Fate of Fermi-arc States in Gapped Weyl Semimetals under Long-ranged Interactions

Abstract

For noninteracting Weyl semimetals (WSMs), Fermi-arc surface states can arise when there exist gapless Weyl nodes in the bulk single-particle spectrum. However, in the presence of electronic correlations, it is not clear whether this bulk-boundary correspondence still holds or not. Recently, novel correlated phases are predicted to appear in WSMs with long-ranged interactions, in which the bulk Weyl nodes can be gapped but without destroying their topological properties. Here, we explore the fate of the Fermi-arc states under the influence of such long-ranged interactions. After mapping the system onto a one-dimensional interacting Su-Schrieffer-Heeger (SSH) model with two open ends, we employ numerical exact diagonalizations to address the issue whether the Fermi-arc states will be modified. By extrapolating our data to the thermodynamic limit, we find that the zero-energy edge states of the corresponding SSH model still exist for those momenta giving the noninteracting Fermi-arc states. Moreover, this observation applies to both the single-particle and the collective edge excitations. Since the locus of these edge states constitutes the Fermi arcs, the robustness of the Fermi-arc states against long-ranged interactions is thus demonstrated. In particular, the Fermi arcs of single-particle nature can survive even when the single-particle gaps at the Weyl nodes are opened by interactions. Our results illustrate the subtlety in identifying the topological phases of interacting WSMs and show the limitation of the approaches simply by examining the nodal structure of the single-particle spectrum.