Interaction-Induced Metallicity in a Two-Dimensional Disordered Non-Fermi Liquid

The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. Instead, we start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.

Figure 1

Schematic RG flow for a disordered 2D fermionic system interacting with the magnetic order parameter fluctuations. The intermediate clean NFL fixed point is unstable to disorder and ultimately leads to a dirty fixed point with the dynamical scaling $z=4$.

Figure 2

The shaded rectangular stands for a bare diffuson (a). The impurity line is denoted by dashed line, and the retarded (advanced) single-particle fermionic propagator is denoted by solid (dash-dotted) line. Dark grey rectangular area represents the diffuson (b) with self-consistent self-energy due to interaction shown in (c). Wavy solid line represents the dynamically screened bosonic propagator. White rectangular area with symbol $H$ stands for the Hikami box which acquires self-consistent corrections (d). Leading in $1/N$ loop corrections to the bosonic self-energy are shown in (e) and the corrected boson-diffuson vertex is presented in (f). Representative diagrams for the tunneling density of states and the free energy are depicted in (g) and (h), respectively.

Figure 3

(a) The RG flow governed by Eqs. (7). The arrows mark direction of RG flow towards the infrared. (b) The functions $f_t(\zeta )$ and $f_{\zeta }(\zeta )$ used in (7). (c) Temperature dependence of the logarithm of conductivity $\ln [g(T)/g]$ as a function of $\ln \ln ({\mathrm{\Lambda }}_4/T)$ (blue curves). The red dashed lines represent an asymptotic behavior (3). The used bare parameters are $t_0=0.3$ and ${\zeta }_0=0.16$, 0.35, 0.60, 1.04, 2.25 from bottom to top.