Microscopic nature of the quantum criticality at the thickness-driven Mott transition in SrVO3 quantum wells: order parameter, emergent phases, and microscopic theory

In situ angle-resolved photoemission on SrVO3 quantum wells shows the low-energy self-energy exponent evolving from the Fermi-liquid value ( $\alpha = 2$ at thicknesses of 6 monolayers and above) to a marginal, non-Fermi-liquid value ( $\alpha = 1$ at 3 monolayers) as the well thickness is reduced toward the dimensional-crossover metal-insulator transition, implying a quantum critical point near the two-dimensional Mott transition. The open problem is to establish the microscopic nature of this quantum criticality: identify the order parameter or collective mode (magnetic, charge, orbital, topological, or its absence) that drives the inferred quantum critical point, construct and test a microscopic theory that links the quantum-well subband structure and the measured exponent evolution to the Mott transition in the two-dimensional limit, determine whether emergent ordered phases — notably superconductivity — can be stabilized near the critical thickness by carrier doping, gating, or interface engineering, and establish whether this dimensional-crossover criticality is intrinsic (rather than disorder-induced) and generic to other correlated-oxide quantum wells.

Background

SrVO3 is a cubic perovskite oxide with one electron per vanadium site in the three $t_{2g}$ orbitals of the V 3d shell; it is the canonical example of a moderately correlated metal, showing quasiparticle mass enhancement but well-defined Fermi-liquid behavior in bulk. A Mott transition is a metal-insulator transition driven by electron-electron repulsion rather than band filling: when the interaction energy exceeds the kinetic energy (bandwidth), the electrons localize and a gap opens. In 2010, Yoshimatsu et al. showed that epitaxial SrVO3 films on SrTiO3 become insulating when the film thickness falls below a critical value of 2-3 monolayers, and attributed this to a dimensional-crossover-driven Mott transition: confinement into a quantum well narrows the effective bandwidth until correlations win. A quantum well (QW) is a thin conducting layer sandwiched between insulating barriers, in which the motion perpendicular to the layer is quantized into discrete subbands; here the SrVO3 layer is the well and SrTiO3 the barrier. Building on this platform, Kobayashi et al. (2017) grew SrVO3 QWs of 2-8 monolayers with monolayer precision and measured them by in situ angle-resolved photoemission spectroscopy (ARPES), which resolves the electronic band dispersion and, through the analysis of momentum-distribution-curve (MDC) linewidths, the imaginary part of the electron self-energy $\operatorname{Im}\Sigma(\omega)$ — the quantity encoding the quasiparticle scattering rate. In a Fermi liquid (the standard interacting-metal state) the scattering rate grows as $\omega^{2}$ , while a non-Fermi liquid shows a slower power law; the marginal case $\operatorname{Im}\Sigma \propto \omega$ ( $\alpha = 1$ ) is a hallmark of strange-metal behavior seen near many quantum critical points (QCPs), i.e. continuous phase transitions occurring at zero temperature where thermal fluctuations are replaced by quantum ones. Kobayashi et al. fitted $|Z\,\operatorname{Im}\Sigma(\omega)| = \Gamma^{\mathrm{imp}} + \beta'(\omega^{2} + (\pi k_{\mathrm{B}}T)^{2})^{\alpha/2}$ (with $Z$ the quasiparticle residue, $\Gamma^{\mathrm{imp}}$ the impurity scattering rate, and $\beta'$ a correlation-strength coefficient) and found the exponent $\alpha$ evolving from about 2 at 6 monolayers and thicker to about 1 at 3 monolayers, the thinnest metallic film, together with a 0.5-0.7 eV gap at 2 monolayers and a single occupied subband at 3-4 monolayers. They concluded that a QCP exists in the neighborhood of the thickness-driven Mott transition in the two-dimensional limit. Crucially, however, the data determine neither the microscopic order parameter — the broken symmetry or collective mode whose critical fluctuations would produce the observed scattering — nor whether the inference survives the effects of disorder: the QCP is inferred from a single-temperature (20 K) measurement of a subband self-energy, and later transport and structural studies of ultrathin SrVO3 films (Wang et al. 2019; Okuma et al. 2022) report oxygen vacancies, cation depletion, and metallic behavior down to 3 monolayers in low-disorder films, attributing the insulating behavior largely to disorder rather than correlations. The authors also noted that a d-electron quantum well near a Mott transition is the structural mirror of hole-doped high-Tc cuprates, suggesting that superconductivity might be stabilized by optimal electron doping near the critical thickness, and presented artificially controllable quantum-well structures of correlated oxides as a unique platform and a new strategy for investigating and designing novel quantum critical phenomena in correlated oxides generally. Subsequent work has mapped parts of this terrain — many-body calculations for the SrVO3 monolayer (Pickem et al. 2021, 2022) find Mott insulating behavior at stoichiometry with antiferromagnetic, ferromagnetic, and stripe/checkerboard orbital-ordering instabilities upon doping, and momentum-differentiated, particle-hole asymmetric self-energies driven by nonlocal spin fluctuations; doping and strain experiments (Takahashi et al. 2022, 2024) have collapsed and re-stabilized the two-dimensional Mott state — but no work has identified the order parameter of the inferred QCP, reproduced the measured thickness-dependent exponent evolution microscopically, or found superconductivity or any other emergent ordered phase near the critical thickness.

Problem Statement

Establish the microscopic nature of the quantum criticality that emerges as metallic SrVO3 quantum wells are thinned toward the dimensional-crossover Mott transition. Concretely, resolve the four linked issues arising from the source experiment: (1) identify the order parameter — the broken symmetry or collective mode (magnetic, charge, orbital, topological, or demonstrate its absence) — whose quantum critical point is inferred from the evolution of the self-energy exponent $\alpha(t)$ from 2 to 1 as the well thickness decreases from 6 to 3 monolayers, including whether the inferred criticality survives the disorder and substrate effects present in the ultimate two-dimensional limit; (2) construct and test a microscopic theory that links the confined quantum-well subband structure (including the role of interactions between the occupied $n=1$ and unoccupied higher subbands and finite-temperature crossover scales) to the measured $\alpha(t)$ evolution and the Mott transition in the two-dimensional limit; (3) determine whether emergent ordered phases — in particular superconductivity, in view of the structural mirror to hole-doped cuprates — can be stabilized near the critical thickness by carrier doping, electrostatic gating, or interface engineering; and (4) establish whether this dimensional-crossover-driven critical behavior is generic to correlated-oxide quantum wells beyond SrVO3. These components jointly serve one objective — a physically grounded account of what the thickness-driven quantum criticality in SrVO3 quantum wells is — and an answer is complete when all four issues are resolved: (1) the order parameter (or collective mode) of the inferred criticality is identified, or its absence is demonstrated (the criticality is real but order-parameter-free), or the criticality itself is shown to be an artifact; (2) the microscopic origin of the measured $\alpha(t)$ evolution is established by an account that reproduces its observed trend (from $\alpha \approx 2$ at 6 monolayers to $\alpha \approx 1$ at 3 monolayers) rather than a qualitative mechanism alone; (3) the feasibility of emergent ordered phases near the critical thickness is determined, where a negative determination (no such phase is stabilized) is itself a complete resolution of this issue; and (4) the genericity of the dimensional-crossover criticality to correlated-oxide quantum wells beyond SrVO3 is established, where demonstrating the same Fermi-liquid-to-non-Fermi-liquid crossover in at least one further correlated-oxide quantum-well system is sufficient for a positive determination. If issue (1) is resolved negatively — the order parameter is shown to be absent, or the criticality is shown to be an artifact — the implications of that finding for issues (2)-(4) must be stated explicitly.

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