Collective modes near a Pomeranchuk instability

Abstract

We consider collective excitations of a Fermi liquid. For each value of the angular momentum $l$, we study the evolution of longitudinal and transverse collective modes in the charge (c) and spin (s) channels with the Landau parameter $F_l^{c(s)}$, starting from positive $F_l^{c(s)}$ and all the way to the Pomeranchuk transition at $F_l^{c(s)}=-1$. In each case, we identify a critical zero-sound mode, whose velocity vanishes at the Pomeranchuk instability. For $F_l^{c(s)}<-1$, this mode is located in the upper frequency half-plane, which signals an instability of the ground state. In a clean Fermi liquid the critical mode may be either purely relaxational or almost propagating, depending on the parity of $l$ and on whether the response function is longitudinal or transverse. These differences lead to qualitatively different types of time evolution of the order parameter following an initial perturbation. A special situation occurs for the $l=1$ order parameter that coincides with the spin or charge current. In this case the residue of the critical mode vanishes at the Pomeranchuk transition. However, the critical mode can be identified at any distance from the transition, and is still located in the upper frequency half-plane for $F_1^{c(s)}<-1$. The only peculiarity of the charge/spin current order parameter is that its time evolution occurs on longer scales than for other order parameters. We also analyze collective modes away from the critical point, and find that the modes evolve with $F_l^{c(s)}$ on a multi-sheet Riemann surface. For certain intervals of $F_l^{c(s)}$, the modes either move to an unphysical Riemann sheet or stay on the physical sheet but away from the real frequency axis. In that case, the modes do not give rise to peaks in the imaginary parts of the corresponding susceptiblities.

References in corpus (33)

• Renormalization Group Approach to Interacting Fermions
• Nematic order in iron superconductors - who is in the driver's seat?
• Evidence for an electron nematic phase transition in underdoped iron pnictide superconductors
• Functional renormalization group approach to correlated fermion systems
• Nematic Fermi Fluids in Condensed Matter Physics
• Divergent nematic susceptibility in an iron arsenide superconductor
• Quantum Theory of a Nematic Fermi Fluid
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Interaction corrections at intermediate temperatures: I. Longitudinal conductivity and kinetic equation
• Preemptive nematic order, pseudogap, and orbital order in the iron pnictides
• Nematicity and quantum paramagnetism in FeSe
• Fermi liquid instabilities in the spin channel
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions
• Transport near the Ising-nematic quantum critical point of metals in two dimensions
• The origin of nematic order in FeSe
• Dynamic generation of spin orbit coupling
• Charge Nematicity and Electronic Raman Scattering in Iron-based Superconductors
• Fermi liquid near Pomeranchuk quantum criticality
• Electronic sound modes and plasmons in hydrodynamic two-dimensional metals
• Spin conservation and Fermi liquid near a ferromagnetic quantum critical point
• Superconductivity near a nematic quantum critical point -- the interplay between hot and lukewarm regions
• Shear sound of two-dimensional Fermi liquids
• Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
• Limits on dynamically generated spin-orbit coupling: Absence of $l=1$ Pomeranchuk instabilities in metals
• Acoustic plasmons at the crossover between the collisionless and hydrodynamic regimes in two-dimensional electron liquids
• The Conditions for $l=1$ Pomeranchuk Instability in a Fermi Liquid
• Fermi-liquid theory and Pomeranchuk instabilities: fundamentals and new developments
• Dynamical susceptibility of a Fermi liquid
• Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors
• Universal and non-universal renormalizations in Fermi liquids
• A unified description of static and dynamic properties of Fermi liquids

Cited by in corpus (14)

• Hydrodynamic approach to two-dimensional electron systems
• Hydrodynamic collective modes in graphene
• Collective modes in interacting two-dimensional tomographic Fermi liquids
• Exceptional points in Fermi liquids with quadrupolar interactions
• A theory of criticality for quantum ferroelectric metals
• Spin-valley collective modes of the electron liquid in graphene
• Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities
• Shear Bernstein modes in a two-dimensional electron liquid
• Probing three-state Potts nematic fluctuations by ultrasound attenuation
• Acoustic plasmons and isotropic short-range interaction in two-component electron liquids
• Laser induced $\mathcal{P}\mathcal{T}$-symmetry breaking in the fluctuations of electronic fluids
• Atypical Behavior of Collective Modes in Two-Dimensional Fermi Liquids
• Intertwined geometries in collective modes of two dimensional Dirac fermions
• Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal