Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Abstract

Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikov-de Haas effect and the de Haas-van Alphen effect. Above all, the large diamagnetism of bismuth had been a long-standing puzzle soon after the establishment of quantum mechanics, which had been resolved eventually in 1970 based on the effective Hamiltonian derived by Wolff as due to the interband effects of a magnetic field in the presence of a large spin-orbit interaction. This Hamiltonian is essentially the same as the Dirac Hamiltonian, but with spatial anisotropy and an effective velocity much smaller than the light velocity. This paper reviews recent progress in the theoretical understanding of transport and optical properties, such as the weak-field Hall effect together with the spin Hall effect, and ac conductivity, of a system described by the Wolff Hamiltonian and its isotropic version with a special interest of exploring possible relationship with orbital magnetism. It is shown that there exist a fundamental relationship between spin Hall conductivity and orbital susceptibility in the insulating state on one hand, and the possibility of fully spin-polarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.

22 pages, 23 figures, submitted to J. Phys. Soc. Jpn

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• Electric field assisted amplification of magnetic fields in tilted Dirac cone systems
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• Electron-phonon superconductivity in CaBi2 and the role of spin-orbit interaction
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• Giant orbital diamagnetism of three-dimensional Dirac electrons in Sr${}_3$PbO antiperovskite
• Capacitive detection of magnetostriction, dielectric constant, and magneto-caloric effects in pulsed magnetic fields
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• Visualizing higher-fold topology in chiral crystals
• Observation of gigantic spin conversion anisotropy in bismuth
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• Angular dependence of magnetoresistance and planar Hall effect in semimetals in strong magnetic fields
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• Two-fold symmetry of in-plane magnetoresistance anisotropy in the superconducting states of BiCh2-based LaO0.9F0.1BiSSe single crystal
• Spin Pumping into Anisotropic Dirac Electrons
• Quantum transport through 3D Dirac materials
• Resonant plasmon-phonon coupling and its role in magneto-thermoelectricity in bismuth
• Magnetotransport properties of the new-type topological semimetal ZrTe
• Analytical Solutions for the Surface States of Bi${}_{1-x}$Sb${}_x$ ($0\le x\lesssim 0.1$)
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• Thermoelectric transport coefficients of a Dirac electron gas in high magnetic fields
• Suppressed magnetic circular dichroism and valley-selective magneto-absorption due to the effective mass anisotropy in bismuth
• Orbital origin of fourfold anisotropic magnetoresistance in Dirac materials
• Different spin relaxation property observed in linearly and circularly polarized laser induced terahertz emission from Bi/Co bilayer
• High-field Studies on Layered Magnetic and Polar Dirac Metals
• Longitudinal and transverse magnetoresistance of SrTiO${}_3$ with a single closed Fermi surface
• Anomalous Spin Transport Properties of Gapped Dirac Electrons with Tilting
• Local Observations of Orbital Diamagnetism and Excitation in Three-Dimensional Dirac Fermion Systems Bi${}_{1-x}$Sb${}_x$
• Anomalous diamagnetism of electride electrons in transition metal silicides
• Tight-Binding Model and Electronic Property of Dirac Nodal Line in Single-Component Molecular Conductor [Pt(dmdt)${}_2$]
• Lorentz Covariance of Dirac Electrons in Solids: Dielectric and Diamagnetic Properties
• Nonperturbative Matrix Mechanics Approach to Spin-Split Landau Levels and g-Factor in Spin-Orbit Coupled Solids
• Weak anti-localization in spin-orbit coupled lattice systems
• Electronic properties of the parabolic Dirac system
• A field-induced reentrant insulator state of a gap-closed topological insulator (Bi_{1-x}Sb_x) in quantum-limit states
• Magnetizations and de Haas-van Alphen oscillations in massive Dirac fermions
• Giant inverse Faraday effect in Dirac semimetals
• Characteristic singular behaviors of nodal line materials emerging in orbital magnetic susceptibility and Hall conductivity
• Nuclear spin relaxation rate near the disorder-driven quantum critical point in Weyl fermion systems
• Inverse Faraday effect in massive Dirac electrons
• Effects of strain-tunable valleys on charge transport in bismuth
• Quantum--classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena
• High-field immiscibility of electrons belonging to adjacent twinned bismuth crystals
• Circular Photon Drag Effect in Dirac electrons by Quantum Geometry
• Localized magnetic states in three dimensional Dirac solids
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• Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class
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• Negative transverse magnetoresistance due to negative off-diagonal mass in linear dispersion materials
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