Lifshitz transition in a holographic finite density flavour brane Weyl semimetal

TL;DR

This work extends a holographic Weyl semimetal model to finite density by incorporating a chemical potential $\mu$ in a D3/D7 framework and computes the fermionic spectral function using two probe fermions of opposite chirality. The analysis reveals Weyl points with linear dispersion at zero density and, at finite density, the emergence of a Fermi surface that undergoes Lifshitz transitions. These transitions can be driven either by tuning the mass parameter $M$, which flattens the band between Weyl points, or by changing $\mu$, which shifts bands relative to the Fermi level. The results highlight how strong coupling holography can capture nontrivial Fermi-surface topology changes relevant for Weyl semimetals and related transport phenomena.

Abstract

We extend a top-down holographic model of a Weyl semimetal to finite charge density and compute the fermionic spectral function by introducing two probe fermions of opposite chirality. The model is controlled by the boundary fermion mass M and the chemical potential $μ$. In the zero density, small-M limit, we recover four energy bands, two Weyl points, and linear dispersion in their vicinity, the hallmarks of a Weyl semimetal. As M increases, the bands between the Weyl points become progressively compressed and the spectral weight associated with those bands is smeared out. At finite charge density, we map the Fermi surface in momentum space and identify a Lifshitz transition: two distinct Fermi pockets, each enclosing a different Weyl point, merge into a single large Fermi surface that encloses both. This transition can be induced by either control parameter. Varying M alters the band structure and thus the band shape, which drives the Lifshitz transition, whereas changing $μ$ shifts the bands relative to the Fermi level without qualitatively changing the band structure, producing the Lifshitz transition by moving the band positions.

Figures (10)

• Figure 1: The band structure obtained from the Weyl semimetal Lagrangian \ref{['Lagrangian']}. (a) For $|\frac{m}{b}|<\frac{1}{2}$, the two bands intersect on the $k_z$ axis at two Weyl points, each exhibiting a linear dispersion. (b) For $|\frac{m}{b}|>\frac{1}{2}$, the band crossing is lifted and a full gap opens.
• Figure 2: Embeddings for different IR boundary conditions at $T=0.05$. The black curve indicates the black brane horizon. The blue curves are the embedding functions $R(r)$ for different IR conditions. (a) It corresponds to the zero density case for $Q =0$; the blue dashed curve represents the Minkowski embedding, which describes the insulating phase, while the blue solid curve corresponds to the black hole embedding, characterizing the Weyl semimetal phase. (b) It corresponds to the finite density case for $Q=1$, we find that only the black hole embedding is realized.
• Figure 3: The profile of $A_t$ as a function of $r$ for $T=0.05$ and $M \approx 0.21650$. The blue curve corresponds to $Q=\frac{1}{4}$, while the red curve corresponds to $Q=1$.
• Figure 4: The spectral function $A(k_z)$ for $T=0.05$, $M \approx 0.02$, and $\omega=0$. The spectral function $A$ exhibits a finite weight contribution at $k_z=\pm \frac{1}{2}$.
• Figure 5: The relation $k_z-\omega$ near a Weyl point. The red line has been fitted to the blue data points. It gives a linear dispersion relation.