Ca₂RuO₄, a quasi-two-dimensional Mott insulator, undergoes an insulator-to-metal transition (IMT) at 357 K. This transition is attributed to the sensitivity of its ground state to octahedral compression, which lifts the degeneracy of Ru t₂g states and induces a Mott insulating gap. The IMT can be triggered not only by temperature but also by various external stimuli, such as chemical substitution, pressure, strain, electric fields, and notably, direct current (d.c.). The current-induced IMT is particularly intriguing because the metallic state persists as long as current flows, representing a unique long-lasting non-equilibrium steady state. While the structural changes associated with the current-induced IMT are distinct from those driven by temperature, the underlying mechanism remains unclear. This research aims to investigate the electronic structure evolution during the current-induced IMT in Ca₂RuO₄ to elucidate the mechanism behind this phenomenon. Understanding this mechanism has implications for non-equilibrium physics and the control of electronic properties in strongly correlated materials. Previous studies have focused primarily on structural aspects; a comprehensive understanding of the electronic response is crucial for a complete picture. The use of transport-ARPES allows for direct probing of the electronic structure under current, potentially offering key insights into this complex transition.

Previous research has extensively studied the insulator-to-metal transition (IMT) in Ca₂RuO₄, focusing on its temperature dependence and the role of structural changes. Braden et al. (1998) and Alexander et al. (1999) established the relationship between the IMT and the change in the *c*-axis lattice parameter. Subsequent studies explored the influence of various external parameters, including chemical substitution (Friedt et al., 2000; Sutter et al., 2017), pressure (Nakamura et al., 2002; Steffens et al., 2005), strain (Dietl et al., 2018; Ricco et al., 2018), and electric fields (Sakaki et al., 2013; Nakamura et al., 2013). Okazaki et al. (2013) first reported the current-induced IMT, highlighting its unique non-equilibrium nature. Further investigations focused on the structural changes accompanying this transition (Bertinshaw et al., 2019; Fürsich et al., 2019; Jenni et al., 2020; Zhao et al., 2019) and the role of Joule heating (Mattoni et al., 2020). Zhang et al. (2019) revealed the formation of a metal-insulator nanostripe pattern at intermediate current densities. However, a detailed understanding of the electronic structure modifications during the current-induced IMT has remained elusive, particularly differentiating it from the thermally driven transition. Recent work by Curcio et al. (2023) provided some insights into the gap reduction but lacked a comprehensive view of the band structure evolution.

This study employs a combined approach of transport and angle-resolved photoemission spectroscopy (transport-ARPES) to directly probe the electronic structure of Ca₂RuO₄ under applied current. High-quality single crystals were grown using the optical floating zone technique and characterized using X-ray Laue diffraction and magnetometry. For transport-ARPES measurements, gold wires were attached to the sample using conductive epoxy, enabling four-probe current application. The experiments were performed at the MAESTRO beamline at the Advanced Light Source and the Quantum Materials Spectroscopy Centre beamline at the Canadian Light Source. A micrometre-size beamspot was used to minimize the effects of stray electric and magnetic fields generated by the current. Core-level spectroscopy (specifically, the Ca 3p core level) served as a reference point to correct for energy shifts induced by the potential gradient across the sample. By aligning the core level spectra, the intrinsic changes in the valence band due to the current-induced IMT were determined. The data were analyzed to investigate the changes in the Fermi surface, charge gap, and Ru band dispersion. Density functional theory (DFT) + dynamical mean field theory (DMFT) calculations were also performed using the crystallographically refined atomic coordinates for the different phases to provide a theoretical framework for comparison with experimental results. The free-energy analysis was performed using Landau theory to understand the interplay between electronic and structural degrees of freedom in driving the IMT.

The combined transport-ARPES measurements revealed several key electronic changes during the current-induced IMT in Ca₂RuO₄: 1. **Charge Gap Reduction:** A clear reduction in the charge gap was observed, evidenced by the appearance of spectral weight at the Fermi level and the overall reduction in the integrated spectral weight across the Brillouin zone. This is consistent with the transition to a metallic state. 2. **Ru Band Dispersion Modification:** Significant changes were observed in the dispersion of the Ru bands along the XM direction (parallel to the *b* axis and the current flow). The spectral weight at specific *k* values decreased, and there was an increase in spectral weight at the X point near the Fermi level. This change indicates a clear modification of the electronic states caused by the current. 3. **Anisotropic Electronic Response:** In contrast to the XM direction, minimal changes were observed in the Ru band dispersion along the YM direction (perpendicular to the current flow). This anisotropy highlights the strong directional dependence of the electronic response to the applied current. The smaller lattice constant change along the *a* axis suggests that the change in orthorhombicity is a key factor in determining the band structure modification. 4. **Distinct Current-Induced Metallic Phase:** The Fermi surface of the current-induced metallic phase (L*) is distinct from that of the high-temperature metallic phase (L), indicating that the former is not simply a consequence of Joule heating. This is further supported by the different momentum distribution curves (MDCs) at the edge of the Brillouin zone. 5. **Free Energy Analysis:** Landau theory calculations confirmed that the current-induced IMT is not solely a temperature effect. The free energy analysis suggests that the transition involves a coupled lattice and orbital response driven by the applied electric field.

The findings demonstrate that the current-induced IMT in Ca₂RuO₄ is not merely a consequence of Joule heating but a unique non-equilibrium phase transition driven by a complex interplay between lattice and electronic degrees of freedom. The anisotropic changes in the Ru band dispersion highlight the importance of the crystallographic direction of current flow, which directly impacts the lattice distortions and the resulting electronic structure. The distinct nature of the current-induced metallic phase, as shown by the free energy analysis, further reinforces this conclusion. This study contributes to a deeper understanding of non-equilibrium phenomena in strongly correlated materials. The directional dependence of the electronic response to the applied current emphasizes the intricate relationship between lattice and orbital degrees of freedom in shaping the electronic properties of this Mott insulator. Further theoretical studies, explicitly considering the non-equilibrium nature of the current, are needed to fully capture the complexities of the current-induced IMT.

This research successfully utilized transport-ARPES to characterize the electronic structure modifications during a current-induced insulator-to-metal transition in Ca₂RuO₄. The findings revealed a distinct current-induced metallic phase, characterized by a reduced charge gap and anisotropic changes in Ru band dispersion. These results underscore the critical interplay between electronic and lattice degrees of freedom in this non-equilibrium phase transition. Future work should focus on developing theoretical models that explicitly incorporate the non-equilibrium effects of the applied current to obtain a comprehensive understanding of the transition mechanism.

While the use of a micrometre-size beamspot minimized the influence of stray fields, some broadening due to the potential gradient remained. Furthermore, the DFT+DMFT calculations used approximate interaction parameters, and the lack of a non-equilibrium DMFT calculation limits the quantitative understanding of the current's role. Finally, the study primarily focused on the electronic structure; investigations incorporating other probes, such as optical spectroscopy or magnetic measurements, could provide a more comprehensive picture.