How many surface modes does one see on the boundary of a Dirac material?

Abstract

We present full expressions for the surface part of polarization tensor of a Dirac fermion confined in a half-space in $3+1$ dimensions. We compare this tensor to the polarization tensor of eventual surface mode (which is a $2+1$ dimensional Dirac fermion) and find essential differences in the conductivities in both Hall and normal sectors. Thus, the interaction with electromagnetic field near the boundary differs significantly in the full model and in the effective theory for the surface mode.

5 pages, 4 figures; slightly improved version, published in Physical Review Letters

References in corpus (7)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Casimir force between Weyl semimetals in a chiral medium
• Signatures of Complex Optical Response in Casimir Interactions of Type I and II Weyl Semimetals
• Coexistence of Fermi arcs with two dimensional gapless Dirac states
• Quantum Dirac fermions in half space and their interaction with electromagnetic field
• Fractional Fermion Number and Hall Conductivity of Domain Walls
• First observation of spin-helical Dirac fermions and topological phases in undoped and doped Bi2Te3 demonstrated by spin-ARPES spectroscopy

Cited by in corpus (10)

• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• The Casimir energy in terms of boundary quantum field theory: the QED case
• Bulk contributions to the Casimir interaction of Dirac materials
• Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals
• Geometric Approach to 3D Interfaces at Strong Coupling
• Holographic Anomalous Chiral Current Near a Boundary
• Anomaly inflow for local boundary conditions
• Holographic Anomalous Current at a Finite Temperature
• Enhancement of Anomalous Boundary Current by High Temperature
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings