Holographic fermions in striped phases

Abstract

We examine the fermionic response in a holographic model of a low temperature striped phase, working for concreteness with the setup we studied in [1,2], in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. We include an ionic lattice that breaks translational symmetry explicitly in the UV of the theory. Thus, this construction realizes spontaneous crystallization on top of a background lattice. We solve the Dirac equation for a probe fermion in the associated background geometry using numerical techniques, and explore the interplay between spontaneous and explicit breaking of translations. We note that in our model the breaking of the U(1) symmetry doesn't play a role in the analysis of the fermionic spectral function. We investigate under which conditions a Fermi surface can form and focus in particular on how the ionic lattice affects its structure. When the ionic lattice becomes sufficiently strong the spectral weight peaks broaden, denoting a gradual disappearance of the Fermi surface along the symmetry breaking direction. This phenomenon occurs even in the absence of spontaneously generated stripes. The resulting Fermi surface appears to consist of detached segments reminiscent of Fermi arcs.

Isolated zeros destroy Fermi surface in holographic models with a lattice

“…This is the question we address in the present work. Most of the earlier works in holography on single fermion spectral functions are restricted to isotropic setups, with the rare exceptions including [9][10][11][12][13][14]. In order to study anisotropy and the effects of the Brillouin zone boundary, we introduce a periodic modulation of the chemical potential, which mimics the ionic lattice, breaks the rotational symmetry down to a discrete group and introduces Bloch momenta.…”

Anisotropic destruction of the Fermi surface in inhomogeneous holographic lattices

“…Therefore it provides a way to disentangle the effects of the Umklapp scattering due to periodicity of the potential, which would disappear when the model is driven to the homogeneous state, and the effects caused by anisotropic breaking of translations, which will remain unaffected. As we will show, the phenomenon observed in the periodic lattices of [18,19] has precisely the same nature as the one seen in the Q-lattice of [23] thus providing a deeper understanding of which aspects of holographic models are relevant for phenomenology of strongly correlated condensed matter systems.…”

“…This effect is well-known in the context of conventional condensed matter theory as electronic topological transition, or Lifshitz transition [40,41], and holographic calculations reproduce it well, as it has been shown already in [16][17][18]35]. Since in our model the potential is sourced by a neutral scalar, and the coupling between the bulk fermion and the lattice occurs indirectly via modulations of the metric, the amplitude of the secondary surfaces, as well as the size of the band gap are considerably smaller than in the case of charged scalar [18]. Nonetheless, the fact that the gap is present in our setting provides a nontrivial test of validity of our treatment.…”

“…The aim of the current study is to clarify the relation between the anisotropic Fermi surface destruction observed in the periodic lattice model of [18,19] and the similar effect found earlier in homogeneous lattices [23,24]. We use the specific model where the periodic potential is introduced via modulation of the extra scalar operator [12].…”

“…The structure of the Brillouin zone (BZ) created by the periodic potential was reproduced, and gaps opened due to Umklapp scattering on the BZ boundary. Recently, a more subtle result has been reported in [18,19], where it was claimed that in the periodic lattices generated by intertwined order parameters the Fermi surface gets anisotropically destroyed.…”