# Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials

## TL;DR

This paper investigates how four-fermion interactions and impurities affect the low-energy electronic states of two-dimensional semi-Dirac materials using renormalization group techniques, revealing phase transitions and non-Fermi liquid behaviors.

## Contribution

It provides a detailed analysis of the interplay between four-fermion interactions and impurities, showing their effects on phase stability and electronic properties in semi-Dirac materials.

## Key findings

- Both trivial insulator and semimetal states are stable against four-fermion interactions.
- Interaction and impurity can induce insulator-semimetal phase transitions.
- Non-Fermi liquid behaviors emerge at low energies.

## Abstract

We study the effects of four-fermion interaction and impurity on the low-energy states of two-dimensional semi-Dirac materials by virtue of the unbiased renormalization group approach. The coupled flow equations that govern the energy-dependent evolutions of all correlated interaction parameters are derived after taking into account one-loop corrections from the interplay between four-fermion interaction and impurity. Whether and how four-fermion interaction and impurity influence the low-energy properties of two-dimensional semi-Dirac materials are discreetly explored and addressed attentively. After carrying out the standard renormalization group analysis, we find that both trivial insulating and nontrivial semimetal states are qualitatively stable against all four kinds of four-fermion interactions. However, while switching on both four-fermion interaction and impurity, certain insulator-semimetal phase transition and the distance of Dirac nodal points can be respectively induced and modified due to their strong interplay and intimate competition. Moreover, several non-Fermi liquid behaviors that deviate from the conventional Fermi liquids are exhibited at the lowest-energy limit.