The holographic Fermions over the ionic lattice with CDW

TL;DR

This work investigates how an ionic lattice combined with a spontaneously formed charge density wave (CDW) shapes holographic fermion spectra and Fermi-surface geometry. Using a four-dimensional gravity model with two gauge fields and a dilaton, the authors compute the fermionic spectral function in a lattice+CDW background by solving the bulk Dirac equation in the probe limit and extracting the retarded Green function. They find that CDW enhances spectral weight and expands the Fermi momentum, but partially screens the lattice potential, leading to smaller Brillouin-zone band gaps; band gaps appear at zone boundaries when the Fermi surface crosses them, with gap size controlled by the lattice amplitude and doping. Commensurability and CDW type crucially modulate Fermi-surface reconstruction, with stronger lock-in effects at certain ratios and a doping-driven crossover from CDW-dominated to itinerant behavior, offering holographic insights into intertwined orders and their ARPES signatures in strongly correlated materials.

Abstract

We study the holographic Fermion as a probe over the background with ionic lattice, which may undergo a phase transition with the development of charge density wave by the spontaneous breaking of the translational symmetry. We focus on the structure of the Fermi surface within different Brillouin zones and demonstrate how the presence of CDW in the background affects the formation of the band gap in the momentum space. Specifically, we find the formation of the CDW enhances the amplitude of spectral function as well as the momentum of the Fermi surface. Furthermore, we are concerned with the change of the Fermi surface with the doping parameter as well as the lattice amplitude. Interestingly, we find that the radius of the Fermi surface expands with the increase of the doping parameter and finally may cross the first Brillouin zone. Additionally, the width of band gap becomes larger with the increase of the lattice amplitude as well, which is consistent with the observation in condensed matter experiments.

Figures (9)

• Figure 1: Spectral function $A(\omega\!\to\!0,\mathbf{k})$ for different doping $X$, where $k_x/\mu_1=0$.
• Figure 2: The Fermi surface for $X=0.6$ (left) and $X=1.0$ (right).
• Figure 3: The Fermi momentum $k_F/\mu_1$ versus the doping parameter $X$ when other parameters are fixed.
• Figure 4: Top: Fermi surface at $X=0.5$ (left), and $0.7$ (right), with fixed $\lambda=0.3$. Bottom:$X=0.8$ at the same $\lambda$, showing ionic lattice (left) versus lattice$+$CDW (right).
• Figure 5: The change of spectral function $A(\omega\!\to\!0,\mathbf{k})$ with the lattice amplitude, where we take $k_x/\mu_1=0.25$.