Large magnetoresistance of a compensated metal ${\mathrm{Cu}}_2\mathrm{Sb}$ correlated with its Fermi surface topology

We report electrical transport properties and electronic structure of a nonmagnetic metal ${\mathrm{Cu}}_2\mathrm{Sb}$ single crystal. ${\mathrm{Cu}}_2\mathrm{Sb}$ was found to be a compensated metal with high carrier density $\sim {10}^{22}\mathrm{c}{\mathrm{m}}^{-3}$ and high carrier mobility $\ge {10}^3\mathrm{c}{\mathrm{m}}^2/\mathrm{Vs}$ for both electron and hole carriers. The current-in-plane magnetoresistance at 2 K and 9 T was 730%, while the current-perpendicular-to-plane magnetoresistance at 2 K and 9 T was 2700% without the saturation. Angle-resolved photoemission spectroscopy throughout the three-dimensional (3D) bulk Brillouin zone signified a quasi-two-dimensional (2D) electron pocket axially centered along the M-A line and a 3D hole pocket at the Γ point, in accordance with the electron-hole compensated nature. The presence of quasi-2D open Fermi surface, in line with the first-principles band-structure calculations, is likely responsible for the observed nonsaturating current-in-plane magnetoresistance. The present result lays the foundation for realizing large magnetoresistance via Fermiology engineering in compensated metals.

Figure 1

(a) Crystal structure of ${\mathrm{Cu}}_2\mathrm{Sb}$. (b) XRD pattern of ${\mathrm{Cu}}_2\mathrm{Sb}$ single crystal. Inset shows the photograph of ${\mathrm{Cu}}_2\mathrm{Sb}$ single crystal cleaved along the $ab$ plane.

Figure 2

(a) Temperature dependence of resistivity along the $a$ axis (${\rho }_{xx}$) at 0 T (blue) and 9 T (red) for ${\mathrm{Cu}}_2\mathrm{Sb}$. The magnetic field was applied along the $c$ axis. Inset shows a magnified view below 0.4 K. Magnetic field dependence of (b) ${\rho }_{xx}$ and (c) ${\rho }_{yx}$ at various temperatures. Inset in (b) shows magnetic field dependence of magnetoresistance for ${\rho }_{xx}$ at 2 K. Temperature dependence of (d) carrier density and (e) mobility of electron (blue) and hole (red) carriers for ${\mathrm{Cu}}_2\mathrm{Sb}$. The fitting results were shown in Table S2, Figs. S4 and S5 in the Supplemental Material [27].

Figure 3

(a) Temperature dependence of resistivity along the $c$ axis (${\rho }_{zz}$) at 0 T (blue) and 9 T (red) for ${\mathrm{Cu}}_2\mathrm{Sb}$. The magnetic field was applied along the $a$ axis. (b) Magnetic field dependence of magnetoresistance for ${\rho }_{xx}$ (blue) and ${\rho }_{zz}$ (red) at 2 K. The magnetic field applied along the $c$ and $a$ axis for ${\rho }_{xx}$ and ${\rho }_{zz}$, respectively. (c) Angular dependence of magnetoresistance at 2 K and 9 T for ${\rho }_{zz}$. Magnetic field was rotated in the $ab$ plane. The inset denotes the measurement geometry.

Figure 4

(a) Bulk Brillouin zone of ${\mathrm{Cu}}_2\mathrm{Sb}$. The $k$-point path (red lines) is taken from the aflow program [32]. (b) Calculated band structure along the high symmetry lines in the bulk Brillouin zone. All the bands are doubly degenerate due to the space-inversion symmetry and the time-reversal symmetry. (c) Plot of calculated partial and total density of states (DOS) as a function of $E_{\mathrm{B}}$. (d) 3D plot of calculated Fermi surfaces in the bulk Brillouin zone. (e) Fermi-surface plots for each band in separate panels where the occupied side of the surfaces is illuminated. The Fermi surfaces were drawn by using fermisurfer program [26].

Figure 5

(a) Calculated Fermi surface in the ΓMAZ plane. (b) ARPES intensity at $E_{\mathrm{F}}$ plotted as a function of $k_{//}$ (parallel to the ΓM cut) and $k_z$ measured by varying $h\nu$ with SX photons ($h\nu =300\text{–}375\mathrm{eV}$). ARPES intensity at $E_{\mathrm{F}}$ is obtained by integrating the intensity within $\pm 30\mathrm{meV}$ of $E_{\mathrm{F}}$. Dashed curves are guides to the eyes to trace the experimental Fermi surface. (c) Corresponding MDC at $E_{\mathrm{F}}$. Triangles indicate the quasi-2D band originating from band 4, whereas dashed vertical lines show 2D-like bands. (d) ARPES-intensity mapping at $E_{\mathrm{F}}$ at $k_z\sim 0$ (bottom) and $k_z\sim \pi$ (top). Calculated Fermi surfaces are also overlaid. Blue arrows indicate the quasi-2D pocket from band 4. (e), (f) ARPES intensity plotted as a function of wave vector and binding energy measured along the XΓM cut ($k_z=0$ plane) at $h\nu =62$ eV and the RZA cut ($k_z=\pi$ plane) at $h\nu =80$ eV, respectively. (g), (h) Same as (e) and (f) but calculated band structures along the $k_z=0$ and π is also overlaid. (i) MDCs along the ΓM cut at $E_{\mathrm{B}}=E_{\mathrm{F}}$, 0.4, and 0.8 eV measured with VUV photons of $h\nu =62$ and 80 eV. (j) MDCs at $E_{\mathrm{F}}$ along the $\mathrm{\Gamma }\mathrm{X}$ cut at different $h\nu$'s in a VUV region (62–80 eV).