Short Range Interaction Effects on the Density of States of Disordered Two Dimensional Crystals with a half--filled band

TL;DR

This paper investigates how short-range electron-electron interactions affect the density of states in disordered two-dimensional crystals at half-filling, revealing positive quantum corrections near the band center due to Bragg reflections.

Contribution

It demonstrates the impact of Bragg reflections on quantum corrections to the DoS, showing a positive correction at half-filling, which contrasts with previous negative corrections.

Findings

Positive logarithmic correction to DoS at half-filling due to Bragg reflections.

Negative logarithmic corrections dominate away from commensurate points.

Bragg reflections significantly alter the quantum correction behavior.

Abstract

The Density of electronic States (DoS) of a two--dimensional square lattice with substitutional impurities is calculated in the presence of short--range electron--electron interactions. In the middle of the energy band, the Bragg reflections off the Brillouin zone boundary are shown to lead to additional quantum corrections to the DoS, the sign of which is opposite to the sign of the Altshuler--Aronov's logarithmic correction. The resulting quantum correction to the DoS at half--filling is positive, i.e. the DoS increases logarithmically as the Fermi energy is approached. However, far from the commensurate points where the Bragg reflections are suppressed, the negative logarithmic corrections to the DoS survive.