Van-Hove singularities and competing instabilities in an altermagnetic metal

TL;DR

This paper investigates how spin-dependent Van-Hove singularities in altermagnetic metals lead to unique interaction-driven instabilities, revealing new stable fixed points and dominant magnetic phases through parquet renormalization group analysis.

Contribution

It introduces the concept of spin-dependent Van-Hove singularities in altermagnets and analyzes their impact on electronic instabilities using parquet RG, identifying new fixed points and magnetic orders.

Findings

Stable fixed points differ from spin-degenerate case.

Transverse spin density wave is the leading instability.

Different instabilities dominate at small and large altermagnetic splitting.

Abstract

Van-Hove (VH) singularities in the single-particle band spectrum are important for interaction-driven quantum phases. Whereas VH points are usually spin-degenerate, in newly proposed altermagnets VH singularities can become spin-dependent, due to momentum-dependent spin polarization of the Fermi surfaces arising from combined rotation and time-reversal symmetry. We consider two altermagnetic models ($d_{x^2-y^2}$- and $d_{xy}$-wave) on a square lattice with spin-polarized VH points, and study their stable fixed-point solutions indicating interaction-induced instabilities using parquet renormalization group. For both models, we find new stable fixed-point solutions of the renormalization group equations which are not connected to the solution in the spin-degenerate limit. This implies that on the square lattice, the system with VH singularities is unstable with respect to altermagnetic perturbations. The leading instability for the $d_{x^2-y^2}$-model is real transverse spin density wave. For the $d_{xy}$-wave model, it is found to be real transverse spin density wave at large altermagnetic splitting. At small altermagnetic splitting both imaginary charge density wave and real longitudinal spin density waves are dominant.