Angle dependence of the orbital magnetoresistance in bismuth

TL;DR

This study investigates how the orbital magnetoresistance in bismuth varies with angle and temperature, revealing anisotropic mobility, inelastic scattering effects, and a spontaneous valley polarization at low temperatures and high magnetic fields.

Contribution

It provides a detailed analysis of angle-dependent magnetoresistance in bismuth, quantifies mobility tensor components, and uncovers a spontaneous valley polarization phenomenon.

Findings

Quadratic temperature dependence of resistivity indicates carrier-carrier scattering dominance.

Angular oscillations match semi-classic transport theory, allowing mobility tensor extraction.

Low-temperature, high-field state shows loss of threefold symmetry and valley polarization.

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 semi-classic transport theory for a multi-valley 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 $2\pi/3$ rotation of magnetic field around the trigonal axis modifies the amplitude of the magneto-resistance below a field-dependent temperature. By following the evolution of this anomaly as a function of temperature and magnetic field, we mapped 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.