# The phase diagram of a two-dimensional dirty tilted Dirac semimetal

## TL;DR

This paper explores how quenched disorder affects two-dimensional tilted Dirac semimetals, revealing different phase diagrams depending on tilt and disorder type through renormalization group analysis.

## Contribution

It provides a detailed renormalization group analysis of disorder effects on tilted Dirac semimetals, considering various disorder types and tilt parameters, and proposes corresponding phase diagrams.

## Key findings

- Disorder effects depend on tilt parameter and disorder type.
- Marginal disorders influence low-energy physics significantly.
- Phase diagrams vary with disorder type and tilt magnitude.

## Abstract

We investigate the effects of quenched disorder on a non-interacting tilted Dirac semimetal in two dimensions. Depending on the magnitude of the tilting parameter, the system can have either Fermi points (type-I) or Fermi lines (type-II). In general, there are three different types of disorders for Dirac fermions in two dimensions, namely, the random scalar potential, the random vector potentials along and perpendicular to the tilting direction, and the random mass. We study the effects of weak disorder in terms of the renormalization group, which is performed by integrating out the modes with large energies, instead of large momenta. Since the parametrization of the low-energy degrees of freedom depends on the structure of the Fermi surface, the resulting one-loop renormalization-group equations depend on the type of tilted Dirac fermions. Whenever the disorder is a marginal perturbation, we examine its role on low-energy physics by a mean-field approximation of the replica field theory or the first-order Born approximation. Based on our analysis, we suggest the phase diagrams of a two-dimensional tilted Dirac fermion in the presence of different types of disorder.