Pairing Instability in a Nematic Fermi Liquid

TL;DR

This paper investigates pairing instabilities in a nematic Fermi liquid with two quantum numbers, revealing how different collective modes mediate interactions that can lead to pairing under specific conditions, with implications for cuprates and quantum Hall systems.

Contribution

It introduces the concept of pairing instability mediated by collective modes in a nematic Fermi liquid with two quantum degrees of freedom, highlighting conditions for pairing.

Findings

Out-of-phase mode mediates attractive interaction between fermions.

In-phase mode mediates repulsive interaction.

Pairing occurs when the in-phase mode is gapped by a lattice potential.

Abstract

Nematic Fermi liquid arises when the system of interacting fermions spontaneously breaks the rotational symmetry while the translational symmetry is preserved. We consider a Nematic Fermi liquid of fermions with two distinct quantum numbers. Two quantum numbers represent the spin degrees of freedom or the layer degrees of freedom of the bilayer system. There are two director modes in this system: the in-phase and out-of-phase modes. We find that the out-of-phase (in-phase) mode mediates an attractive (repulsive) interaction between fermions with different quantum numbers. Pairing instability occurs under certain conditions when the in-phase mode is gapped due to a lattice potential. Implications to the stripe phase of Cuprates and the quantum Hall effect of two dimensional electron systems are discussed.