Collective effects in an incompressible electronic liquid

TL;DR

This paper investigates conditions under which an electronic liquid becomes incompressible, revealing implications for quantum spin liquids, and classifies collective modes in different regimes and dimensions.

Contribution

It identifies specific Landau parameter conditions leading to incompressibility and explores their effects on collective modes and quantum spin liquid states.

Findings

Incompressibility occurs under specific Landau parameter conditions.

Different collective modes behave distinctly under the two incompressibility conditions.

Proposes possible nematic quantum spin liquid states and a hierarchy of gapless QSL states.

Abstract

Starting from the Landau's kinetic equation, we show that an electronic liquid in $d=2,3$ dimensions depicted by a Landau type effective theory will become incompressible on condition that the Landau parameters satisfy either (i) $1+F_{1}^{s}/d=0$ or (ii) $F_{0}^{s}\to{}+\infty$. The condition (i) is the Pomeranchuk instability in the current channel and suggests a quantum spin liquid (QSL) state with a spinon Fermi surface; while the condition (ii) means that the strong repulsion in the charge channel and leads to a conventional charge and thermal insulator. In the collisionless regime ($\omega\tau\gg{}1$) and the hydrodynamic regime ($\omega\tau\ll{}1$), the zero and first sound modes have been studied and classified by symmetries, including the longitudinal and transverse modes in $d=2,3$ and the higher angular momentum modes in $d=3$. The sufficient (and/or necessary) conditions of these collective modes have been revealed. It has been demonstrated that some of these collective modes will behave in quite different manners under two incompressibility conditions (i) or (ii). Possible nematic QSL states and a hierarchy structure for gapless QSL states have been proposed in $d=3$.