TY - JOUR

T1 - Conditions for l=1 Pomeranchuk instability in a Fermi liquid

AU - Wu, Yi Ming

AU - Klein, Avraham

AU - Chubukov, Andrey V.

N1 - Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/4/2

Y1 - 2018/4/2

N2 - We perform a microscopic analysis of how the constraints imposed by conservation laws affect q=0 Pomeranchuk instabilities in a Fermi liquid. The conventional view is that these instabilities are determined by the static interaction between low-energy quasiparticles near the Fermi surface, in the limit of vanishing momentum transfer q. The condition for a Pomeranchuk instability is set by Flc(s)=-1, where Flc(s) (a Landau parameter) is a properly normalized partial component of the antisymmetrized static interaction F(k,k+q;p,p-q) in a charge (c) or spin (s) subchannel with angular momentum l. However, it is known that conservation laws for total spin and charge prevent Pomeranchuk instabilities for l=1 spin- and charge-current order parameters. Our study aims to understand whether this holds only for these special forms of l=1 order parameters or is a more generic result. To this end we perform a diagrammatic analysis of spin and charge susceptibilities for charge and spin density order parameters, as well as perturbative calculations to second order in the Hubbard U. We argue that for l=1 spin-current and charge-current order parameters, certain vertex functions, which are determined by high-energy fermions, vanish at Fl=1c(s)=-1, preventing a Pomeranchuk instability from taking place. For an order parameter with a generic l=1 form factor, the vertex function is not expressed in terms of Fl=1c(s), and a Pomeranchuk instability may occur when F1c(s)=-1. We argue that for other values of l, a Pomeranchuk instability may occur at Flc(s)=-1 for an order parameter with any form factor.

AB - We perform a microscopic analysis of how the constraints imposed by conservation laws affect q=0 Pomeranchuk instabilities in a Fermi liquid. The conventional view is that these instabilities are determined by the static interaction between low-energy quasiparticles near the Fermi surface, in the limit of vanishing momentum transfer q. The condition for a Pomeranchuk instability is set by Flc(s)=-1, where Flc(s) (a Landau parameter) is a properly normalized partial component of the antisymmetrized static interaction F(k,k+q;p,p-q) in a charge (c) or spin (s) subchannel with angular momentum l. However, it is known that conservation laws for total spin and charge prevent Pomeranchuk instabilities for l=1 spin- and charge-current order parameters. Our study aims to understand whether this holds only for these special forms of l=1 order parameters or is a more generic result. To this end we perform a diagrammatic analysis of spin and charge susceptibilities for charge and spin density order parameters, as well as perturbative calculations to second order in the Hubbard U. We argue that for l=1 spin-current and charge-current order parameters, certain vertex functions, which are determined by high-energy fermions, vanish at Fl=1c(s)=-1, preventing a Pomeranchuk instability from taking place. For an order parameter with a generic l=1 form factor, the vertex function is not expressed in terms of Fl=1c(s), and a Pomeranchuk instability may occur when F1c(s)=-1. We argue that for other values of l, a Pomeranchuk instability may occur at Flc(s)=-1 for an order parameter with any form factor.

UR - http://www.scopus.com/inward/record.url?scp=85045148591&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.97.165101

DO - 10.1103/PhysRevB.97.165101

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AN - SCOPUS:85045148591

SN - 2469-9950

VL - 97

JO - Physical Review B

JF - Physical Review B

IS - 16

M1 - 165101

ER -