Hydrodynamics of Fermi arcs: Bulk flow and surface collective modes

Abstract

The hydrodynamic description of the Fermi arc surface states is proposed. In view of the strong suppression of scattering on impurities, the hydrodynamic regime for Fermi arc states should be, in principle, plausible. By using the kinetic theory, the Fermi arc hydrodynamics is derived and the corresponding effects on the bulk flow and surface collective modes are studied. For the bulk flow, the key effect of the proposed Fermi arc hydrodynamics is the modification of the corresponding boundary conditions. In a slab geometry, it is shown that, depending on the transfer rates between the surface and bulk, the hydrodynamic flow of the electron fluid inside the slab could be significantly altered and even enhanced near the surfaces. As to the spectrum of the surface collective modes, in agreement with earlier studies, it is found that the Fermi arcs allow for an additional gapless spectrum branch and a strong anisotropy of the surface plasmon dispersion relations in momentum space. The gapped modes are characterized by closed elliptic contours of constant frequency in momentum space. I. INTRODUCTIONWeyl semimetals are materials with a relativisticlike energy spectrum in the vicinity of isolated Weyl nodes in the Brillouin zone. (For recent reviews on Weyl semimetals, see Refs. [1][2][3].) The nodes have nonzero topological charges with the monopolelike Berry curvature [4] and always occur in pairs of opposite chirality [5,6]. In each pair, the Weyl nodes can be separated in energy and/or momentum, which indicates breaking of the parity-inversion (PI) and/or time-reversal (TR) symmetries, respectively. The nontrivial topology and the relativisticlike nature of quasiparticles also affect the transport properties of Weyl semimetals, e.g., leading to a negative longitudinal magnetoresistivity that was first predicted in Ref. [7]. (For recent reviews of the transport phenomena, see .)The nontrivial bulk topology of Weyl semimetals is also reflected in unusual surface states known as the Fermi arcs [11]. Unlike surface states in ordinary materials, the Fermi arcs form open segments in momentum space that connect Weyl nodes of opposite chirality [11,12]. The surface states in Weyl semimetals were first observed via the angle-resolved photoemision spectroscopy [2,[13][14][15][16][17][18] and reconfirmed later by the observation of the quasiparticle interference patterns [19][20][21][22]. It is important to note that the energy dispersion of the Fermi arc states is effectively one dimensional and linear (see, e.g., Ref. [23]). This may suggest that their transport properties are similar to that of the one-dimensional chiral fermions and should be nondissipative. However, as we showed in Ref. [24], the Fermi arc transport is, in fact, dissipative because of the scattering between the surface and bulk states in Weyl semimetals. The dissolution of Fermi arcs in the presence of strong disorder was also confirmed numerically in Refs. [25,26].Electronic collective excitations provide additional powerful probes of the nontrivial pro...

Dynamical density and spin response of Fermi arcs and their consequences for Weyl semimetals

“…The reason for this is that only the charge susceptibility appears in the denominators in the RPA expressions, for example in Eq. (50).…”

“…On the other hand, Eq. (50) shows that in equilibrium the physical spin response and consequently the spin susceptibilities are not affected by the electron interaction at the RPA level. This is because the crossed densityspin functions vanish in equilibrium, as discussed above.…”

“…Surface plasmons for Weyl semimetals were previously studied in Refs. [46][47][48][49][50]. Song and Rudner [46] used classical electrodynamics in a simple phenomenological model to obtain surface plasmons based on the boundary conditions.…”

“…Hofmann and Das Sarma [47] have studied surface plasmon polaritons using the similar technique deep in the retarded regime, i.e., for surface plasmon wave numbers q ∼ ω/c. Gorbar et al [50] presented a hydrodynamic description of surface collective modes. They found one gapped and one (linear) gapless branch.…”

“…On the other hand, exploring the coupled density and spin response reveals the existence of novel collective excitations, i.e, spin plasmons, which provide another experimental signature of WSMs [45]. While the surface plasmon excitations of the FA states have been investigated [46][47][48][49][50], an unified study of the density, spin, and current response of the FA states has been lacking but is desirable as it reflects the rich physics of the FA states.…”