Design Principles for Topological Thermoelectrics

TL;DR

The paper tackles the fundamental and practical challenge of achieving high thermoelectric efficiency in conventional metals and semiconductors by leveraging topological band structures. It develops a coherent framework that highlights three key topological ingredients—topologically protected band touching points, electron-hole degenerate lowest Landau levels in a magnetic field, and Berry curvature—that can enhance longitudinal and transverse thermoelectric responses. It derives explicit design principles for selecting materials across Dirac/Weyl, nodal-line, and compensated semimetals, and demonstrates how magnetothermoelectric effects can yield large $zT$ values, including in the extreme quantum limit. A high-throughput TMDB-based search identifies 29 candidate topological semimetals, including 12 novel materials, offering practical targets for near-future experiments and potential route to high-performance, solid-state thermoelectrics with topological features.

Abstract

Conventional metals, insulators, and semimetals are constrained by fundamental limitations in terms of their thermoelectric performance. Topological materials offer certain features that allow them to circumvent these constraints, and potentially to form the basis for thermoelectric devices with unprecedented efficiency. In this article we review the thermoelectric performance of topological materials, focusing specifically on nodal semimetals, such as Weyl and nodal-line semimetals. We discuss how certain unique ``topological'' features of these materials -- namely their topologically protected band touching points, electron-hole degenerate lowest Landau level, and Berry curvature -- allow them to exhibit thermoelectric properties that go beyond what is possible in conventional materials, particularly in the presence of an applied magnetic field. We focus our discussion on the goal of achieving large figure of merit $zT$, and for each material class we summarize optimal \emph{design principles} for selecting materials that maximize thermoelectric efficiency. We then use these optimal design principles to design and implement a high-throughput database search for topological semimetals that are promising as thermoelectrics. In addition to highlighting a number of materials that are already known to have large magnetothermoelectric effects, our search uncovers twelve additional materials that are especially promising for near-future experiments.

Figures (9)

• Figure 1: The Seebeck coefficient $S_{xx}$ can be defined either (a) in terms of the ratio $(\Delta V)_x / (\Delta T)_x$ under conditions of zero current, or (b) in terms of the ratio between the heat current and the electric current under conditions of uniform temperature. The Nernst coefficient similarly has two equivalent definitions, depicted in (c) and (d).
• Figure 2: The Seebeck coefficient $S_{xx}$ of a non-magnetic Weyl or Dirac semimetal in the absence of magnetic field is plotted as a function of $k_B T / \mu$, where $\mu$ is the chemical potential [see Eq. (\ref{['eq:Sweylsimple']})]. Details of the scattering mechanism can change the precise values of this curve (and $\mu$ in general is temperature-dependent at higher temperatures), but the appearance of a peak $S_{xx} \sim k_B/e$ at $k_B T \sim \mu$ is universal. The inset shows the Dirac/Weyl dispersion relation, with the conduction band (blue) and valence band (orange) meeting at a point in momentum space.
• Figure 3: (a) The evolution of the Fermi surface is depicted as a function of magnetic field $B$ in the $z$ direction. A spherical Fermi surface is broken up into discrete "cylinders" associated with constant kinetic energy in the transverse direction. In the EQL, only one such cylinder is occupied, and the dispersion becomes effectively one-dimensional. (b) The dispersion relation $E(k_z)$ for a Dirac or Weyl semimetal in a magnetic field is shown for both conduction band and valence band states with different Landau level index $N$ [see Eqs. (\ref{['eq:ENWeyl']}) and (\ref{['eq:E0Weyl']})].
• Figure 4: Theoretical calculation of the Seebeck coefficient $S_{xx}$ for a Weyl semimetal with a perpendicular magnetic field. The red curve shows a calculation using the semiclassical approach, which is valid at $B \ll B_\text{EQL}$, while the blue curve shows a calculation using Eq. (\ref{['eq:entropypercharge']}), which is valid at $B \gg B_1$. This example uses $k_BT / E_\text{F} = 0.03$ and assumes a temperature-independent scattering time. Figure adapted with permission from Ref. kozii_thermoelectric_2019.
• Figure 5: (a) Schematic depiction of the Fermi surface surrounding a nodal line at constant energy, including a short cylindrical segment of the Fermi surface (adapted from Ref. syzranov_electron_2017). (b) The dispersion relation along that segment, showing an energy $E$ that depends linearly on the momentum $k_\perp$ transverse to the nodal line.