Quantum critical points of Helical Fermi Liquids

TL;DR

This paper investigates quantum phase transitions in helical Fermi liquids, revealing complex critical modes and non-Fermi liquid behavior near ferromagnetic order, with implications for topological insulator edge states.

Contribution

It provides a detailed analysis of quantum critical points in helical Fermi liquids, identifying multiple critical modes and their effects on quasiparticles, extending understanding of spin-orbit coupled systems.

Findings

Presence of both z=3 over-damped and z=2 propagating modes at criticality

Non-Fermi liquid behavior induced by z=3 mode on the Fermi surface

Goldstone mode is over-damped except along special directions

Abstract

Following our previous work, we study the quantum phase transitions which spontaneously develop ferromagnetic spin order in helical fermi liquids which breaks continuous spin-space rotation symmetry, with application to the edge states of 3d topological band insulators. With finite fermi surface, the critical point has both z = 3 over-damped and z = 2 propagating quantum critical modes, and the z = 3 mode will lead to non-fermi liquid behavior on the entire fermi surface. In the ordered phase, the Goldstone mode is over-damped unless it propagates along special directions, and quasiparticle is ill defined on most parts of the fermi surface except for special points. Generalizations of our results to other systems with spin-orbit couplings are also discussed.