Properties of electrons near a Van Hove singularity

TL;DR

This paper reviews how electrons near a Van Hove singularity in cuprates influence weak coupling instabilities, highlighting the phase diagram and Fermi surface deformations using a renormalization group approach.

Contribution

It provides a comprehensive review of the physical processes and phase behavior of two-dimensional systems near Van Hove singularities, focusing on antiferromagnetism and superconductivity.

Findings

Phase diagram characteristics near Van Hove singularity

Deformations of the Fermi surface due to singularity proximity

Role of renormalization group in understanding instabilities

Abstract

The Fermi surface of most hole-doped cuprates is close to a Van Hove singularity at the M point. A two-dimensional electronic system, whose Fermi surface is close to a Van Hove singularity shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. The renormalization group approach is reviewed with emphasis on the underlying physical processes. General properties of the phase diagram and possible deformations of the Fermi surface due to the Van Hove proximity are described.