Kavli Affiliate: Yi Zhou
| First 5 Authors: Jian-Jian Miao, Hui-Ke Jin, Yi Zhou, ,
| Summary:
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 ($omegataugg{}1$)
and the hydrodynamic regime ($omegataull{}1$), 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 $d=3$.
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