Abstract
We investigate holographic fermions in uni-directional striped phases, where the breaking of translational invariance can be generated either spontaneously or explicitly. We solve the Dirac equation for a probe fermion in the associated background geometry. When the spatial modulation effect becomes sufficiently strong, we see a spectral weight suppression whenever the Fermi surface is larger than the first Brillouin zone. This leads to the gradual disappearance of the Fermi surface along the symmetry breaking direction, in all of the cases we have examined. This effect appears to be a generic consequence of strong inhomogeneities, independently of whether translational invariance is broken spontaneously or explicitly. The resulting Fermi surface is segmented and has features reminiscent of Fermi arcs.
Highlights
One being the homogeneous holographic lattices of [8,9,10], which simulate the effects of translational symmetry breaking while retaining the homogeneity of the spacetime geometry
We investigate holographic fermions in uni-directional striped phases, where the breaking of translational invariance can be generated either spontaneously or explicitly
Our expectation was that the spectral weight suppression is a general property in holography and that it should not be very sensitive to the specific type of spatial modulation present in the system
Summary
We will work within the Einstein-Maxwell-scalar framework, and consider models that can be captured by examining various cases of. We can obtain the retarded Green’s function for the fermionic operator of the strongly coupled field theory by solving the bulk Dirac equation with infalling boundary conditions at the horizon. To provide a representation of the band structure in the extended zone scheme we work with the following “unfolded” expression for the spectral function, A(ω, kx = k0 + nK, ky) = Tr Im[GRα,n;α ,n(ω, k0, ky)] ,. The integer n denotes once again the momentum level or Brillouin zone number Since this spectral function representation doesn’t implement any folding procedure, it will allow for a more direct comparison of our results with the ARPES measurements, which are a direct probe of the electronic band structure in the extended Brillouin zone scheme. As we will show in this paper, our main result, i.e. the spectral weight suppression in the presence of strong lattice inhomogeneity, is independent of which representation we adopt
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