Chiral Spin Waves in Fermi Liquids with Spin-Orbit Coupling

Abstract

We predict the existence of chiral spin waves-collective modes in a two-dimensional Fermi liquid with the Rashba or Dresselhaus spin-orbit coupling. Starting from the phenomenological Landau theory, we show that the long-wavelength dynamics of magnetization is governed by the KleinGordon equations. The standing-wave solutions of these equations describe "particles" with effective masses, whose magnitudes and signs depend on the strength of the electron-electron interaction. The spectrum of the spin-chiral modes for arbitrary wavelengths is determined from the Dyson equation for the interaction vertex. We propose to observe spin-chiral modes via microwave absorption of standing waves confined by an in-plane profile of the spin-orbit splitting.Introduction.-The rapidly developing field of spintronics aims to manipulate electron spins by electric rather than magnetic fields. Since spin-orbit (SO) interaction allows for such a coupling, electron systems with SO interaction have been under intense study. A particularly interesting issue is the role of the electronelectron interaction in such systems [1,2]. SO-coupled Fermi liquids (FLs) are expected to exhibit a rich variety of effects, which arise only from a combination of the electron-electron and SO interactions, such as spinsplit and Rashba phases [3,4], unusual Friedel oscillations [5,6], and spin textures [7], to name just a few. The focus of this Letter is on the collective excitations in a SO-coupled FL.

Chiral Spin Mode on the Surface of a Topological Insulator

“…By comparing the data with calculations, we identify this excitation as the transverse collective chiral spin mode supported by spin-polarized surface Dirac fermions. Such collective modes -first predicted for nontopological systems [21][22][23][24][25][26]36] but hitherto unobserved -are "peeled off" from the continuum of particle-hole excitations by the exchange interaction.Chiral surface states in a 3D TI are described by the Hamiltonian [40]:where m * is the effective mass,σ = (σ 1 ,σ 2 ,σ 3 ) are the Pauli matrices,σ 0 is the 2×2 unit matrix, andThe z component ofk describes hexagonal warping of the surface states away from the Dirac point [40]. The spectrum of Eq.…”

“…By comparing the data with calculations, we identify this excitation as the transverse collective chiral spin mode supported by spin-polarized surface Dirac fermions. Such collective modes -first predicted for nontopological systems [21][22][23][24][25][26]36] but hitherto unobserved -are "peeled off" from the continuum of particle-hole excitations by the exchange interaction.…”

“…However, the many-body interactions leading to collective effects in TIs remain largely unexplored. An essential aspect of this physics is an interplay between the Coulomb interaction and SOC, which is expected to give rise to a new type of collective spin excitations -chiral spin waves [21][22][23][24][25][26]. In the long wavelength (q = 0) limit, these modes are completely decoupled from the charge channel and thus distinct from spin-plasmons [27,28], Dirac plasmons [29,30], and surface plasmons in TIs [30,31].…”

Intrinsic Damping of Collective Spin Modes in a Two-Dimensional Fermi Liquid with Spin-Orbit Coupling

“…3,4 Combining many-body interactions with broken SU(2) symmetry, one obtains a special-"chiral"-kind of Fermi liquid (FL) [5][6][7] that supports a new type of collective modes, "chiral-spin waves"-oscillations of the spin density in zero magnetic field. [8][9][10][11] In the absence of SOC, electron-electron interaction (eei) 12 does not affect certain properties of an electron system given that some symmetries are preserved. For example, the conductivity and cyclotron-resonance frequency of a Galilean-invariant system are not affected by eei; same is true for the de Haas-van Alphen (dHvA) frequency in an isotropic system 13 and for the Larmor frequency in the presence of an SU(2)-symmetric interaction.…”

Controlling hole spins in quantum dots and wells

“…In contrast, a quantitative understanding of the more correlated lowdensity regime including spin-orbit coupling is not yet possible. Various aspects of this problem have been examined in the theoretical literature, including quasiparticle properties (effective mass and lifetime) [29,30,31,32,33,34,28], screening and plasmon excitations [35,36,37,34], and more exotic collective excitations, including chiral spin waves [38]. Other works have considered ground-state properties including the repopulation of the spin bands [39], the Hartree-Fock theory of broken-symmetry spinpolarized states [40,41,42], and low-density inhomogeneous phases [43].…”