Gauge fermions with flat bands and anomalous transport via chiral modes from breaking gauge symmetry

TL;DR

This paper explores how flat bands in condensed matter systems can induce gauge symmetries in fermions, leading to emergent chiral modes and anomalous transport phenomena, especially under magnetic fields.

Contribution

It demonstrates that flat bands can generate gauge symmetries in fermionic systems and studies the resulting chiral modes and transport effects in a 3D Lieb lattice model.

Findings

Flat bands induce gauge symmetry in fermionic systems.

Magnetic fields break gauge symmetry, revealing chiral modes.

Emergent chiral modes lead to anomalous electric transport phenomena.

Abstract

The dispersionless longitudinal photon in Maxwell theory is thought of as a redundant degree of freedom due to the gauge symmetry. We find that when there exist exactly flat bands with zero energy in a condensed matter system, the fermion field may locally transform as a gauge field and the system possesses a gauge symmetry. As the longitudinal photon, the redundant degrees of freedom from the flat bands must be gauged away from the physical states. As an example, we study spinless fermions on a generalized Lieb lattice in three dimensions. The flat band of the longitudinal fermion induces a gauge symmetry. An external magnetic field breaks this gauge symmetry and emerges a bunch of non-topologically chiral modes. Combining these emergent chiral modes with the chiral anomaly mode which is of an opposite chirality, rich anomalous electric transport phenomena exhibit and are expected to be observed in Pd$_3$Bi$_2$S$_2$ and Ag$_3$Se$_2$Au.