Topological invariants for holographic semimetals

Abstract

We study the behavior of fermion spectral functions for the holographic topological Weyl and nodal line semimetals. We calculate the topological invariants from the Green functions of both holographic semimetals using the topological Hamiltonian method, which calculates topological invariants of strongly interacting systems from an effective Hamiltonian system with the same topological structure. Nontrivial topological invariants for both systems have been obtained and the presence of nontrivial topological invariants further supports the topological nature of the holographic semimetals. 1

Weyl semimetal/insulator transition from holography

“…In particular, holographic models for strongly interacting Weyl semimetals have been constructed in [9,10] in which the anomalous Hall conductivity is an order parameter to characterize the quantum topological phase transition. The effects of the surface state [11] and topological invariants [12] in this holographic model exhibit key features of topological Weyl semimetals. Therefore with strong interaction topological Weyl semimetal still exits and holography is a practical tool to explore its property.…”

Chiral vortical conductivity across a topological phase transition from holography

“…It was shown in [24,25] that in the holographic Weyl semimetal model there is a quantum phase transition between the topologically nontrivial phase and a trivial phase by tuning the ratio between the mass parameter and the time reversal symmetry breaking parameter. Other aspects of the holographic Weyl semimetal have been explored in [26][27][28][29][30][31][32][33]. A recent review on the holographic Weyl semimetals can be found in [34].…”

Holographic topological semimetals

“…Eigenvalues of −G −1 (0, k x ) for M/b 0.0013. Red colour is for bands I and blue colour is for bands II.Figure from[48].…”