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arXiv:cond-mat/0504661 · Physical Review B

Fermi liquid parameters in two dimensions with spin-orbit interaction

Daniel S. Saraga, Daniel Loss

Published Nov 11, 2005• 42 citations
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Abstract

We derive analytical expressions for the quasiparticle lifetime $\ensuremath{\tau}$, the effective mass ${m}^{*}$, and the Green's function renormalization factor $Z$ for a two-dimensional Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. We find that the modifications are independent of the Rashba band index $\ensuremath{\rho}$, and occur in second order of the spin-orbit coupling $\ensuremath{\alpha}$. In the derivation of these results, we also discuss the screening of the Coulomb interaction, as well as the susceptibility and the self-energy in small $\ensuremath{\alpha}$.

DOI
10.1103/physrevb.72.195319

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We derive analytical expressions for the quasiparticle lifetime \ensuremathτ\ensuremath{\tau}\ensuremathτ, the effective mass m∗{m}^{*}m∗, and the Green's function renormalization factor ZZZ for a two-dimensional Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. We find that the modifications are independent of the Rashba band index \ensuremathρ\ensuremath{\rho}\ensuremathρ, and occur in second order of the spin-orbit coupling \ensuremathα\ensuremath{\alpha}\ensuremathα. In the derivation of these results, we also discuss the screening of the Coulomb interaction, as well as the susceptibility and the self-energy in small \ensuremathα\ensuremath{\alpha}\ensuremathα.
We investigate normal-state properties of spin-orbit-coupled Fermi gases with repulsive sss-wave interaction, in the absence of molecule formation, i.e., in the so-called ``upper branch.'' Within the framework of random-phase approximation, we derive analytical expressions for the quasiparticle lifetime ${\ensuremath{\tau}}_{s}$, the effective mass ms∗{m}_{s}^{*}ms∗​, and the Green's function renormalization factor Zs{Z}_{s}Zs​ in the presence of Rashba spin-orbit coupling. In contrast to spin-orbit-coupled electron gas with Coulomb interaction, we show that the modifications are dependent on the Rashba band index sss and occur in the first order of the spin-orbit-coupling strength. We also calculate experimental observables such as spectral weight, density of state, and specific heat, which exhibit significant differences from their counterparts without spin-orbit coupling. We expect our microscopic calculations of these Fermi-liquid parameters would have immediate applications to the spin-orbit-coupled Fermi gases in the upper branch of the energy spectrum.
A long-range interaction via virtual particle-hole pairs between Fermi-liquid quasiparticles leads to a nonanalytic behavior of the spin susceptibility $\ensuremath{\chi}$ as a function of the temperature (T)(T)(T), magnetic field (B)(\mathbf{B})(B), and wave number. In this paper, we study the effect of the Rashba spin-orbit interaction (SOI) on the nonanalytic behavior of $\ensuremath{\chi}$ for a two-dimensional electron liquid. Although the SOI breaks the SU(2) symmetry, it does not eliminate nonanalyticity but rather makes it anisotropic: while the linear scaling of ${\ensuremath{\chi}}_{zz}$ with TTT and ∣B∣|\mathbf{B}|∣B∣ saturates at the energy scale set by the SOI, that of ${\ensuremath{\chi}}_{xx}$ $(={\ensuremath{\chi}}_{yy})$ continues through this energy scale until renormalization of the electron-electron interaction in the Cooper channel becomes important. We show that the renormalization group flow in the Cooper channel has a nontrivial fixed point and study the consequences of this fixed point for the nonanalytic behavior of $\ensuremath{\chi}$. An immediate consequence of SOI-induced anisotropy in the nonanalytic behavior of $\ensuremath{\chi}$ is a possible instability of a second-order ferromagnetic quantum phase transition with respect to a first-order transition to an XYXYXY ferromagnetic state.
The main topic of the present thesis is represented by the many-body effects which characterize the physical behavior of an electron liquid in various realizations. We begin by studying the problem of the response of an otherwise homogeneous electron liquid to the potential of an impurity embedded in its bulk. The most dramatic consequence of this perturbation is the existence of so called Friedel density oscillations. We present calculations of their amplitude valid in two as well as in three dimensions. The second problem we will discuss is that of the correlation effects in a three dimensional electron liquid in the metallic density regime. A number of quasiparticle properties are evaluated: the electron self-energy, the quasiparticle effective mass and the renormalization constant. We also present an analysis of the effective Landé g-factor as well as the compressibility. The effects of the Coulomb interactions beyond the random phase approximation have been treated by means of an approach based on the many-body local field factors theory and by utilizing the latest numerical results of Quantum Monte Carlo numerical simulations. The final chapter includes the results of our extensive work on various aspects regarding the two dimensional Fermi liquid in the presence of linear Rashba spin-orbit coupling. By using a number of many-body techniques, we have studied the interplay between spin-orbit coupling and electron-electron interaction. After proving an extension to the famous Overhauser Hartree-Fock instability theorem, a considerable amount of work will be presented on the problem of the density and spin response functions. For the study of the spin response, we will present the results of extensive numerical calculations based on the time dependent mean field theory approach.
We discuss by analytic means the theory of the high-density limit of the unpolarized two-dimensional electron liquid in the presence of Rashba or Dresselhaus spin-orbit coupling. A generalization of the ring-diagram expansion is performed. We find that in this regime the spin-orbit coupling leads to small changes of the exchange and correlation energy contributions, while modifying also, via repopulation of the momentum states, the noninteracting energy. As a result, the leading corrections to the chirality and total energy of the system stem from the Hartree-Fock contributions. The final results are found to be vanishing to lowest order in the spin-orbit coupling, in agreement with a general property valid to every order in the electron-electron interaction. We also show that recent quantum Monte Carlo data in the presence of Rashba spin-orbit coupling are well understood by neglecting corrections to the exchange-correlation energy, even at low density values.
We present a quantitative study of the quasiparticle properties of a three-dimensional electron Fermi liquid. Our approach is based on the theory of the many-body local field factors which we use to include vertex corrections associated with charge and spin fluctuations. Extensive use is made of the results of recent quantum Monte Carlo calculations. Several models for the wave-vector dependence of the spin-antisymmetric many-body local field factor ${G}_{\ensuremath{-}}$, for which no numerical results are currently available, are discussed and compared. Both the real and imaginary parts of the self-energy as well as the quasiparticle renormalization constant and the enhancement of the effective mass are calculated in the experimentally accessible range of electron densities. The results obtained by means of the on-shell approximation are critically compared with those given by a self-consistent solution of the Dyson equation. An ultraviolet catastrophe in the Coulomb-hole part of the self-energy is identified and a satisfactory resolution of this impasse is presented. The same many-body local field factors are also used to obtain the Landau interaction function. This allows us to obtain both the spin susceptibility and the proper compressibility of the system.
We calculate the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependences of the spin components of the scattering vertex, the Landau function, and the spin susceptibility are found to be linear. T-linear terms in the effective mass and in the "charge-sector" quantities are found to cancel to second order in the interaction, but the cancellation is argued not to be generic. The connection with previous studies of the 2D Fermi-liquid parameters is discussed.