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Chinese Physics B

Collective modes of Weyl fermions with repulsive S-wave interaction*

Xun-Gao Wang, Huan‐Yu Wang, J. M. Zhang, Wu-Ming Liu

Published Sep 28, 2020• 0 citations
Publisher

Abstract

We calculate the spin and density susceptibility of Weyl fermions with repulsive S-wave interaction in ultracold gases. Weyl fermions have a linear dispersion, which is qualitatively different from the parabolic dispersion of conventional materials. We find that there are different collective modes for the different strengths of repulsive interaction by solving the poles equations of the susceptibility in the random-phase approximation. In the long-wavelength limit, the sound velocity and the energy gaps vary with the different strengths of the interaction in the zero sound mode and the gapped modes, respectively. The particle–hole continuum is obtained as well, where the imaginary part of the susceptibility is nonzero.

DOI
10.1088/1674-1056/abbbdb

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We calculate the spin and density susceptibility of Weyl fermions with repulsive S-wave interaction in ultracold gases. Weyl fermions have a linear dispersion, which is qualitatively different from the parabolic dispersion of conventional materials. We find that there are different collective modes for the different strengths of repulsive interaction by solving the poles equations of the susceptibility in the random-phase approximation. In the long-wavelength limit, the sound velocity and the energy gaps vary with the different strengths of the interaction in the zero sound mode and the gapped modes, respectively. The particle–hole continuum is obtained as well, where the imaginary part of the susceptibility is nonzero.
Three-dimensional type-II Weyl fermions possess overtilted cone-like low-energy band dispersion. Unlike the closed ellipsoidal Fermi surface for type-I Weyl fermions, the Fermi surface is an open hyperboloid for type-II Weyl fermions. We evaluate the spin and density susceptibility of type-II Weyl fermions with repulsive S-wave interaction by means of Green’s functions. We obtain the particle–hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively. We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.
We investigate the collective modes in the spin-orbit-coupled Fermi gas with repulsive sss-wave interaction. The interplay between spin-orbit coupling and atom-atom interactions plays the crucial role in the collective behaviors of Fermi gas. In contrast with ordinary Fermi liquid, spin-orbit-coupled Fermi gas has strongly correlated spin and density excitations. Within the scheme of random-phase approximation, we classify collective modes based on the symmetry group and determine their properties via the poles of corresponding correlation functions. Besides, the particle-hole continuum is obtained, where the imaginary part of these correlation functions becomes nonvanishing. We also propose an experimental protocol for detecting these collective modes and discuss corresponding experimental signatures in the ultracold Fermi gases experiment.
We investigate collective excitations in a dipolar and non-dipolar Fermi gas mixture at zero temperature.We obtain the density-density correlation functions of the mixtures in the ring diagram approximation.We analyze the dispersion relation determined by the poles of the density-density correlation functions and find two different types of collective modes: the undamped zero sound and the overdamped modes.We show that the undamped zero sound mode exists only at long wavelengths and the speed of undamped zero sound varies with the propagation direction due to an anisotropy of the dipolar interaction between dipolar fermions.We also show that the decay rate of the overdamped mode decreases as the inter-particle interaction strength between dipolar and non-dipolar fermions increases and the overdamped mode is replaced by unstable one if the inter-particle interaction strength is much strong.
Abstract The longstanding view of the zero sound mode in a Fermi liquid is that for repulsive interaction it resides outside the particle-hole continuum and gives rise to a sharp peak in the corresponding susceptibility, while for attractive interaction it is a resonance inside the particle-hole continuum. We argue that in a two-dimensional Fermi liquid there exist two additional types of zero sound: “hidden” and “mirage” modes. A hidden mode resides outside the particle-hole continuum already for attractive interaction. It does not appear as a sharp peak in the susceptibility, but determines the long-time transient response of a Fermi liquid and can be identified in pump-probe experiments. A mirage mode emerges for strong enough repulsion. Unlike the conventional zero sound, it does not correspond to a true pole, yet it gives rise to a peak in the particle-hole susceptibility. It can be detected by measuring the width of the peak, which for a mirage mode is larger than the single-particle scattering rate.
We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the ${d}_{{r}^{2}\ensuremath{-}3{z}^{2}}$ type in three dimensions and of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tridiagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal ppp-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.
We consider a gas of fermions with parabolic dispersion and N spin components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. The ground-state Bethe ansatz integral equations are solved numerically for both repulsive and attractive interactions to obtain the energy, the chemical potential, and the magnetic susceptibility as a function of the band filling and the interaction strength. For the repulsive interaction the Fermi gas has the properties of a Luttinger liquid. In the attractive case, on the other hand, the fermions in the ground-state form bound states of up to N fermions of different spin components. The spectrum of elemental charge and spin excitations is derived for the repulsive and attractive situations. The spectrum is discussed in the limits of vanishing interaction strength and very strong coupling. For the repulsive interaction the low-lying charge excitations can be characterized by the Fermi momentum and the Fermi velocity. The range of the spin-wave excitations is correlated with the Fermi momentum of the charges. The spin wave velocity is inversely proportional to the magnetic susceptibility. The spin-wave excitations become soft in the infinite-repulsive-coupling limit. In the attractive case in zero field all excitation branches except that of bound states of N fermions have an energy gap. It requires a finite energy to break these bound states and hence there is no response to a field smaller than a critical field. The low-T specific heat is proportional to the temperature.