Metal-Insulator-Like Behavior in Semimetallic Bismuth and Graphite

When high quality bismuth or graphite crystals are placed in a magnetic field directed along the $c$ axis (trigonal axis for bismuth) and the temperature is lowered, the resistance increases as it does in an insulator but then saturates. We show that the combination of unusual features specific to semimetals, i.e., low carrier density, small effective mass, high purity, and an equal number of electrons and holes (compensation), gives rise to a unique ordering and spacing of three characteristic energy scales, which not only is specific to semimetals but which concomitantly provides a wide window for the observation of apparent field-induced metal-insulator behavior. Using magnetotransport and Hall measurements, the details of this unusual behavior are captured with a conventional multiband model, thus confirming the occupation by semimetals of a unique niche between conventional metals and semiconductors.

Figure 1

Temperature dependence of the $ab$-plane resistivity ${\rho }_{xx}$ for a graphite crystal at the $c$-axis magnetic fields indicated in the legend. The solid lines are the fits to the data using the six parameters derived from the three-band analysis described in the text. The shadowed region in the inset and its mapping onto the data in the main panel indicate the interval defined by Eq. (1).

Figure 2

Temperature dependence of the longitudinal resistivity for a bismuth crystal at magnetic fields ranging from 0 to 1 T in 0.1 T steps from top to bottom. The magnetic field and the current are along the trigonal and binary axes, correspondingly. In zero field, the resistance is approximately linear in temperature.

Figure 3

Longitudinal resistivity ${\rho }_{xx}$ (top panel) and transverse resistivity ${\rho }_{xy}$ (bottom panel) versus applied field $B$ for graphite at the temperatures indicated in the legend. The solid lines are determined by a fitting procedure that simultaneously includes both sets of data into a three-band model described in the text. The inset in the bottom panel, with the same units on each axis, magnifies the low-field region, where the contribution from the third band with a lower carrier density makes a major contribution that cannot be fit by solely using the two majority bands.

Figure 4

Temperature dependence of the fitting parameters (graphite) for the bands indicated in the legends of each panel. The near equality of the carrier densities of the two majority bands (lower panel) indicates good compensation at low fields ($B<200\mathrm{mT}$) and the linear dependence of the scattering rate on $T$ (upper panel, dashed line) with a slope of 0.065(3) in units of $k_B/\hslash$ is consistent (see the text) with electron-phonon scattering.