PHYSICAL REVIEW X 9, 011032 (2019)

Nano-Resolved Current-Induced -Metal Transition in the Mott Insulator Ca2RuO4

Jiawei Zhang,1,* Alexander S. McLeod,2,* Qiang Han,2,* Xinzhong Chen,1 Hans A. Bechtel,3 Ziheng Yao,1 S. N. Gilbert Corder,1 Thomas Ciavatti,1 Tiger H. Tao,4 Meigan Aronson,5 G. L. Carr,6 Michael C. Martin,3 Chanchal Sow,7 Shingo Yonezawa,7 Fumihiko Nakamura,8 Ichiro Terasaki,9 D. N. Basov,2 † ‡ Andrew J. Millis,2,10, Yoshiteru Maeno,7, and Mengkun Liu1,¶ 1Department of , Stony Brook University, Stony Brook, New York 11794, USA 2Department of Physics, Columbia University, New York, New York 10027, USA 3Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 4State Key Laboratory of Transducer Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China 5Department of Physics, Texas A&M University, College Station, Texas 77843, USA 6NSLS-II Photon Sciences, Brookhaven National Laboratory, Upton, New York 11973, USA 7Department of Physics, Kyoto University, Kyoto 606-8502, Japan 8Department of Education and Creation Engineering, Kurume Institute of Technology, Fukuoka 830-0052, Japan 9Department of Physics, Nagoya University, Nagoya 464-8602, Japan 10Center for Computational Quantum Physics, The Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA

(Received 29 July 2018; revised manuscript received 16 December 2018; published 15 February 2019)

The Mott insulator Ca2RuO4 is the subject of much recent attention following reports of emergent nonequilibrium steady states driven by applied electric fields or currents. In this paper, we carry out infrared nano-imaging and optical-microscopy measurements on bulk single crystal Ca2RuO4 under conditions of steady current flow to obtain insight into the current-driven insulator-to- metal transition. We observe macroscopic growth of the current-induced metallic , with nucleation regions for metal and insulator phases determined by the polarity of the current flow. A remarkable metal-insulator-metal microstripe pattern is observed at the phase front separating metal and insulator phases. The microstripes have orientations tied uniquely to the crystallographic axes, implying a strong coupling of the electronic transition to lattice degrees of freedom. Theoretical modeling further illustrates the importance of the current density and confirms a submicron-thick surface metallic layer at the phase front of the bulk metallic phase. Our work confirms that the electrically induced metallic phase is nonfilamentary and is not driven by Joule heating, revealing remarkable new characteristics of electrically induced insulator-metal transitions occurring in functional correlated .

DOI: 10.1103/PhysRevX.9.011032 Subject Areas: Strongly Correlated Materials

I. INTRODUCTION observations of current- or field-driven transitions are reported, interpretation in terms of true nonequilibrium Electric control of nonthermal phase transitions in strongly phases is complicated by the possibilities of Joule heating correlated materials (SCEMs) is a central theme of (which could imply that the current simply heats the system modern-day condensed-matter research [1–9].Whilemany into the higher-temperature phase) and microscopic phase separation. This possibility is especially true for SCEMs, since the competition between many degrees of freedom *These authors contributed equally to the present work. † including orbital, lattice, and magnetic ordering can yield the Corresponding authors. coexistence of multiple phases in the same crystal, triggered [email protected] ‡ [email protected] by minute perturbations of the electronic and lattice ¶[email protected] subsystems. Field-induced filament growth and temper- ature-induced phase percolation at microscopic scales are Published by the American Physical Society under the terms of extensively reported in 3d transition-metal oxides, including the Creative Commons Attribution 4.0 International license. – Further distribution of this work must maintain attribution to vanadates, manganites, and cuprates [10 17]. Therefore, the author(s) and the published article’s title, journal citation, direct insight into the spatial structure and thermal aspects of and DOI. quantum phase transitions is urgently needed.

2160-3308=19=9(1)=011032(8) 011032-1 Published by the American Physical Society JIAWEI ZHANG et al. PHYS. REV. X 9, 011032 (2019)

In this paper, we study the paradigmatic 4d transition- II. CURRENT-INDUCED INSULATOR-TO-METAL metal Ca2RuO4. At thermal equilibrium, Ca2RuO4 is TRANSITION “ ” a Mott insulator at room temperature and a bad metal at A. Macroscopic imaging high temperatures [18]. Both heating above Tc ¼ 357 K [19] and applying hydrostatic pressure above 0.5 GPa Our experiments examine Ca2RuO4 single crystals, with ∼1 ∼1 ∼200 μ [20–22] can induce the insulator-to-metal transition (IMT). typical dimension of mm × mm × m (thick- It was recently found that an astonishingly small electric ness). Current is introduced to the sample via needlelike 40 μ field of 40 V=cm can also induce the IMT, with exper- electrodes with a width of approximately m deposited imental evidence excluding the major role of Joule heating on opposite edges of the crystal, enabling two terminal I-V [23,24]. Furthermore, x-ray diffraction measurements characteristics to be obtained simultaneously with the reveal a possible intermediate electronic and lattice state acquisition of optical micrographs and s-SNOM imaging preceding the full metallic phase, maintained by dc current across the IMT. Schematics of the experimental setup are [25]. These current-induced states in Ca2RuO4 can persist shown in Fig. S1 [27] of Supplemental Material. The main to low temperatures, where strong was panel in Fig. 1(a) presents the two-terminal I-V character- discovered at a current density of merely 10 A=cm2 [2]. istic. Simultaneously acquired optical micrographs Therefore, a mounting body of evidence suggests the obtained under visible light illumination are shown as importance of current-induced nonequilibrium phenomena insets. As the current is increased from zero, the sample in Ca2RuO4. However, the microscopic spatial structure of remains insulating (low I-V ratio, region 1) up to a critical ∼ 50 the metallic phase and the transition itself have heretofore voltage of about 5 V (electric field E V=cm for our not been clarified. sample dimension). The corresponding optical micrograph We use IR nanospectroscopy and nano-imaging tech- shows that the sample is insulating (visibly bright) at zero niques based on scattering-type scanning near-field optical voltage. This phase is labeled as the S phase to be microscopy (s-SNOM) [26,27]. The experiments are per- consistent with the previously reported S-Pbca lattice formed at room temperature and ambient pressure, under structure of the insulating phase [33,34]. At slightly above conditions of a controlled constant current flow. The IR 5 V, the current discontinuously jumps to a higher value. At nanospectroscopy covers a wide frequency range from 400 the same time, a visibly dark region (identified as the to 2000 cm−1 (25–5 μm) capturing both the and metallic L-Pbca state and denoted here as L) nucleates from electronic optical response with 20 nm spatial resolution. In the negative electrode and expands with an increasing addition, CO2 laser-based IR nano-imaging at approxi- current. The boundary of the L phase is seen to have a mately 900 cm−1 (about 11 μm) with the same spatial convex arclike shape surrounding the effectively pointlike resolution is used to investigate the current-induced insu- electrode, suggesting the IMT occurs only where the lator-metal phase boundary across different stages of the current density exceeds a critical value, thus determining [27]. In agreement with previous results, the location of the insulator-metal boundary. As the current we find that at low current densities the sample is entirely increases, the area of the metallic (dark) region increases. The insulating, while at high current densities the sample is I-V curve (curve 2) correspondingly displays a negative entirely metallic. At intermediate currents, we find new differential resistance which correlates with the optically effects: As the current is increased above a critical value, an identified volume fraction of the metal. The sample is apparently uniform (nonfilamentary) metallic phase grows completely transformed at sufficiently high currents. out of the negative electrode, covering a progressively Remarkably, as demonstrated in Figs. 1(b) and 1(c), the greater portion of the sample until it is entirely transformed. L phase consistently emerges from the negative electrodes Reversing the polarity of the electrodes reverses the for all samples we test. Reversing the polarity of the applied electrode from which the metallic phase emerges and the voltage also reverses the electrode from which the L phase direction of phase propagation. This polarity dependence emerges. These observations strongly weaken the impor- rules out Joule heating as a fundamental transition mecha- tance of Joule heating, which should be a scalar quantity nism. Moreover, IR s-SNOM imaging of the insulator- independent of the direction of the current. We also exclude metal phase boundary sustained by the electric current a bulk Peltier effect as the dominant driving mechanism. reveals exotic stripelike patterns of phase coexistence which, The Peltier effect in Ca2RuO4 leads to a temperature to the best of our knowledge, have not been observed in gradient across the two electrodes, which might, in prin- previous studies of the IMT in single crystals of correlated ciple, drive the interface towards the positive electrode via electron oxides [28–32]. We formulate a minimal theory thermoelectric heating. This scenario implies that the accounting for the current density-sustained IMT and the nucleated L state has already reached Tc and the movement influence of long-range strain which identifies the sponta- of the phase boundary is purely due to local heating of the neous stripe pattern as the hallmark of strong coupling sample. However, as shown in Fig. S6 [27], we find that between the nonequilibrium and induced further heating of the entire sample within 18 K does not structural distortions of the Ru-O6 octahedra. move the phase boundary. This observation counterindicates

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FIG. 1. dc transport characterization and optical photographs of a Ca2RuO4 bulk single crystal at different stages of the IMT. (a) A dc I-V curve with optical images taken by a CCD camera in the visible range. The insets show the emergence and expansion of the L phase (dark region) at each stage of the phase transition. The white dashed line in the bottom inset outlines the silver paint electrodes on the sample surface. (b) and (c) show the switching of the L phase from the right to left electrode via reversing the polarity of the two electrodes (outlined by the white dashed lines). a thermoelectric mechanism and supports the scenario of an 20 nm spatial resolution [Fig. 2(a)]. At 0 V, the nano-IR intrinsic electric-current-induced IMT in which bulk Joule or spectrum reveals a peak at approximately 603 cm−1 with an thermoelectric heating plays at most a minor role. apparent dip at about 680 cm−1 (gray curve, S state). We The microscopic origin of the polarity-dependent - identify this peak as the previously reported trans- ing most likely arises from the strong electron-hole verse optical in-plane Ru-O stretching mode of Ca2RuO4 asymmetry of the many-body of frontier [39–41]. The amplitude of this phonon response is contin- (the t2g symmetry Ru d) orbitals. At room temperature uously suppressed with an increasing electric current, and its in equilibrium, the gap in insulating Ca2RuO4 is formed peak position is weakly blueshifted (approximately 8 cm−1), between an xy-orbital-derived valence band and xz=yz- which we take as signifiers of an intermediate state labeled as orbital-derived upper-Hubbard bands. The resulting many- the S0 state (blue curve; see also Fig. S3 [27]). The nano-IR body density of states is highly asymmetric about the Fermi spectrum collected in the L phase (golden curve) shows a level, with the filled bands exhibiting a large peak at the totally different behavior: The infrared signal presents an band edge and the empty states having a smoother spectral approximately fourfold increase over the entire spectrum structure [35]. During the IMT, there is a considerable range without the phonon peak at 603 cm−1. This increase, in redistribution of from doubly occupied xy (and combination with the visible brightness reduction in the singly occupied xz=yz) orbitals in the insulating phase to metallic L phase, suggests that the L (metallic) phase is approximately equal the occupancy of each orbital in the characterized by a large spectral weight transfer from higher – metallic phase [36 38]. Therefore, under small changes in energies (visible light frequencies) to lower energies (IR and the electrochemical potential, the strong electron-hole dc) consistent with the onset of a Drude response. While the asymmetry yields much more pronounced hole electromagnetic response of inhomogeneous mixtures is compared with electron doping in the metallic L phase. complicated, the absolute normalization and spatial resolu- This vast asymmetry in the electrostatic susceptibility of tion of our nano-IR spectroscopy shows that the IR signal of Ca2RuO4 may explain the initial nucleation of the L phase 0 −1 the S state above 700 cm is comparable to S but much at negative electrodes and may imply a current-dependent 0 lower than L, ruling out the possibility that the S state force across a domain wall. 0 comprises any mixture of L and S phases. We attribute S to a nonequilibrium intermediate state emerging under the electric B. Nanoscale imaging and spectroscopy current flow, distinct from S and L phases, in agreement with We collect broadband nano-IR spectra at different other experimental observations in Ca2RuO4 under similar current-controlled stages of the IMT with approximately steady-state current conditions [23,25].

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FIG. 2. (a) IR nano spectra of S, S0, and L states. The spectrum of S (gray) is taken without a current, while the spectra of S0 (blue) and L (golden) are taken at two different regions several microns apart across the L-S0 phase boundary under the same current. The spectra are normalized to that of a thick gold film. Inset: Schematic of the nanospectroscopy setup and the optical photo of the L-S0 PB. (b) IR s-SNOM imaging (second harmonic) of the L-S0 boundary stripes at the phase boundary at a frequency of 900 cm−1 marked by a red arrow in (a).

We next report in Fig. 2(b) IR nano-imaging of the L-S0 response and to probe the genuine Drude response of phase boundary (PB) which is observed at intermediate the charge carriers in metallic Ca2RuO4. The higher IR currents. The probe laser at approximately 900 cm−1 response (more metallic) is rendered golden in false color, (11 μm wavelength, or about 110 meV) is chosen to avoid whereas dark blue represents a lower IR response character- energetic overlap with the transverse optical phonon istic of insulating regions. A striking pattern of alternating

FIG. 3. Oriented stripe formation across the PB. (a)–(c) IR s-SNOM imaging (second harmonic) of S0-L phase boundaries on three different Ca2RuO4 samples. Lower panels in (b) and (c): Line cuts of the s-SNOM signal along the dashed lines in the upper panels. (d),(e) Results of the numerical minimization of the free energy for PB oriented at 45° and 90° to the crystalline bo direction [27]. Yellow indicates metal, and blue insulator. (f) shares the same parameter as (d) except using a larger driving force gradient B. The gray arrows in (a)–(f) indicate the direction of the L state expansion (normal of the PB) under an increasing current.

011032-4 NANO-RESOLVED CURRENT-INDUCED INSULATOR-METAL … PHYS. REV. X 9, 011032 (2019) bright and dark stripes (lines of metallic and insulating the IMT induces a stress, which we model as a misfit stress behavior) is found to spontaneously develop within a few σxxðrÞ¼σ ½ϕMðrÞ − ϕI within the crystal, with the direc- microns of the PB. The number and periodicity of these tion of stress (x) aligned to the bo axis. The strain fields stripes vary in different regions. In some regions, no stripes induced by this spontaneous stress extend throughout the at all are visible with only a simple steplike change in the crystal and are computed using the isotropic approxi- optical response [Fig. 3(c)]. mation of linear elasticity. As shown in Sec. III in Supplemental Material [27], after integration of the strain III. ANALYSIS OF INSULATOR-METAL over the z direction, the energy corresponding to the stress PHASE BOUNDARY induced by a given spatial configuration of the order parameter may be expressed as an interaction between A. Minimal model for stripe formation the domain walls (regions of high-order parameter gra- We argue that the stripes arise from the difference in stress dient) separating metallic and insulating states [integration exerted by the electrons on the lattice in the two phases. by parts from elastic energy Felastic in Eq. (S2) in While the insulating and metallic phases of Ca2RuO4 share Supplemental Material [27] ]: the same Pbca symmetry, their lattice parameters are Z ∂ϕð Þ ∂ϕð 0 0Þ distinct. This difference leads to an elastic mismatch stress 0 2 0 0 x;y 0 x ;y F ∝−ðσxxÞ dxdydx dy Gxxðr;⃗r⃗Þ 0 : at insulator-metal phase boundaries. We focus here on the elastic ∂x ∂x large in-plane orthorhombic anisotropy developed across Here, G is an elastic theory Green’s function with the Ca2RuO4 structural transition [21,23,42]. The difference appropriate boundary conditions enforcing net zero strain in the “ao” lattice parameter between the metallic L-Pbca phase and the S0 state phase is within 0.03 Å, whereas the throughout the immobilized crystal, and the integral covers the crystal surface area spanning the x and y lateral directions. difference in the “b ” lattice parameters is ∼0.15 Å [43], o To complete the theory, we include the domain-wall energy developing a spontaneous strain of approximately 3%. We density: argue that the elastic energy cost of the bo-axis misfit stress 0 1 can be mitigated by a striped alternation of L and S ∝ j∇ϕð⃗Þj2 fDW W r ; structural phases parallel to the ao axis. 2 To analyze this effect theoretically, we consider a where W is the domain-wall energy parameter [27].Wesee minimal model for an electronic IMT strongly coupled 0 to strain, while including a heuristic driving force asso- that Felastic comprises an attractive interaction between walls “ ” ½∂ϕð Þ ∂ ciated with the electrical current density. As explained in with the same orientation (the same sign of x; y = x) more detail below and in Supplemental Material [27], and, if comparable to fDW, can induce spontaneous stripe experimental and theoretical evidence suggests that, formation. although a bulk metallic phase is sustained in the region near the negative electrode (far from the PB) [23,25], the B. Emergence of surface stripes metallic phase gradually reduces in depth closer to the PB, We minimize the resulting free energy numerically tapering essentially into a thin layer at the top surface of with respect to the spatial configuration ϕðx; yÞ of the the sample amid the striped coexistence region at the PB order parameter [27]; representative results are shown in [Fig. 4(c)]. Thus, in our theoretical model, we assume that Figs. 3(d)–3(f). We find that stripes can afford the minimal in the vicinity of the phase boundary there persists a thin energy configuration of coexistent metal and insulator metallic layer of depth d much smaller than the sample phases at the PB. This configuration particularly depends thickness D (Fig. S7 [27]). We express the spatially on the magnitude of the current density gradient, the resolved free energy density associated with a first-order relative values of the domain wall and elastic energies, structure transition involving two locally stable phases: a and the orientation of the phase boundary with respect to metallic phase (order parameter ϕ ¼ ϕM) and an insulating the crystallographic axes (see Supplemental Material [27] phase (order parameter ϕ ¼ ϕI). Our free energy contains a for details of the calculation). We find that stripes are most ¼ − driving term fcurrent fM fI, a difference in the energy easily produced when the PB normal coincides with the density of the metallic and insulating phases, that increases direction of spontaneous stress—that is, when the direction ⃗ linearly with the in-plane position (r) along the direction of the current is aligned to the in-plane bo (x) axis. Once (nˆ) of the current flow. This term is due physically to the formed, these stripes align perpendicular to the direction of spatial variation of the current density (as discussed in the greatest elastic mismatch. The spatial extent of the Sec. III in Supplemental Material [27]; the Peltier effect striped region is set by the gradient of the current density ¼ ˆ ð⃗− ⃗Þϕð⃗Þ may also play a role). We write fcurrent An · r r0 r . change (denoted as B in Supplemental Material [27]) across In the insulating phase near the transition the in-plane the PB from L to the S0 state, whereas the width of the orthorhombic lattice parameters ao and bo are nearly equal, stripes is set by the interplay of the domain wall and elastic but in the metallic phase bo is longer by 2%, implying that energies. When B is large enough, no stripes form

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FIG. 4. Topography and progression or regression of the PB. (a) Top: The sample topography overlaid with the s-SNOM image in Fig. 2. For a larger height change from the L to S0 state, fewer stripes are observed. (b) AFM topography (top) and IR s-SNOM signal S2 imaging (middle) of eight stripes across the PB. The bottom figure shows that the variation in topography (red curve) has a one-to-one correspondence to the IR signal (black curve). (c) Schematic of a striped surface metallic layer at the PB, L phase bulges due to a larger out-of-plane lattice constant; red arrows represent the magnitude and direction of the current density. (d),(e) Progression or regression of the PB taken with repeated IR s-SNOM imaging on three different samples under a current fluctuation around 12 mA. (d) The occurrence of new metallic and insulating stripes with a width on the order of approximately 100–200 nm during the retraction of the phase front. (e) The fluctuation of the phase front. The current fluctuation and the time elapsed between the consecutive images taken in all the subfigures are less than 0.1 mA and 20 min, respectively.

[comparison between Fig. 3(d) and 3(f)]. The relative widths much as 2% (cL=cs ¼ 1.023). Therefore, the surface metallic of the insulating (or metallic) stripes shrink gradually layer near the vicinity of the PB is estimated to be no more towards the homogeneous phases [Fig. 3(e)], which coin- than a few hundred nanometers in depth. This estimate is cides with our experimental observations [Fig. 3(b)]. The much smaller than the full thickness of the crystal, which is stripe periodicity is set by a combination of elastic energy, the hundreds of microns. These findings therefore justify the use gradient of the current density change, and the thickness d of of a thin metallic layer in our theoretical model. We also note the metallic layer. that the alternative theoretical assumption of a domain wall We next present results for the sample topography from extending approximately vertically over the whole thickness atomic force microscopy, conducted concurrently with our of the sample is not compatible with the spontaneous IR nano-imaging. In Fig. 4(a), the s-SNOM image in Fig. 2 formation of stripes. is overlaid with corresponding topography, demonstrating a To conclude our findings, we demonstrate dynamic gradual rise of the IR response (black curves) toward the characteristics of the electrically induced PB. Figure 4(d) higher end of the metallic side. Since the probing depth of shows the retraction of the L phase when the current is s-SNOM is typically less than 50 nm [44,45], this gradual decreased by approximately 0.1 mA from 12.0 mA. The top increase of the IR response suggests a growing depth of the and bottom panels show the same sample region imaged by metallic layer from the S0 state to the L phase across the PB, consecutive scans. Rather than a translational shift of as schematically shown in Fig. 4(c). In addition, Fig. 4(b) preexisting stripe patterns, we observe that outer metallic reveals that the topography over the metallic stripes is stripes disappear (“3” and “4”) or become narrower at their approximately 1 nm higher than the insulating phase, which same fixed locations (“1” and “2”), whereas a new stripe can be understood through the fact that the S0-to-L transition (“0”) nucleates at locations prescribed by the stripe perio- is accompanied by an out-of-plane lattice expansion by as dicity. In Fig. 4(e), multiple stripes are shown to emerge or

011032-6 NANO-RESOLVED CURRENT-INDUCED INSULATOR-METAL … PHYS. REV. X 9, 011032 (2019) vanish relative to the existing stripes. Such self-organized All authors contributed to the writing and editing of the spontaneous phase separation mediated by long-range strain manuscript. interactions remains an underexplored phenomenon in the The authors declare no competing financial interests. context of the IMT in single crystals, motivating future study by nano-imaging probes with time-resolved capabilities.

IV. CONCLUSION [1] F. Chudnovskiy, S. Luryi, and B. Spivak, Switching Device In conclusion, we have used a combination of visible- Based on First-Order Metal-Insulator Transition Induced frequency microscopy and infrared nano-imaging to resolve by External Electric Field,inFuture Trends in Microelec- tronics: The Nano Millenium, edited by S. Luriy, J. M. Xu, the spatial structure and dynamics of the current-driven A. Zaslavsky (John Wiley and Sons Ltd, New York, 2002), nonequilibrium IMT in Ca2RuO4 single crystals. The phase pp. 148–155. transition is initiated by a polarity-asymmetric nucleation of [2] C. Sow, S. Yonezawa, S. Kitamura, T. Oka, K. Kuroki, F. the current-induced bulk metallic phase at the negative Nakamura, and Y. Maeno, Current-Induced Strong Dia- electrode, consistent with strong electrostatic susceptibility in the Mott Insulator Ca2RuO4, Science 358, due to electron-hole asymmetric electronic structure of the 1084 (2017). insulating S phase. The phase nucleation proceeds by [3] L. Cario, B. Corraze, A. Meerschaut, and O. Chauvet, expansion of the metal phase across the sample as the Dielectric Breakdown and Current Switching Effect in the ð Þ current density is increased. A spontaneous surface stripe Incommensurate Layered Compound LaS 1.196VS2, Phys. texture of coexisting metal and insulating phases is observed Rev. B 73, 155116 (2006). [4] S. Yamanouchi, Y. Taguchi, and Y. Tokura, Dielectric at the global metal-insulator phase boundary. We argue that Breakdown of the Insulating Charge-Ordered State in this stripe formation is driven by the minimization of elastic La2−xSrxNiO4, Phys. Rev. Lett. 83, 5555 (1999). mismatch strain and is well described by a minimal theory [5] C. Vaju, L. Cario, B. Corraze, E. Janod, V. Dubost, T. Cren, considering a thin surface metallic layer. Our results support D. Roditchev, D. Braithwaite, and O. Chauvet, Electric- an electrically induced insulator-metal transition scenario Pulse-Driven Electronic Phase Separation, Insulator-Metal which is fundamentally distinct from the filamentary met- Transition, and Possible in a Mott allization common to high-field resistive switching reported Insulator, Adv. Mater. 20, 2760 (2008). in other oxides [46,47]. Future studies will include low- [6] V. Dubost, T. Cren, C. Vaju, L. Cario, B. Corraze, E. Janod, temperature experiments of Ca2RuO4 single crystals and F. Debontridder, and D. Roditchev, Resistive Switching at epitaxial thin films driven through the electrically induced the Nanoscale in the Mott Insulator Compound GaTa4Se8, IMT. Nano-imaging experiments under in situ applied strain Nano Lett. 13, 3648 (2013). [7] B. Corraze et al. Electric Field Induced Avalanche Break- would provide valuable insight to orbital ordering under down and Non-Volatile Resistive Switching in the Mott static strain [48] to further clarify the microscopic mecha- Insulators AM4Q8, Eur. Phys. J. Spec. Top. 222, 1046 (2013). nism of current-induced metallization in this compound. [8] V. Guiot, L. Cario, E. Janod, B. Corraze, V. T. Phuoc, M. Rozenberg, P. Stoliar, T. Cren, and D. Roditchev, Avalanche ACKNOWLEDGMENTS Breakdown in GaTa4Se8−xTex Narrow-Gap Mott Insula- tors, Nat. Commun. 4, 1722 (2013). This work was supported by JSPS KAKENHI [9] Y. Taguchi, T. Matsumoto, and Y. Tokura, Dielectric (No. JP15H05851, No. JP15H05852, No. JP15K21717, Breakdown of One-Dimensional Mott Insulators Sr2CuO3 and No. JP17H06136) and the JSPS Core-to-Core and SrCuO2, Phys. Rev. B 62, 7015 (2000). program. C. S. acknowledges support of the JSPS [10] M. M. Qazilbash et al. Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging, Science 318, International Research Fellowship (No. JP17F17027). 1750 (2007). A. S. M. and D. N. B. are supported by DOE-BES [11] A. S. McLeod et al. Nanotextured Phase Coexistence GrantNo. DE-SC0012375. D. N. B. is supported by the in the Correlated Insulator V2O3, Nat. Phys. 13, 80 (2016). Gordon and Betty Moore Foundation’s EPiQS Initiative [12] J. Zhang, X. Tan, M. Liu, S. W. Teitelbaum, K. W. Post, through Grant No. GBMF4533. The authors gratefully F. Jin, K. A. Nelson, D. N. Basov, W. Wu, and R. D. Averitt, acknowledge the efforts of M. Raschke and his group in Cooperative Photoinduced Metastable Phase Control in developing the SINS instrument at the Advanced Light Strained Manganite Films, Nat. Mater. 15, 956 (2016). Source. The Advanced Light Source is supported by the [13] M. H. Hamidian et al. Atomic-Scale Electronic Structure of Director, Office of Science, Office of Basic Energy the Cuprate d-Symmetry Form Factor Density Wave State, Nat. Phys. 12, 150 (2016). Sciences, of the U.S. Department of Energy under [14] C. McGahan, S. Gamage, J. Liang, B. Cross, R. E. Marvel, Contract No. DE-AC02-05CH11231. G. L. C. acknowl- R. F. Haglund, and Y. Abate, Geometric Constraints on edges DOE DE-SC0012704. The work of A. J. M. and Phase Coexistence in Vanadium Dioxide Single Crystals, Q. H. was supported by the U.S. Department of Energy, Nanotechnology 28, 085701 (2017). Office of Science, Office of Basic Energy Sciences under [15] J. Wu, Q. Gu, B. S. Guiton, N. P. De Leon, L. Ouyang, Award No. DE-SC-0012375. and H. Park, Strain-Induced Self Organization of Metal-

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