Critical conductance of a one-dimensional doped Mott insulator

We consider the two-terminal conductance of a one-dimensional Mott insulator undergoing the commensurate-incommensurate quantum phase transition to a conducting state. We treat the leads as Luttinger liquids. At a specific value of compressibility of the leads, corresponding to the Luther-Emery point, the conductance can be described in terms of the free propagation of noninteracting fermions with charge $e∕\sqrt{2}$. At that point, the temperature dependence of the conductance across the quantum phase transition is described by a Fermi function. The deviation from the Luther-Emery point in the leads changes the temperature dependence qualitatively. In the metallic state, the low-temperature conductance is determined by the properties of the leads, and is described by the conventional Luttinger-liquid theory. In the insulating state, conductance occurs via activation of $e∕\sqrt{2}$ charges, and is independent of the Luttinger-liquid compressibility.

Figure 1

Phase diagram of the CI transition for temperatures smaller than the gap $\Delta$, see text. A quantum phase transition with exponents ${\nu }_r=1∕2$ and $z=2$ separates the commensurate, $r>0$, and the incommensurate, $r<0$, phases. The CI Hamiltonian (2.13) controls the vicinity of the quantum critical point. The quantum critical regime occurs within a cone $T\sim {\mid r\mid }^{{\nu }_{r}z}=\mid r\mid$.

Figure 2

First order corrections to the current autocorrelator. The straight line represents fermionic $\Psi$ propagators, the wiggled line is the interaction, and the dot is the current vertex $\sqrt{2}{e}_{\mathrm{CI}}v{\sigma }^3$.

Figure 3

Temperature dependence of two-terminal conductance close to the Mott transition for different values of the tuning parameter $r$. On the metallic side, $r<0$, at $T=0$ the conductance is determined by the Luttinger parameter of the leads, $K_L$; $G_0=2e^2∕h$ is the conductance quantum. In the insulating phase, $r>0$, at lowest temperature the conductance is thermally activated with a universal exponential prefactor involving the fractional charge, $e_{\mathrm{CI}}=e∕\sqrt{2}$, of the critical degrees of freedom, $G_{\mathrm{CI}}=2e_{\mathrm{CI}}^2∕h$. In the quantum critical regime, $\mid r\mid <T$, of the phase diagram, see Fig. 1, the conductance is determined by its critical value, $G_{\mathrm{cr}}$, see Eq. (1.5), that depends both on the Luttinger parameter, $K_L$, and on the fractional charge, $e_{\mathrm{CI}}$.