Quantum oscillations of thermopower in ${\mathrm{WTe}}_2$ thin films

Few-layer ${\mathrm{WTe}}_2$ displays fascinating phenomena, which are believed to be closely related to the topological character of its band structure. In this work we investigate quantum oscillations of thermopower in thin ${\mathrm{WTe}}_2$ films. Besides four oscillation frequencies commonly observed in bulk materials, we observe an additional oscillation frequency, which has previously been attributed to topological surface states [Nat. Commun. 8, 2150 (2017)]. Through analysis of the temperature, angular, and film thickness dependence of the frequency, we conclude that it is not due to the cyclotron resonance of the surface Fermi arcs in Weyl semimetals, but rather from the bulk bands. Emergence of these bulk bands at the Fermi level is due to a band reconstruction in thin layers. They contribute to transport and may be responsible for some properties of few-layer ${\mathrm{WTe}}_2$.

Figure 1

Quantum oscillations of MTEP and magnetoresistance. (a) MTEP at 1.5 K with the magnetic field along the $\widehat{c}$ axis for sample A (21.5 nm thick). The inset shows an optical image of the device with a scale bar representing $10\mu \mathrm{m}$. The thermal gradient is along the $\widehat{a}$ axis. (d) MTEP at 1.5 K with the magnetic field along the $\widehat{c}$ axis for sample B (14.5 nm thick). The inset shows an optical image of the device. The thermal gradient is along the $\widehat{b}$ axis. MTEP for both samples shows pronounced quantum oscillations. (b) and (e) Comparison of fast Fourier transform (FFT) spectra of quantum oscillations between bulk and thin films. The spectrum of the bulk is from magnetoresistance, while the spectra of thin films are from MTEP. FFT is performed for MTEP in different field ranges. An additional oscillation frequency $P_x$ appears when high field data are included. (c) Three MR traces of sample A at 1.5 K ($I\parallel \widehat{a}$) with $\vec{B}\parallel \widehat{a}, \widehat{b}$, and $\widehat{c}$, respectively. MR is positive in all three configurations. (f) Same as in (c), except it is for sample B ($I\parallel \widehat{b}$). Negative longitudinal MR clearly appears in the case of $I\parallel \vec{B}\parallel \widehat{b}$ (blue solid line).

Figure 2

Angle dependence of quantum oscillations in MTEP at 1.5 K. (a) Angle dependence of the FFT spectra for sample A with field rotated from the $\widehat{c}$ axis ($0^{\circ }$) to the $\widehat{a}$ axis. The red dashed line indicates the evolution of $P_x$. (b) Angle dependence of the frequency of $P_x$ for sample A. The blue line is a $1/cos\left(\theta \right)$ fit, where $\theta$ is the rotation angle. The red line is an ellipsoid fit. (c) FFT spectra for sample B with field rotated from the $\widehat{c}$ axis ($0^{\circ }$) to the $\widehat{a}$ axis. (d) Angle dependence of the frequency of $P_x$ for sample B.

Figure 3

Temperature dependence of quantum oscillations in MTEP. (a) Oscillation part of MTEP for samples A and B as a function of $1/B$ for various temperatures. (b) FFT amplitudes of oscillations versus temperature for $P_x$ and $P_1–P_4$. Solid lines are fits to $A\left(T\right)$ derived from the Lifshitz-Koservich formula.

Figure 4

Origin of $P_x$. (a) Expected oscillation frequency of the Weyl orbit $F{}_{\text{Weyl}}$ and the actual frequency $P_x$ as a function of thickness. (b) A schematic representation of the band structure of $\gamma , \eta , \zeta$, and $P_1–P_4$ near the Fermi level. The figure is not drawn to scale.