Large Enhancement of Thermoelectric Efficiency Due to a Pressure-Induced Lifshitz Transition in SnSe

The Lifshitz transition, a change in Fermi surface topology, is likely to greatly influence exotic correlated phenomena in solids, such as high-temperature superconductivity and complex magnetism. However, since the observation of Fermi surfaces is generally difficult in the strongly correlated systems, a direct link between the Lifshitz transition and quantum phenomena has been elusive so far. Here, we report a marked impact of the pressure-induced Lifshitz transition on thermoelectric performance for SnSe, a promising thermoelectric material without a strong electron correlation. By applying pressure up to 1.6 GPa, we have observed a large enhancement of the thermoelectric power factor by more than 100% over a wide temperature range (10–300 K). Furthermore, the high carrier mobility enables the detection of quantum oscillations of resistivity, revealing the emergence of new Fermi pockets at $\sim 0.86\mathrm{GPa}$. The observed thermoelectric properties linked to the multivalley band structure are quantitatively reproduced by first-principles calculations, providing novel insight into designing the SnSe-related materials for potential valleytronic as well as thermoelectric applications.

Figure 1

Temperature profiles of in-plane (a) resistivity $\rho$, (b) thermopower $S$, and (c) power factor $\mathrm{PF}=S^2/\rho$ for a SnSe single crystal at various pressures up to 1.6 GPa. The electrical and heat currents were applied within the $bc$ plane. Inset: Crystal structure of orthorhombic SnSe ($Pnma$), consisting of black-phosphorus-type buckled layers.

Figure 2

Field ($B$) dependence of (a) magneto-resistivity $\rho (B)/\rho (0)-1$ and (b) Hall resistivity ${\rho }_{\mathrm{H}}$ along the $bc$ plane at various pressures at 2 K. The magnetic field was applied along the $a$ axis (out of plane). For clarity, each curve of the magneto-resistivity is shifted vertically by 0.1 in panel (a). Inset: temperature dependence of oscillatory part of $\rho$ at 1.5 GPa plotted versus $1/B$. As a typical behavior of the SdH oscillation, the amplitude is progressively suppressed with increasing temperature. (c) Plots of the fast Fourier transform of the oscillatory part of $\rho$ at 2 K at various pressures.

Figure 3

Pressure variation of (a) electronic band structures and (b) Fermi surfaces on the $k_a=0$ plane. The Fermi level, which is set to zero in panel (a), was determined to provide the fixed carrier density $n_h=4\times {10}^{-4}e/\text{unit cell}$ for each pressure. This value corresponds to $n_h=1.9\times {10}^{18}{\mathrm{cm}}^{-3}$ for the unit cell volume at 0 GPa, nearly agreeing with the carrier density estimated from the experimental Hall coefficient ($2.3\times {10}^{18}{\mathrm{cm}}^{-3}$). Schematic illustration of the Fermi surfaces exhibiting the Lifshitz transition from (c) a two-valley state to (d) a four-valley one. The shaded plane corresponds to the plotted area in panel (b).

Figure 4

(a) Calculated and (b) experimental values of extremal cross section of Fermi surfaces perpendicular to the $a$ axis, $S_{\mathrm{F}}$, versus pressure. The former is the result from the first-principles calculations, while the latter is estimated from the SdH frequencies. The corresponding (c) PF, (d) $S$, and (e) $\rho$ along the $bc$ plane at 300 and 150 K are also plotted. The experimental (theoretical) results are denoted by closed (open) symbols. For calculating $\rho$, we assume a constant relaxation time independent of pressure at each temperature, which is determined to be $1.5\times {10}^{-14}\mathrm{s}$ ($4.6\times {10}^{-14}\mathrm{s}$) at 300 K (150 K) so as to reproduce the experimental $\rho$ value at ambient pressure. We also assume a common relaxation time irrespective of the valence bands. The direction of the current and thermal gradient is set along the $b$ axis in the calculations.