Abstract
We discuss the stability of the topological invariant of the strongly interacting Weyl semi-metal at finite temperature. We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable even in the case the Fermi surface become fuzzy. We give an argument to show that although the self energy changes the spectral function significantly to make the Fermi surface fuzzy, it cannot change the singularity structure of the Berry phase, which leads to the stability of the topology. We also find that depending on the mass term structure of the fermion Lagrangian, topological dipoles can be created.
Highlights
With topological dipoles, where Weyl points are separated by only a small distance in momentum space
We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable even in the case the Fermi surface become fuzzy
We give an argument to show that the self energy changes the spectral function significantly to make the Fermi surface fuzzy, it cannot change the singularity structure of the Berry phase, which leads to the stability of the topology
Summary
We briefly review a quantum field theoretical (QFT) model for Weyl semi-metal (WSM). WSM has the separate band crossing points in momentum space which can be achieved by breaking time-reversal symmetry of Dirac semi-metal. Expanding Ψ in momentum basis e−i(ωt−k·x)ψ, the equation of motion is given by i&K& − M − iBνγ5γν ψ = 0. The dispersion relations has four branches given by. For |Bz| > M , the band crossing happens at (kx, ky, kz) = (0, 0, ± Bz2 − M 2) and the spectrum is gapless. For |Bz| < M , a gap opens and its size is given by 2∆ = 2(M −Bz).
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