Universal transport near a quantum critical Mott transition in two dimensions

TL;DR

The authors study universal transport near a zero-temperature, continuous Mott transition in two dimensions, where a Fermi liquid transitions to a spin-liquid with a spinon Fermi surface. Using a slave-rotor formulation and a controlled large-$N$ expansion, they show that emergent gauge fluctuations damp charge transport and produce a universal zero-temperature resistivity jump $\rho_b = R\hbar/e^2$ with $R\approx 49.8$, alongside a universal scaling function collapsing $\rho$ across temperature and pressure via $\rho-\rho_m = (\hbar/e^2) G(\delta^{z\nu}/T)$ with $z=1$, $\nu\approx 0.672$. They also predict a universal jump in thermal transport $\kappa/T$ due to gauge breaking of conformal invariance, and a violation of Wiedemann-Franz law quantified by $(k_B/e)^2 KR$, where $K$ and $R$ are dimensionless constants tied to the Mott QCP. The results connect to organic salts under pressure as potential realizations, and they provide a framework for interpreting finite-$T$ transport through a critical Fermi surface, with implications for spin-charge separation in 2D quantum critical metals.

Abstract

We discuss the universal transport signatures near a zero-temperature continuous Mott transition between a Fermi liquid (FL) and a quantum spin liquid in two spatial dimensions. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the spin liquid, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We present a controlled calculation of the value of the zero temperature universal resistivity jump predicted to occur at the transition. More generally, the behavior of the universal scaling function that collapses the temperature and pressure dependent resistivity is derived, and is shown to bear a strong imprint of the emergent gauge fluctuations. We further predict a universal jump of the thermal conductivity across the Mott transition, which derives from the breaking of conformal invariance by the damped gauge field, and leads to a violation of the Wiedemann-Franz law in the quantum critical region. A connection to organic salts is made, where such a transition might occur. Finally, we present some transport results for the pure rotor O(N) CFT.

Figures (16)

• Figure 1: Jump of the universal resistivity, $\rho$, and Lorentz number, $\kappa/\sigma T$, at $T=0$ as a function of $\delta$, which is proportional to ratio of the bandwidth to the Hubbard repulsion, Eq. (\ref{['eq:de']}). The latter jump signals a violation of the Wiedemann-Franz law by the critical Fermi surface state. $\kappa$ is the thermal conductivity; $R, K$ are universal constants associated with the Mott QCP. In particular, they strongly depend on the emergent gauge boson associated with the electron fractionalization. The resistivity becomes infinite in the SL, and as a consequence so does the Lorentz number.
• Figure 2: The phase diagram of the quantum critical Mott transition. $\delta$ tunes the ratio of onsite repulsion to the bandwidth away from its critical value, and can be put in correspondence with $P-P_c$, the deviation from the QC pressure, $P_c$. The dark shaded (blue) region is the quantum critical region, where the Landau quasiparticle is destroyed but a "critical Fermi surface" nonetheless exists. It separates the spin liquid (SL) and the Fermi liquid (FL). The intermediate-$T$ states (with prefix 'M'), the marginal SL and FL, differ from the low temperature ones by the fact that the spinons and gauge bosons still behave as in the QC region.
• Figure 3: Sketch of low temperature behaviour of the resistivity near the quantum critical (QC) Mott transition. Panel c) shows the resistivity vs $T$ for different values of the onsite repulsion over the bandwidth (tuned by $\delta$), with the corresponding cuts shown in the phase diagram in a). Panel d) shows the resistivity vs $\delta$ at different temperatures, with the corresponding cuts shown in the phase diagram in b). In c) and d), the markers correspond to the location of the resistivity jump upon entering the QC state from the FL. The value of the jump is universal: $R\hbar/e^2$. Our calculations yield $R=49.8$, which translates to a jump of $\sim 8 h/e^2$.
• Figure 4: Charge excitations near the Mott transition. a) Triangular lattice at half-filling; the small shaded disks represent electrons. The double-occupied (empty) sites are identified by a red/left (blue/right) circle. These are encoded in the charge rotor excitations, the holons and doublons, respectively. Under an applied electric field, they will move in opposite directions. b) By virtue of the emergent particle-hole symmetry between doublons and holons, it is possible to have a state with zero momentum, $P$, but finite current, $J$. This allows interactions to dissipate current while conserving momentum.
• Figure 5: Illustration of the main scattering mechanisms determining the resistivity in the QC region. The blue disk corresponds to a holon excitation with charge $+e$. In addition to the usual scattering between critical charge fluctuations (mediated by the $\lambda$ field), the static emergent gauge fluctuations generate a random "magnetic field", ${\bm \nabla}\times{\bm a}$, that scatters the holons and doublons. A schematic configuration of this emergent magnetic field (which is always perpendicular to the plane) is shown, where the scale gives its strength and direction, the latter dictated by the sign.