Pomeranchuk-Nematic instability in the presence of a weak magnetic field

TL;DR

This paper investigates how a weak magnetic field influences the Pomeranchuk-Nematic instability in a two-dimensional Fermi liquid, revealing the need for higher-order corrections and mapping the phase transition diagram.

Contribution

It provides a detailed analysis of the magnetic field's effect on the nematic instability, emphasizing the importance of second-order corrections in the Landau-Silin equation.

Findings

Critical phase diagram in terms of F_2 and magnetic field

Higher-order corrections are essential for accurate analysis

Identification of slow oscillation modes near quantum critical point

Abstract

We analyze a two-dimensional Pomeranchuk-Nematic instability, trigger by the Landau parameter $F_2<0$, in the presence of a small magnetic field. Using Landau Fermi liquid theory in the isotropic phase, we analyze the collective modes near the quantum critical point $F_2=-1,\omega_c=0$ (where $\omega_c$ is the cyclotron frequency). We focus on the effects of parity symmetry breaking on the Fermi surface deformation. We show that, for studying the critical regime, the linear response approximation of the Landau-Silin equation is not sufficient and it is necessary to compute corrections at least of order $\omega_c^2$. Identifying the slowest oscillation mode in the disordered phase, we compute the phase diagram for the isotropic/nematic phase transition in terms of $F_2$ and $\omega_c$.