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Toroidal Fermi-surface geometry and phonon-limited transport in nodal-line semimetals

Aman Anand, Alessandro De Martino

Abstract

Nodal-line semimetals (NLSs) can display unconventional quasiparticle dynamics and charge transport properties due to their extended band degeneracy and the peculiar geometry of their Fermi surface. We consider electron-acoustic phonon scattering as the dominant relaxation mechanism and compute the quasiparticle decay rate and dc conductivity by solving the linearized semiclassical Boltzmann equation in a minimal model of a doped circular NLS. We find that the toroidal geometry of the Fermi surface gives rise to two parametrically distinct Bloch-Grüneisen temperatures, associated with momentum transfers along the poloidal and toroidal directions, respectively. As a result, an intermediate temperature window opens between these two scales, in which the decay rate follows $Γ\propto T^2$, while the conductivity follows $σ\propto T^{-2}$. We also obtain the low- and high-temperature asymptotic behaviors, and discuss implications for ARPES and transport measurements in candidate NLS materials.

Toroidal Fermi-surface geometry and phonon-limited transport in nodal-line semimetals

Abstract

Nodal-line semimetals (NLSs) can display unconventional quasiparticle dynamics and charge transport properties due to their extended band degeneracy and the peculiar geometry of their Fermi surface. We consider electron-acoustic phonon scattering as the dominant relaxation mechanism and compute the quasiparticle decay rate and dc conductivity by solving the linearized semiclassical Boltzmann equation in a minimal model of a doped circular NLS. We find that the toroidal geometry of the Fermi surface gives rise to two parametrically distinct Bloch-Grüneisen temperatures, associated with momentum transfers along the poloidal and toroidal directions, respectively. As a result, an intermediate temperature window opens between these two scales, in which the decay rate follows , while the conductivity follows . We also obtain the low- and high-temperature asymptotic behaviors, and discuss implications for ARPES and transport measurements in candidate NLS materials.
Paper Structure (23 sections, 92 equations, 3 figures, 1 table)

This paper contains 23 sections, 92 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model
  3. Electronic model
  4. Phonon model
  5. Electron-phonon interaction
  6. Temperature scales
  7. Boltzmann Equation
  8. Linearized BTE
  9. Transport lifetimes
  10. Quasiparticle decay rate
  11. Conductivity
  12. Conclusions
  13. Linearized Boltzmann equation
  14. Solution of the BTE
  15. Momentum transfer
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Shown are the toroidal Fermi surface, the associated toroidal coordinates $(\kappa,\theta,\varphi)$, and the unit vector $\hat{e}_{\kappa}$, defined in Eq. \ref{['Eq: toroidal-unit-vector-definition']}.
  • Figure 2: Temperature dependence of the quasiparticle decay rate $\Gamma(T)$ obtained from a direct numerical evaluation of Eq. \ref{['Eq: decay-rate4']}. Results are shown for $c_l/v_0=10^{-2}$ and for several chemical potentials (see legend), with $\Gamma_0$ defined in Eq. \ref{['Gamma0-defined']}. The red markers indicate $T = T_{\mathrm{BG}}^{(\mathrm{pol})}$. Dashed black lines represent asymptotic power-law fits across the three temperature regimes.
  • Figure 3: Temperature dependence of the transport scattering rates $\Gamma_\text{tr}^z(T)$ (solid line) and $\Gamma_\text{tr}^x(T)$ (dotted line) obtained from direct numerical evaluation of Eqs. \ref{['Eq: transport-lifetime-main-integral-x']} and \ref{['Eq: transport-lifetime-main-integral-z']}. Results are shown for $c_l/v_0=10^{-2}$ and for several chemical potentials (see legend), with $\Gamma_0$ defined in Eq. \ref{['Gamma0-defined']}. The red markers indicate $T = T_{\mathrm{BG}}^{(\mathrm{pol})}$. Note that for the red curve, the poloidal BG temperature $T_{\mathrm{BG}}^{(\mathrm{pol})}$ falls outside the temperature window displayed. Dashed black lines represent asymptotic power-law fits across the three temperature regimes.