Cusped Electrical Conductivity in Spin-1 Chiral Fermion Systems Arising from Multifold Band Degeneracy

TL;DR

This work investigates the energy-dependent electrical conductivity of 3D spin-1 chiral fermion systems in the presence of disorder using the self-consistent Born approximation with vertex corrections. A cusp-like feature in the conductivity, occurring at a characteristic energy $\epsilon_c$ away from the Dirac point, emerges from the multifold band-crossing structure and is controlled by impurity strength $W$ and trivial-band curvature $c$. Using a three-band model with Hamiltonian $\hat{\mathcal{H}} = \hbar v \hat{\mathbf{S}}\cdot \mathbf{k} + c'[ (\hat{\mathbf{S}}\cdot \mathbf{k})^2 - k^2 \hat{S}_0]$ and Gaussian impurities, the study shows that impurity-induced energy broadening is essential for the cusp, with $|\epsilon_c|$ and $\sigma_c$ increasing with $W$ and decreasing $|c|$. The findings illuminate how multifold-band crossings in topological semimetals govern unconventional transport, offering a theoretical basis for observed anomalies in spin-1 chiral fermion systems.

Abstract

The energy-dependent electrical conductivity in spin-1 chiral fermion systems with disorder is studied using the self-consistent Born approximation. A distinct cusp-like feature appears at an energy different from the band-crossing point, arising from the multifold band-crossing structure formed by the Dirac and trivial bands. The energy position of the cusp and the corresponding value of the electrical conductivity are found to depend sensitively on both the impurity scattering strength and the curvature of the trivial band. These findings demonstrate the critical role of multifold band crossings and disorder-induced broadening of energy levels in determining the transport properties, offering theoretical insight into the unconventional conductivity behavior observed in topological semimetals hosting spin-1 chiral fermions.

Figures (3)

• Figure 1: (Color online) Conductivity as a function of energy for various values of the impurity parameter $W$ and the curvature parameter $c$. Panel (a) shows the $W$-dependence of the conductivity spectra at a fixed curvature $c = 0.1$, for $W = 2, 5, 10$. Panel (b) shows the $c$-dependence at a fixed impurity strength $W = 2$, for $c = -0.2$ to $0.2$.
• Figure 2: (Color online) Conductivity as a function of energy for different impurity strengths $W = 2, 5, 10$ with fixed curvature parameter $c = 0.1$. The upper panels (a–c) show the total conductivity, while the lower panels (d-f) show the decomposed contributions: green lines correspond to intraband processes within Dirac bands ("Dirac--Dirac"), orange lines to interband processes between Dirac and trivial bands ("Dirac--trivial"), and red lines to intraband processes within trivial bands ("trivial--trivial").
• Figure 3: (Color online) Conductivity as a function of energy for different curvatures $c = 0, 0.01, 0.2$ with fixed impurity strength $W = 2$. The upper panels (a-c) show the total conductivity, while the lower panels (d-f) show the decomposed contributions: green lines correspond to intraband processes within Dirac bands ("Dirac--Dirac"), orange lines to interband processes between Dirac and trivial bands ("Dirac--trivial"), and red lines to intraband processes within trivial bands ("trivial--trivial").