptual challenge for studying polarons is their bulk-like character, while SPM is a surface technique. As polarons can migrate into bulk regions inaccessible to surface-sensitive SPM, their detection becomes progressively challenging. Furthermore, the physics of polarons is known to be sensitive to defects. It is well documented that the defect concentrations on the order of 0.1% can dramatically influence polaron properties, 68 which means that even subsurface defects 10 layersdeepinfluencethemeasurements.Thisisamajorchallengein most SPM studies of polarons 42,68–70 and a promising strategy is preparing the polaronic system in the form of a thin film or using a fully 2D material. CONCLUSIONS The SPM community has successfully performed the key proof-of-concept experiments, such as resolving polarons in both space and time, controlling their creation, and mapping their energy states and locations. These results open new directions that can answer the key questions in polaron physics, such as understanding the mechanisms of migration, quantifying the activation energies for specific processes, or understanding the coupling between multiple polarons and their interaction with defects. This knowledge can be possibly translated into material engineering, as polarons are central to many physical and chemical properties. Although technical challenges remain, recent progress gives strong hope SPM will bring substantial advances in polaron physics. FIG. 3. Manipulating single charges with combined AFM/STM. (a) An Au adatom (arrow) on a NaCl surface, marked for voltage pulse application. (b) Change of appearance of the adatom with the voltage pulse, without any change in position. (d) Tunneling current measurement revealing a sudden drop post-pulse, indicating a charge-state transition in the adatom. (e) Kelvin parabola showing the chargestate switching when noncontact AFM is employed. (a)–(d) Reproduced with permission from Repp et al., Science 305(5683), 493–495 (2004). 61 Copyright 2004 AAAS. (e) Reproduced with permission from Gross et al., Science 324(5933), 1428–1431 (2009). 62 Copyright 2009 AAAS. Applied Physics Letters PERSPECTIVE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 140502 (2025); doi: 10.1063/5.0288242 127, 140502-4 V CAuthor(s) 2025 09 October 2025 13:30:45 ACKNOWLEDGMENTS Authors acknowledge support from the Ministry of Sports and Education (MSMT), project ERC CZ “PoTr”LL2324, and the Grant Agency of the Czech Republic (GACR), project 20-21727X. AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose. Author Contributions Sreehari Sreekumar: Conceptualization (equal); Writing –original draft (equal); Writing –review & editing (equal). Pavel Koc an: Writing –original draft (equal); Writing –review & editing (equal). 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