Extremely large magnetoresistance induced by hidden three-dimensional Dirac bands in nonmagnetic semimetal InBi

Extremely large positive magnetoresistance (XMR) was found in a nonmagnetic semimetal InBi. Using several single crystals with different residual resistivity ratios ($RRR\mathrm{s}$), we revealed that the XMR strongly depended on the $RRR$ (sample quality). Assuming that there were no changes in effective mass $m^{*}$ and carrier concentrations in these single crystals, this dependence was explained by a semiclassical two-carrier model. First-principle calculations including the spin-orbit interactions (SOIs) unveiled that InBi had a compensated carrier balance and SOI-induced “hidden” three-dimensional (3D) Dirac bands at the $M$ and $R$ points. Because the small $m^{*}$ and the large carrier mobilities will be realized, these hidden 3D Dirac bands should play an important role for the XMR in InBi. We suggest that this feature can be employed as a novel strategy for the creation of XMR semimetals.

Figure 1

(a) Crystal structure of the layered semimetal InBi. InBi has a cleavage plane between ${\mathrm{InBi}}_4$-tetrahedron layers. Perspective views of the (b) $bc$ plane and (c) $ab$ plane. (d) Grown single crystals of InBi. (e) X-ray diffraction pattern from the cleaved surface of the single crystal. The inset shows the two-dimensional pattern obtained from the x-ray diffraction of the single crystal.

Figure 2

(a)–(c) Temperature dependencies of the $ab$-plane resistivity ${\rho }_{ab}$ under various magnetic fields $H(0–7$ T) in the InBi single crystals with $RRR\mathrm{s}$ of 91, 200, and 271. The inset shows the magnetic-field dependence of the MR for tilt angles $\theta$ from $0^{\circ }$ to ${90}^{\circ }$ for a large-$RRR$ crystal ($RRR\sim 271$) at $T=1.8$ K. (d) Temperature dependence of the MR and the corresponding average carrier mobility ${\mu }_{\mathrm{ave}}^2$ for the crystals with different $RRR\mathrm{s}$ at $H=7$ T, where the applied field is parallel to the $c$ axis. (e) Magnetic-field dependence of the MR for the crystals with different $RRR\mathrm{s}$ at $T=1.8$ K.

Figure 3

(a) MR as a function of $H^2$ for the crystals with different $RRR\mathrm{s}$ of approximately 91, 200, and 271, at $T=1.8$ K, where the applied field is parallel to the $c$ axis. (b) $RRR$ dependence of the average carrier mobility ${\mu }_{\mathrm{ave}}$ at $T=1.8$ K and $H=7$ T. (c) MR as a function of $RR{R}^2$ at $T=1.8$ K and $H=7$ T.

Figure 4

(a) Electronic band structures of InBi (left) without SOI and (right) with SOI. (b) 3D Fermi surfaces, with the tetragonal first Brillouin zone, the symmetry points are labeled according to the standard notation. Enlarged views of the electronic band structure near the Fermi level ($E_{\mathrm{F}}$) around the (c) $M$ and (d) $R$ points (left) without SOI and (right) with SOI. (e) 3D plots of energy versus $xy$ momentum visualizing the hidden 3D Dirac bands around the $M$ and $R$ points with SOI.