Theory of a continuous Mott transition in two dimensions

TL;DR

This paper develops a gauge-theoretic, slave-rotor description of a continuous Mott transition in two dimensions from a Fermi liquid to a spinon Fermi surface spin liquid. It shows that the quasiparticle residue vanishes and the effective mass diverges at criticality, while the spin susceptibility stays finite and the compressibility vanishes, reflecting diverging Landau parameters. At the quantum critical point there is a sharp critical Fermi surface without Landau quasiparticles, with a specific heat C_v ∼ T ln(1/T) and a universal residual resistivity jump Δρ ∼ (R h)/e^2 across the metal–insulator transition; two-stage crossovers yield a Marginal Fermi Liquid regime on the metallic side and a marginal spinon liquid on the insulating side. The theory yields distinct finite-temperature crossover scales T^* and T^{**} and predicts experimental signatures, including a universal resistivity jump, that can be tested in layered organic Mott systems such as κ-(ET)$_2$Cu$_2$(CN)$_3$.

Abstract

We study theoretically the zero temperature phase transition in two dimensions from a Fermi liquid to a paramagnetic Mott insulator with a spinon Fermi surface. We show that the approach to the bandwidth controlled Mott transition from the metallic side is accompanied by a vanishing quasiparticle residue and a diverging effective mass. The Landau parameters $F^0_s, F^0_a$ also diverge. Right at the quantum critical point there is a sharply defined `critical Fermi surface' but no Landau quasiparticle. The critical point has a $Tln\frac{1}{T}$ specific heat and a non-zero $T = 0$ resistivity. We predict an interesting {\em universal resistivity jump} in the residual resistivity at the critical point as the transition is approached from the metallic side. The crossovers out of the critical region are also studied. Remarkably the initial crossover out of criticality on the metallic side is to a Marginal Fermi Liquid metal. At much lower temperatures there is a further crossover into the Landau Fermi liquid. The ratio of the two crossover scales vanishes on approaching the critical point. Similar phenomena are found in the insulating side. The filling controlled Mott transition is also studied. Implications for experiments on the layered triangular lattice organic material $κ-(ET)_2Cu_2(CN)_3$ are discussed.

Figures (4)

• Figure 1: Possible schematic zero temperature phase diagram for a half-filled single band repulsive Hubbard model on a non-bipartite lattice. $U$ is the Hubbard interaction strength and $t$ is the hopping amplitude.
• Figure 2: Evolution of the extrapolated $T = 0$ conductivity across the Mott transition. The conductivity $\sigma$ jumps twice - once from its value $\sigma_m$ in the metal to its value $\sigma_c$ at the critical point, and then again to zero on moving to the insulating phase. Neither of the jumps are universal. However the jump in the in-plane sheet resistivity$\rho$ on going from the metal to the Mott critical point is a universal constant $\frac{Rh}{e^2}$ with $R$ of order $1$.
• Figure 3: Schematic phase diagram showing finite temperature crossovers near the Mott transition studied in this paper. The black dotted lines represent the crossover scale $T^*$ and the red dotted lines the crossover at $T^{**}$. The quantum critical metal at $T = 0$ has a sharp critical Fermi surface. The electron spectral function at the Fermi surface sharpens into the marginal Fermi liquid form on cooling through $T^*$. It eventually acquires the usual Landau quasiparticle peak only below the much lower scale $T^{**}$. The Mott insulating ground state is a spin liquid with a spinon Fermi surface. A different spin liquid which also has a spinon Fermi surface appears in the intermediate temperature regime in the insulator. The critical Fermi surface evolves into the spinon Fermi surface in the insulator.
• Figure 4: Schematic phase diagram showing finite temperature crossovers near the filling controlled Mott transition in two dimensions. $\mu$ is the chemical potential. The Mott insulating ground state is a spin liquid with a spinon Fermi surface. The black dashed line is the crossover scale $T^*$ and the red dashed line is the crossover scale $T^{**}$. There are two non-fermi liquid regimes near the critical point denoted NFL$_1$ and NFL$_2$. The former appears right above the quantum critical point, and has weak singularities on a critical Fermi surface. $NFL_2$ appears between $T^*$ and $T^{**}$ on the metallic side and has strong singularities at the critical Fermi surface. The Landau Fermi liquid obtains only below $T^{**}$.