Dirac dispersion generates unusually large Nernst effect in Weyl semimetals

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Dirac dispersion generates unusually large Nernst effect in Weyl semimetals

Sarah J. Watzman, Timothy M. McCormick, Chandra Shekhar, Shu-Chun Wu, Yan Sun, Arati Prakash, Claudia Felser, Nandini Trivedi, and Joseph P. Heremans

Phys. Rev. B 97, 161404(R) – Published 18 April 2018

Abstract

Weyl semimetals contain linearly dispersing electronic states, offering interesting features in transport yet to be thoroughly explored thermally. Here we show how the Nernst effect, combining entropy with charge transport, gives a unique signature for the presence of Dirac bands and offers a diagnostic to determine if trivial pockets play a role in this transport. The Nernst thermopower of NbP exceeds its conventional thermopower by a 100-fold, and the temperature dependence of the Nernst effect has a pronounced maximum. The charge-neutrality condition dictates that the Fermi level shifts with increasing temperature toward the energy that has the minimum density of states (DOS). In NbP, the agreement of the Nernst and Seebeck data with a model that assumes this minimum DOS resides at the Dirac points is taken as strong experimental evidence that the trivial (non-Dirac) bands play no role in high-temperature transport.

Received 27 July 2017
Revised 8 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.161404

Physics Subject Headings (PhySH)

Nernst effect Thermoelectric effects

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sarah J. Watzman¹, Timothy M. McCormick², Chandra Shekhar³, Shu-Chun Wu³, Yan Sun³, Arati Prakash², Claudia Felser³, Nandini Trivedi², and Joseph P. Heremans^1,2,4,*

¹Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, Ohio 43210, USA
²Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
³Max Planck Institute for Chemical Physics of Solids, Dresden, Germany, 01187
⁴Department of Materials Science and Engineering, The Ohio State University, Columbus, Ohio 43210, USA

^*Corresponding Author: heremans.1@osu.edu

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Issue

Vol. 97, Iss. 16 — 15 April 2018

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Images

Figure 1
Electrochemical potential band structure and motion with temperature. (a) Two-dimensional electronic dispersion relation (Eq. (S6) in Supplemental Material [15]) used in modeling NbP transport properties. (b) Two-dimensional dispersion around a single Dirac cone where, at low temperatures, the electrochemical potential lies in the valence band at an energy $μ_{0}$ below the Dirac point. (c) Calculated $μ (T)$ temperature dependence shows it moving toward the Weyl node energy with increasing temperature, from $| μ_{0} |$ , whether in the conduction or valence band. The energy scale is set to unity at $| μ_{0} |$ , and the temperature scale to unity at $| μ_{0} / k_{B} |$ .
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Figure 2
Nernst thermopower, $α_{x y z}$ magnetic field dependence. (a) Measured Nernst thermopower as a function of applied magnetic field at various temperatures. The sharper slope for $| H |$ below $\sim 2 T$ is the low-field regime; above $\sim 3 T$ is the high-field regime. Systematic geometric error on the Nernst thermopower field dependence is $\sim 17 %$ . Data are not symmetrized. Inset shows the Nernst voltage magnetic-field dependence measured at 4.92 K in a 2.17-mK temperature gradient. SDH oscillations are visible and correspond to DHVA periods measured in the magnetization. (b) Calculated at select temperatures, Nernst thermopower magnetic-field dependence given in SI and natural units that correspond well experimentally. The magnetic field is the product of the in-plane lattice constant $a$ and magnetic length $L_{B} \equiv \sqrt{ℏ c / e B}$ ; thermopower is $k_{B} / e$ , and temperature is given in units of $| μ_{0} / k_{B} |$ .
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Figure 3
Nernst coefficient, $N_{x y z}$ temperature dependence. (a) Measured Nernst coefficient plotted as a function of temperature (low-field regime in red, high-field in blue). The Nernst coefficient peaks near 50 K (low field) and 90 K (high field). Inset shows conventional thermopower temperature dependence, with a maximum near $8 μ V / K$ , over two orders of magnitude smaller than the maximum Nernst thermopower. No magneto-thermopower is observed when a 9 T magnetic field is applied parallel to the $〈 001 〉$ axis. Error bars represent a $95 %$ confidence interval on the systematic error standard deviation, excluding geometric error on the sample mount. (b) Calculated temperature dependence of the Nernst coefficient in the low-field (red) and high-field (blue) regimes. The given SI and natural units correspond very well without fitting.
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Figure 4
Electrochemical potential at 0 K from DHVA periods and DFT calculations. Calculated (data points) and experimental (horizontal lines) values of the DHVA oscillation periods are shown as a function of $μ_{0}$ in the 0 K limit, as measured from the $W 2$ Dirac point. The $μ_{0} = - 8.2 \pm 0.7$ -meV values are represented by the hatched region, with the best overall fit in that box.
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