Magnetoresistance and valley degree of freedom in bulk bismuth

Abstract

In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence, the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semi-classical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed-matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system.

A topic review for JPCM, 22 pages, 18 figures

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Cited by in corpus (24)

• Magnetoresistance from Fermi Surface Topology
• The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons
• Huge linear magnetoresistance due to open orbits in $\gamma$-PtBi${}_2$
• Fermi Surface and Carriers Compensation of pyrite-type PtBi${}_2$ Revealed by Quantum Oscillations
• Magneto-Seebeck effect in bismuth
• Formation of an electron-phonon bi-fluid in bulk antimony
• Observation of gigantic spin conversion anisotropy in bismuth
• Angular dependence of magnetoresistance and planar Hall effect in semimetals in strong magnetic fields
• Avoided level crossing at the magnetic field induced topological phase transition due to spin-orbital mixing
• Magnetism and Magnetotransport in the Kagome Antiferromagnet ${\text{Mn}}_3\text{Ge}$
• Negative magnetoresistance and sign change of the planar Hall effect due to the negative off-diagonal effective-mass in Weyl semimetals
• Anomalous Electrical Transport in the Kagome Magnet YbFe${}_6$Ge${}_6$
• Orbital origin of fourfold anisotropic magnetoresistance in Dirac materials
• Nonperturbative Matrix Mechanics Approach to Spin-Split Landau Levels and g-Factor in Spin-Orbit Coupled Solids
• Observation of Temperature Independent Anomalous Hall Effect in Thin Bismuth from Near Absolute Zero to 300 K Temperature
• Quantum--classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena
• Effects of strain-tunable valleys on charge transport in bismuth
• High-field immiscibility of electrons belonging to adjacent twinned bismuth crystals
• Pseudo anomalous Hall effect in semiconductors and semimetals: A classical perspective
• Anomalous Hall Effect in Thin Bismuth
• Magnetoresistance in the Extreme Quantum Limit: Field-Induced Crossover to the Unitarity Limit
• Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film
• Negative transverse magnetoresistance due to negative off-diagonal mass in linear dispersion materials
• Classical transport theory for the planar Hall effect with threefold symmetry