Disorder-driven quantum transition in relativistic semimetals: functional renormalization via the porous medium equation

Abstract

In the presence of randomness, a relativistic semimetal undergoes a quantum transition towards a diffusive phase. A standard approach relates this transition to the $U(N)$ Gross-Neveu model in the limit of $N\to 0$. We show that the corresponding fixed point is infinitely unstable, demonstrating the necessity to include fluctuations beyond the usual Gaussian approximation. We develop a functional renormalization group method amenable to include these effects and show that the disorder distribution renormalizes following the so-called porous medium equation. We find that the transition is controlled by a nonanalytic fixed point drastically different from that of the $U(N)$ Gross-Neveu model. Our approach provides a unique mechanism of spontaneous generation of a finite density of states and also characterizes the scaling behavior of the broad distribution of fluctuations close to the transition. It can be applied to other problems where nonanalytic effects may play a role, such as the Anderson localization transition.

5+9 pages, 2+3 figures

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• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Topological diffusive metal in amorphous transition metal monosilicides
• Fermi arcs and surface criticality in dirty Dirac materials
• BCS-like disorder-driven instabilities and ultraviolet effects in nodal-line semimetals
• Non-Anderson critical scaling of the Thouless conductance in 1D
• Surface quantum critical phenomena in disordered Dirac semimetals
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions
• Boundary critical behavior of the Gross-Neveu-Yukawa model