Electronic response of a Mott insulator at a current-induced insulator-to-metal transition

Ca₂RuO₄, a quasi-two-dimensional material with RuO₆ octahedra layers, undergoes an insulator-to-metal transition (IMT) above T_IMT = 357 K. The low-temperature insulating phase (S phase) and high-temperature metallic phase (L phase) are distinguished by their *c*-axis length. Octahedral compression in the S phase lifts Ru *t*_2g state degeneracy, creating a Mott insulating gap. The system's sensitivity to external perturbations allows IMT tuning via temperature, chemical substitution, pressure, strain, electric fields, and notably, direct current (d.c.). The current-induced metallic phase persists as long as the current flows, representing a unique long-lasting non-equilibrium steady state. While current-induced structural changes differ from temperature-driven changes, the mechanism of current-induced IMT remains unclear. To understand this mechanism, this study investigates the electronic structure evolution between the insulating and current-driven steady states using a combined transport and angle-resolved photoemission spectroscopy (transport-ARPES) approach. This technique allows for the differentiation of crystal defects from intrinsic microscale phenomena by integrating data from an integrative probe (transport) and a scanning probe (ARPES). Previous transport-ARPES applications faced challenges from stray electric and magnetic fields. This study addresses these challenges through a micrometer-size beamspot and core-level spectroscopy, creating a common binding energy reference for different current magnitudes. This method provides insights into the current-driven IMT in Ca₂RuO₄.

Previous research extensively explored the structural changes accompanying the current-induced IMT in Ca₂RuO₄. Studies have demonstrated the transition's dependence on current density and direction, with observations of metal-insulator nanostripe patterns at intermediate current densities applied parallel to the *b* axis. The zero-current IMT is understood to result from the *c*-axis shortening, but the mechanism behind the current-induced IMT was not fully established. Investigations revealed that current-induced structural changes differ from those driven by temperature; the insulating (S*) and metallic (L*) states exhibit slightly larger and smaller *c*-axes than their zero-current counterparts, respectively. Current also suppresses the antiferromagnetic order below T_N = 110 K. While the IMT is observed regardless of whether current is applied in the *ab* plane or along the *c* axis, an unusual metal-insulator nanostripe pattern emerges at intermediate current densities parallel to the *b* axis. These previous works lay the groundwork for this study's focus on the electronic structure evolution to elucidate the current-driven IMT mechanism.

High-quality Ca₂RuO₄ single crystals were grown using the optical floating zone technique. Samples were characterized using X-ray Laue diffraction and magnetometry to confirm crystal quality and the absence of impurities. Samples were shaped into rectangular forms to ensure homogeneous current flow. Equilibrium ARPES measurements were conducted at the Canadian Light Source, while transport-ARPES experiments were performed at the Advanced Light Source. In transport-ARPES experiments, a four-probe configuration applied current parallel to the *b* axis, using a Keithley 2400 Source Measure Unit. The sample was kept at 180 K under constant cooling to prevent Joule heating. High-temperature ARPES measurements were performed at 380 K. To address stray electric and magnetic field effects, a 15 μm diameter beamspot was employed along with core-level spectroscopy for establishing a common binding energy reference at different currents. The potential gradient causing energy deviations and spectral broadening was analyzed by tracking the Ca 3p core-level binding energy as the beam moved along the current flow direction. Core-level shifts were then applied to valence band spectra to identify intrinsic current-induced modifications near the chemical potential. To minimize current-induced broadening, a 15 μm diameter beamspot was used. Data were acquired with σ-polarized light at 74 eV. DMFT calculations were performed using crystallographically refined atomic coordinates for the S, S*, L*, and L phases, obtained from neutron diffraction. DFT calculations were performed using VASP code, and the Kohn-Sham wavefunctions were downfolded to an effective Wannier basis. A three-band model representing the Ru t2g states was used, incorporating crystal field distortions and spin-orbit coupling. The interaction was approximated by the rotationally invariant Kanamori operator, and DMFT impurity models were solved using the continuous-time hybridization-expansion quantum Monte Carlo solver of the TRIQS library. Analytic continuation of the self-energy was performed using a maximum-entropy method. Landau theory was applied for a free-energy analysis, expanding the free energy up to the fourth power and coupling order parameters related to orbital population imbalance.

Transport-ARPES measurements revealed clear signatures of the current-induced IMT in Ca₂RuO₄'s electronic structure: a global reduction of the charge gap and a change in the low-energy Ru bands at the Brillouin zone edge. These dispersion changes occurred exclusively parallel to the axis with the largest structural modification under current, indicating intertwined electronic and structural changes driving the IMT. The Fermi surface in the current-induced metallic state (L*) was found to be distinct from the high-temperature L phase Fermi surface, confirming that the current-induced phase is not simply due to Joule heating. Analysis of the Ca 3p core levels demonstrated that the energy shifts observed were primarily due to the electrostatic potential gradient, rather than chemical shifts. The reduction in the charge gap was confirmed by comparing the spectral weight integrated over the entire Brillouin zone in the S and L* phases. Changes in Ru band dispersion along the XM direction were observed upon application of current, indicated by an increased spectral weight at the X point and decreased weight at k*. These changes were consistent with DMFT calculations. However, no significant modifications in Ru dispersion were observed along the YM direction, besides a redistribution of spectral weight between Ru bands. This anisotropy was attributed to the larger structural change along the *b* axis than the *a* axis. Comparison of the current-induced L* phase Fermi surface with the high-temperature L phase Fermi surface showed clear differences, confirming that the current-induced phase is electronically distinct from the high-temperature phase, and therefore not a result of Joule heating. A free-energy analysis using Landau theory with two order parameters (one for orbital population disproportion and another for electron population imbalance) qualitatively captured the field-induced IMT, supporting the experimental observations and indicating distinct electronic behavior of the current- and temperature-induced metallic states.

The findings directly address the research question of the mechanism underlying the current-induced IMT in Ca₂RuO₄ by demonstrating that it involves a distinct electronic phase transition rather than solely a thermal effect. The observation of anisotropic changes in the Ru band dispersion suggests a strong coupling between electronic and structural degrees of freedom, with the structural changes along the *b* axis primarily driving the electronic changes. The discrepancy between the current-induced L* and high-temperature L phases highlights the non-equilibrium nature of the current-induced IMT and the limitations of solely relying on thermal models to explain the phenomenon. This research significantly advances the understanding of non-equilibrium physics in strongly correlated materials, showing that current can drive a long-lived electronic phase distinct from the equilibrium high-temperature metallic phase. The detailed electronic structure changes identified provide crucial insights into the microscopic mechanisms governing current-induced phase transitions in Mott insulators.

This study successfully employed transport-ARPES to unravel the electronic structure changes during the current-induced IMT in Ca₂RuO₄. The results demonstrated that the current-induced metallic phase is electronically distinct from its high-temperature counterpart, highlighting the importance of non-equilibrium effects in the IMT. The anisotropic changes in the Ru band dispersion underscore the close interplay between electronic and structural degrees of freedom. This research opens up new avenues for investigating current-induced phase transitions in strongly correlated materials using advanced spectroscopic techniques. Future studies might focus on exploring the temporal evolution of the electronic structure during the current-induced transition, employing time-resolved ARPES techniques.

The study's spatial resolution is limited by the beamspot size (15 μm). This might mask finer details of the electronic structure changes, such as potential inhomogeneities within the sample. While stray electric and magnetic fields were accounted for, residual effects might still influence the data. The free-energy analysis provides a qualitative understanding of the IMT, but a more quantitative analysis using non-equilibrium DMFT might offer more precise insights.