Topological Fermi arcs in superfluid3He

Abstract

We consider fermionic states bound on domain walls in a Weyl superfluid 3 He-A and on interfaces between 3 He-A and a fully gapped topological superfluid 3 He-B. We demonstrate that in both cases the fermionic spectrum contains Fermi arcs that are continuous nodal lines of energy spectrum terminating at the projections of two Weyl points to the plane of surface states in momentum space. The number of Fermi arcs is determined by the index theorem that relates bulk values of the topological invariant to the number of zero-energy surface states. The index theorem is consistent with an exact spectrum of Bogolubov-de Gennes equation obtained numerically, meanwhile, the quasiclassical approximation fails to reproduce the correct number of zero modes. Thus we demonstrate that topology describes the properties of the exact spectrum beyond the quasiclassical approximation.

Symmetry protected topological superfluid3He-B

“…The topology of the ABM state that spontaneously breaks time-reversal symmetry is characterized by the mirror Chern number [51,56]. The zero-energy flat band appears in the edge, vortex, and domain wall [143,374,375,376,377,378], which is protected by topologically stable Fermi points in momentum space [379,380]. Furthermore, the integer and half-quantized vortices are accompanied by chiral Majorana fermions protected by the mirror reflection symmetry that yield non-Abelian statistics [192,56].…”

“…A magnetic field in the ca-plane or the d-vector rotation in the high field phase in the B-phase does not obscure the topological protection since the combination of the mirror reflection M ca and the time-reversal is not broken while each of them is not. Here note that while the Majorana valley has a close similarity to the topological Fermi arcs in 3 He-A phase [59,374,293], their topological origins are totally different: The time-reversal breaking is essential for the topological Fermi arcs in 3 He-A phase, but the timereversal breaking is not necessary for the Majorana valley.…”

Structure and consequences of vortex-core states inp-wave superfluids

“…If δ > 2 F , then the density of bosons is exponentially small 12 in the parameter exp − δ−2 F F S , where S is defined below in Eq. (30). Since the density of bosons…”

“…This analysis yields the magnitudes of the coupling constant g of the two-channel model (11), as well as the dimensionless constant c 2 which sets the maximum density of bosons, and thus the coherence length ξ = c 2 /(1 + c 2 ) in our dimensionless units. The scaling of the axes relative to the dimensionless units used in the bulk of this paper is set by the factor S [see (30)], , the subgap spectrum can be given as a function of the detuning δ, resulting in Fig. 9.…”

“…We then focus particularly on the nature of the first excited subgap state, as opposed to a number of previous studies that focused on the zero modes. 26,[28][29][30][31][32] Based on a numerical study of the BdG equations, we identify the regime with the best prospects for realizing TQC in p-wave superfluid cold atomic gases, i.e., the regime maximising the energy of the first subgap state 1 as a function of the detuning.…”