Anisotropic phonon-mediated electronic transport in chiral Weyl semimetals

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Anisotropic phonon-mediated electronic transport in chiral Weyl semimetals

Christina A. C. Garcia, Dennis M. Nenno, Georgios Varnavides, and Prineha Narang

Phys. Rev. Materials 5, L091202 – Published 27 September 2021

Abstract

The discovery and observations of exotic, quantized optical and electrical responses have sparked renewed interest in nonmagnetic chiral crystals. Within this class of materials, six group V transition metal ditetrelides, that is, $X Y_{2}$ ( $X = V$ , Nb, Ta and $Y = Si$ , Ge), host composite Weyl nodes on high-symmetry lines, with Kramers-Weyl fermions at time-reversal invariant momenta. In addition, at least two of these materials, $Nb {Ge}_{2}$ and $Nb {Si}_{2}$ , exhibit superconducting transitions at low temperatures. The interplay of strong electron-phonon interactions and complex Fermi-surface topology presents an opportunity to study both superconductivity and hydrodynamic electron transport in these systems. Towards this broader question, we present an ab initio theoretical study of the electronic transport and electron-phonon scattering in this family of materials, with a particular focus on $Nb {Ge}_{2}$ vs $Nb {Si}_{2}$ , and the other group V ditetrelides. We shed light on the microscopic origin of $Nb {Ge}_{2}$ 's large and anisotropic room-temperature resistivity and contextualize its strong electron-phonon scattering with a presentation of other relevant scattering lifetimes, both momentum relaxing and momentum conserving. Our work explores the intriguing possibility of observing hydrodynamic electron transport in these chiral Weyl semimetals.

Received 18 December 2020
Revised 29 June 2021
Accepted 25 August 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.L091202

Physics Subject Headings (PhySH)

Carrier dynamics Phonons Superconductors Topological phases of matter Transport phenomena

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christina A. C. Garcia ¹, Dennis M. Nenno^1,2, Georgios Varnavides ^1,3, and Prineha Narang ^1,*

¹John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
²Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
³Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*prineha@seas.harvard.edu

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Vol. 5, Iss. 9 — September 2021

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Images

Figure 1
(a) Electronic band structure (left panel) and density of states (right panel) of $Nb {Ge}_{2}$ in space groups No. 180 and No. 181 color coded by Nb contribution to the bands. The unit cell of $Nb {Ge}_{2}$ in space group No. 180 (b) and space group No. 181 (c) is displayed viewed along the $c$ axis and from the side (d). (e) Brillouin zone of the hexagonal unit cell with high-symmetry paths (from Ref. [21]).
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Figure 2
(a) Resistivity vs temperature for $Nb {Ge}_{2}$ , $Nb {Si}_{2}$ , $Ta {Ge}_{2}$ , and $Ta {Si}_{2}$ . Experimental data by Remeika et al. [14] and Gottlieb et al. [6] are overlaid for comparison. (b) Computed room-temperature momentum-relaxing electron-phonon lifetimes plotted on the electronic band structures of $Nb {Ge}_{2}$ and $Nb {Si}_{2}$ . While there are small variations in these lifetimes across the band structures for all six materials, the lifetimes of $Nb {Ge}_{2}$ are roughly an order of magnitude shorter than those of $Nb {Si}_{2}$ and the other five materials (see Supplemental Material [23]), indicating stronger momentum-relaxing electron-phonon (e-ph) scattering. This stronger e-ph scattering can be explained by a one to two orders of magnitude difference in the e-ph coupling. (c) The electron-phonon lifetimes plotted on the Fermi surface of $Nb {Ge}_{2}$ for 10 and 298 K shown on the (0001) surface. The hexagon marks the boundary of the first Brillouin zone.
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Figure 3
Phonon dispersion of (a) $Nb {Ge}_{2}$ and (b) $Nb {Si}_{2}$ along the high-symmetry path in the Brillouin zone [Fig. 1], with the marker area indicating the imaginary part of phonon-electron self-energy. The corresponding Eliashberg spectral function $α^{2} F (ω)$ [see Supplemental Material Eq. (9)] is plotted as a function of frequency in the right panel. In contrast to $Nb {Si}_{2}$ , $Nb {Ge}_{2}$ presents a noticeable anisotropy, with the in-plane dispersion directions ( $Γ - M - K - Γ$ ) exhibiting much larger phonon linewidths due to electron-phonon interactions. Further, we note the two orders of magnitude difference in the two Eliashberg spectral function side panels, highlighting the considerably stronger electron-phonon coupling in $Nb {Ge}_{2}$ .
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Figure 4
(a) Predicted temperature-dependent lifetimes averaged over the Fermi surface for different scattering processes in $Nb {Ge}_{2}$ and $Nb {Si}_{2}$ . The momentum-relaxing electron-phonon scattering lifetime ( $τ_{e-ph}^{MR}$ ) is shorter than the momentum-conserving Coulomb-mediated electron-electron scattering lifetime ( $τ_{e-e}$ ) until low temperatures in both materials. The phonon-mediated electron-electron scattering lifetime ( $τ_{e-e}^{ph}$ ) is shorter than these and is the dominant scattering process at all temperatures. At low temperatures, small-angle scattering dominates and suppresses momentum-relaxing electron-phonon scattering, as evident in comparing the electron-phonon scattering lifetime ( $τ_{e-ph}$ ) to $τ_{e-ph}^{MR}$ . (b) Prediction of hydrodynamic flow regimes in $Nb {Ge}_{2}$ (blue lines) and $Nb {Si}_{2}$ (red lines) for different impurity mean free paths. The color scale denotes the curvature of the current profile in a channel of width $W$ for different momentum-relaxing ( $l_{mr}$ ) and momentum-conserving ( $l_{mc}$ ) mean free paths. The superimposed trajectories, obtained from our ab initio calculations, in $Nb {Ge}_{2}$ (blue) and $Nb {Si}_{2}$ (red), for a channel width of 1 $μ m$ , run from 298 to 4 K.
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