Abstract
We present an extensive study of angle-dependent transverse magnetoresistance in bismuth, with a magnetic field perpendicular to the applied electric current and rotating in three distinct crystallographic planes. The observed angular oscillations are confronted with the expectations of semiclassic transport theory for a multivalley system with anisotropic mobility and the agreement allows us to quantify the components of the mobility tensor for both electrons and holes. A quadratic temperature dependence is resolved. As Hartman argued long ago, this indicates that inelastic resistivity in bismuth is dominated by carrier-carrier scattering. At low temperature and high magnetic field, the threefold symmetry of the lattice is suddenly lost. Specifically, a rotation of magnetic field around the trigonal axis modifies the amplitude of the magnetoresistance below a field-dependent temperature. By following the evolution of this anomaly as a function of temperature and magnetic field, we map the boundary in the (field, temperature) plane separating two electronic states. In the less symmetric state, confined to low temperature and high magnetic field, the three Dirac valleys cease to be rotationally invariant. We discuss the possible origins of this spontaneous valley polarization, including a valley-nematic scenario.
- Received 7 January 2015
DOI:https://doi.org/10.1103/PhysRevX.5.021022
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Published by the American Physical Society
Popular Summary
Bismuth occupies a prime role in condensed-matter physics because of its extremely mobile carriers with very long Fermi wavelengths. The magnetoresistance amplitude of bismuth is known to be extremely large and very anisotropic at low temperatures. Here, we conduct an extensive study of the angle-dependent magnetoresistance in bismuth using a magnetic field () rotating in three distinct crystallographic planes kept perpendicular to the applied current. We focus on the three Dirac valleys of bismuth on its Fermi surface as we conduct experiments at temperatures between 2 and 300 K.
It is known that magnetic fields can affect how electricity is conducted through a solid. Resistivity sometimes increases by orders of magnitude in the presence of a magnetic field, an effect that has been observed in semimetals such as graphite and bismuth. The low-mass electrons in bismuth are very mobile and explain the changes in orbital magnetoresistance that have been experimentally observed. We trace the amplitude of the magnetoresistance as a function of temperature and magnetic field using single bismuth crystals with dimensions measured in millimeters. We presume that the mobility of each electron pocket on the Fermi surface has four different components; all possess an inverse quadratic temperature dependence. We also record a phase transition associated with the loss of the threefold symmetry of the underlying lattice. Below a field-dependent temperature, a 120-degree rotation of the magnetic field does not leave the electron fluid invariant. This electronic phase may qualify as the first case of a valley-nematic state in three dimensions.
Our results show that elemental bismuth is an appealing platform to explore the possible existence of electronic equivalents of liquid crystals.
