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arXiv:2112.05076 · Physical review. B./Physical review. B

Collinear scattering and long-lived excitations in two-dimensional electron fluids

Serhii Kryhin, Leonid S Levitov

Published May 16, 2023• 16 citations
arXivHTMLPDF

Abstract

For a long time, it has been thought that two-dimensional (2D) Fermi gases could support long-lived excitations, owing to the collinear quasiparticle scattering controlled by phase-space constraints at a 2D Fermi surface. We present a direct calculation that reveals such excitations. The excitation lifetimes are found to exceed the fundamental bound set by the Landau Fermi-liquid theory by a factor as large as ${({T}_{F}/T)}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}2$. These excitations represent Fermi-surface modulations of an odd parity, one per each odd angular momentum. To explain this surprising behavior, we employ a connection between the linearized quantum kinetic equation and the dynamics of a fictitious quantum particle moving in a 1D reflectionless ${\mathrm{sech}}^{2}$ potential. In this framework, we identify the long-lived excitations in Fermi gases as zero modes that arise from supersymmetry.

DOI
10.1103/physrevb.107.l201404

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For a long time, it has been thought that two-dimensional (2D) Fermi gases could support long-lived excitations, owing to the collinear quasiparticle scattering controlled by phase-space constraints at a 2D Fermi surface. We present a direct calculation that reveals such excitations. The excitation lifetimes are found to exceed the fundamental bound set by the Landau Fermi-liquid theory by a factor as large as (TF/T)\ensuremathα{({T}_{F}/T)}^{\ensuremath{\alpha}}(TF​/T)\ensuremathα with \ensuremathα\ensuremath≈2\ensuremath{\alpha}\ensuremath{\approx}2\ensuremathα\ensuremath≈2. These excitations represent Fermi-surface modulations of an odd parity, one per each odd angular momentum. To explain this surprising behavior, we employ a connection between the linearized quantum kinetic equation and the dynamics of a fictitious quantum particle moving in a 1D reflectionless sech2{\mathrm{sech}}^{2}sech2 potential. In this framework, we identify the long-lived excitations in Fermi gases as zero modes that arise from supersymmetry.
Two-dimensional electron systems offer an appealing platform to explore long-lived excitations arising due to collinear carrier scattering enabled by phase-space constraints at the Fermi surface. Recently it was found that these effects can boost excitation lifetimes over the fundamental bound set by Landau’s Fermi-liquid theory by a factor as large as (TF/T)α with α≈2. Long-lived degrees of freedom possess the capability to amplify the response to weak perturbations, producing lasting collective memory effects. This leads to non-Newtonian hydrodynamics in 2D electron fluids driven by multiple viscous modes with scale-dependent viscosity. We describe these modes as Fermi surface modulations of odd parity evolving in space and time, and discuss their implications for experimental studies of electron hydrodynamics.
We demonstrate that 2D Fermi liquids can support peculiar excitations that are not subject to Landau's T2T^2T2 dissipation. The long-lived excitations relax through correlated angular dynamics involving "lock-step" angular displacements along the Fermi surface occurring in collinear two-particle collisions, a surprising behavior that is unique to 2D systems. We develop a microscopic picture of the non-Brownian random walk, describing the angular dynamics as anomalous diffusion ("superdiffusion") on the Fermi surface. Strongly-correlated dynamics with directional memory, mediated by novel undamped excitations, dominates at moderately long times, pushing the onset of conventional hydrodynamics to abnormally large timescales. This exotic behavior can be directly probed by momentum-resolved tunneling techniques.
Pauli blocking in Fermi liquids imposes strong phase-space constraints on quasiparticle lifetimes, leading to a well-known quadratic-in-temperature decay rate of quasiparticle modes at low temperatures. In two-dimensional systems, however, even longer-lived modes are predicted (dubbed “odd-parity” modes) that involve a collective deformation of the Fermi distribution. Here, we present an efficient method to evaluate the full spectrum of relaxational eigenmodes of a Fermi liquid within kinetic theory. We employ this method to study the experimentally relevant case of a Fermi liquid with screened Coulomb interactions and map out the decay rates of quasiparticle modes beyond the asymptotic low-temperature limit up to the Fermi temperature, thus covering the entire temperature range of typical experiments. We confirm the existence of anomalously long-lived odd-parity modes and provide a comprehensive classification and detailed analysis of the relaxation spectrum. In particular, we find that (i) the odd-parity effect in the decay rates extends to temperatures as large as T = 0.15 T F , (ii) there is only a small number of long-lived odd-parity modes, with an infinite number of remaining modes that show standard Fermi-liquid scaling, and (iii) the ratio between the odd- and even-parity lifetimes is tunable with the Coulomb interaction strength, in addition to temperature, which reflects a difference in the microscopic relaxation mechanism of the modes. Our findings provide a comprehensive description of the nonequilibrium relaxation behavior of two-dimensional electron gases and bridge a significant gap in our understanding of these systems.
Abstract Two-dimensional electron gases are predicted to possess an anomalous “tomographic” transport regime that is marked by an odd-even effect in the relaxation times, with odd-parity deformations of the Fermi surface becoming long-lived in comparison to even-parity ones. In this work, we establish that neutral two-component atomic Fermi gases also exhibit this tomographic effect. By diagonalizing the Fermi liquid collision integral, we identify odd-parity modes with anomalously long lifetimes below temperatures T≤0.15T F , which is within reach of cold atom experiments. Furthermore, in contrast to electron gases, we find that the odd-even effect in neutral gases is widely tuneable with interactions along the BCS-BEC crossover and is suppressed on the BEC side. We propose as an experimental signature of the odd-even effect the damping rate of quadrupole oscillations, which is anomalously enhanced due to the presence of long-lived odd-parity modes. Our findings suggest that the dynamics of two-dimensional Fermi gases is richer than previously thought and should include additional long-lived modes.
A precise characterization of the recently discovered crossover to hydrodynamic transport in electron liquids, and in particular of a conjectured exotic odd-parity transport regime, requires a full solution of the Fermi-liquid collision integral at all temperatures beyond state-of-the-art analytic leading-logarithmic approximations. We develop a general basis expansion of the linearized collision integral applicable at all temperatures, and employ this to determine the decay rates of Fermi surface perturbations in two-dimensional electron liquids. In particular, we provide exhaustive data on the decay rates for a new odd-parity regime, in which parity-even Fermi surface deformations decay rapidly but odd-parity modes are anomalously longlived. We find that this transport regime exists at fairly large temperatures $T\ensuremath{\lesssim}0.1\phantom{\rule{0.16em}{0ex}}{T}_{F}$, putting this regime within the reach of current experiments.
We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated ``tomographic'' transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless. We derive expressions for both the longitudinal and the transverse conductivity and discuss the collective mode spectrum along the collisionless-tomographic-hydrodynamic crossover. Longitudinal modes cross over from zero sound in the collisionless regime to hydrodynamic first sound in the tomographic and hydrodynamic regime, where odd-parity damping appears as a subleading correction to the lifetime. In charged Fermi liquids with long-range Coulomb coupling, these modes reduce to plasmons with a strongly suppressed odd-parity correction to the damping. The transverse response, by contrast, has a specific tomographic transport regime with two imaginary odd-parity modes, one of which requires a finite repulsive interaction, distinct from both the shear sound in the collisionless regime and an overdamped diffusive current mode in the hydrodynamic limit. Our work demonstrates that there are deep many-body aspects of interacting Fermi liquids, which are often thought to be well understood theoretically, remaining unexplored.