Electronic Structure Basis for the Extraordinary Magnetoresistance in ${\mathrm{WTe}}_2$

The electronic structure basis of the extremely large magnetoresistance in layered nonmagnetic tungsten ditelluride has been investigated by angle-resolved photoelectron spectroscopy. Hole and electron pockets of approximately the same size were found at low temperatures, suggesting that carrier compensation should be considered the primary source of the effect. The material exhibits a highly anisotropic Fermi surface from which the pronounced anisotropy of the magnetoresistance follows. A change in the Fermi surface with temperature was found and a high-density-of-states band that may take over conduction at higher temperatures and cause the observed turn-on behavior of the magnetoresistance in ${\mathrm{WTe}}_2$ was identified.

Figure 1

Electronic structure of ${\mathrm{WTe}}_2$ mapped by ARPES at 20 K through two extended surface Brillouin zones along the $\overline{\mathrm{\Gamma }}\text{−}\overline{Y}$ ($k_y$) direction. Constant energy maps were extracted (a) at the Fermi level $E_F$ and 100 meV below (b). Only a portion of the zone that extends to $\pm 0.9{\AA }^{-1}$ was mapped along the $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ ($k_x$) direction. (c) Band dispersion along $\overline{\mathrm{\Gamma }}\text{−}\overline{Y}$ at the point $k_x=0.24{\AA }^{-1}$ with the highest intensity at the Fermi level. Excitation energy $h\nu =21\mathrm{eV}$; sampling around $k_z=2.7{\AA }^{-1}$ (${\mathrm{\Gamma }}_6$). Top: Schematic view of the crystal structure, and bulk (BZ) and surface (SBZ) Brillouin zones. Right: Sketch of the ARPES scans performed in (a)–(c).

Figure 2

(a) Dispersion of ${\mathrm{WTe}}_2$ bands along the $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction taken with the excitation energy of $h\nu =54\mathrm{eV}$. The $k_z$ dependence of the states at the Fermi level $E_F$ shown in (b) was obtained by combining many of such spectra taken in the 40–70 eV range of excitation energies. The band structure in (a) represents the cut at $k_z=4.02{\AA }^{-1}$, which is the center of the ninth extended Brillouin zone ${\mathrm{\Gamma }}_9$.

Figure 3

(a)–(c) Constant energy contours at $T=20\mathrm{K}$ in the region of the Brillouin zone where the bands of ${\mathrm{WTe}}_2$ cross the Fermi level $E_F$. Electronlike and holelike pockets are marked with $e$ and $h$, respectively. Excitation energy was $h\nu =21\mathrm{eV}$. The mapping has been carried out by 0.5° polar rotation. Dashed circles have been added as a guide to the eye. Along the top: Sketch of the band structure and constant energy cuts being made in (a)–(c).

Figure 4

High-resolution band dispersion ARPES scans along a few lines parallel to the $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction of the surface Brillouin zone. Evolution of a tiny electron pocket is visible around $k_x=0.33{\AA }^{-1}$, as well as two holelike bands traversing the Fermi level around $k_x=0.22{\AA }^{-1}$. The spectra have been extracted from a map taken with a 0.5° step in the polar angle. Excitation energy was $h\nu =68\mathrm{eV}$. The $k_y=0$ spectrum is shown twice for the purpose of tracing and labeling the bands, following their overall shape and ordering from Figs. 6 and 7 in Ref. [5].

Figure 5

(a)–(c) Constant energy contours of the electron ($e$) and hole ($h$) pockets in ${\mathrm{WTe}}_2$ band structure close to the Fermi level $E_F$ taken at $T=100\mathrm{K}$. The mapping has been carried out by polar rotations of 0.25°. (d) Low-energy band dispersion acquired along the $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction at $T=100\mathrm{K}$.