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.
Highlights
We present full expressions for the surface part of polarization tensor of a Dirac fermion confined in a half-space in 3 þ 1 dimensions
Introduction.—Modern interest to the physics of Dirac fermions occupying a bounded region in space is mostly related to new advanced materials, such as topological insulators (TIs)—see reviews [1,2] and a monograph [3]
A lot of exciting physics of TIs is due to the presence of surface modes, that are Dirac fermions though in one dimension less
Summary
Introduction.—Modern interest to the physics of Dirac fermions occupying a bounded region in space is mostly related to new advanced materials, such as topological insulators (TIs)—see reviews [1,2] and a monograph [3]. How Many Surface Modes Does One See on the Boundary of a Dirac Material? We present full expressions for the surface part of polarization tensor of a Dirac fermion confined in a half-space in 3 þ 1 dimensions. We compare this tensor to the polarization tensor of eventual surface mode (which is a 2 þ 1 dimensional Dirac fermion) and find essential differences in the conductivities in both Hall and normal sectors.
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