Magnetoresistance and valley degree of freedom in bulk bismuth

Quantum-classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena

The three-dimensional magneto-conductivity tensor was derived in a gauge invariant form based on the Kubo formula considering quantum effects under a magnetic field, such as the Landau quantization and quantum oscillations. We analytically demonstrated that the quantum formula of the magneto-conductivity can be obtained by adding a quantum oscillation factor to the classical formula. This result establishes the quantum-classical correspondence, which has long been missing in magnetotransport phenomena. Moreover, we found dissipative-to-dissipationless crossover in the Hall conductivity by paying special attention to the analytic properties of the thermal Green's function. Finally, by calculating the magnetoresistance of semimetals, we identified a phase shift in quantum oscillation originating from the dissipationless transport predominant at high fields.

Observation of large spin conversion anisotropy in bismuth

While the effective g-factor can be anisotropic due to the spin-orbit interaction (SOI), its existence in solids cannot be simply asserted from a band structure, which hinders progress on studies from such viewpoints. The effective g-factor in bismuth (Bi) is largely anisotropic; especially for holes at T-point, the effective g-factor perpendicular to the trigonal axis is negligibly small (<0.112), whereas the effective g-factor along the trigonal axis is very large (62.7). We clarified in this work that the large anisotropy of effective g-factor gives rise to the large spin conversion anisotropy in Bi from experimental and theoretical approaches. Spin-torque ferromagnetic resonance was applied to estimate the spin conversion efficiency in rhombohedral (110) Bi to be 17 to 27%, which is unlike the negligibly small efficiency in Bi(111). Harmonic Hall measurements support the large spin conversion efficiency in Bi(110). A large spin conversion anisotropy as the clear manifestation of the anisotropy of the effective g-factor is observed. Beyond the emblematic case of Bi, our study unveiled the significance of the effective g-factor anisotropy in condensed-matter physics and can pave a pathway toward establishing novel spin physics under g-factor control.

Orbital magnetization of three-dimensional Dirac electrons in the quantum limit

In this study, we evaluated the dependence of magnetization of three-dimensional Dirac electrons in the quantum limit on the magnetic field and temperature. The magnetization was calculated by differentiating the free energy with respect to the magnetic field. The field and temperature dependence of the chemical potential were entirely considered under the canonical ensemble condition. The total magnetizationMconsisted of two contributions from the conductionMcand valenceMvbands.Mvwas insensitive to temperature and exhibited sub-linear field dependence, which is consistent with the previous research on Dirac electrons. By contrast,Mcwas sensitive to both temperature and magnetic field, yielding a non-trivial contribution to the totalM. As a result, the properties of totalMchanged at approximatelykBT≃EF, whereEFis the Fermi energy measured from the band bottom andkBis the Boltzmann constant. At low temperatureskBT≲EF,Mexhibited sub-linear field dependence, whereasMexhibited super-linear field dependence at high temperatureskBT≳EF. This qualitative change in the field dependence ofMwill play a significant role in the magnetization of Dirac electrons with smallEF.

Negative transverse magnetoresistance due to the negative off-diagonal mass in linear dispersion materials

This study calculated the magnetoresistance (MR) in the Dirac electron system, Dresselhaus-Kip-Kittel (DKK) model, and nodal-line semimetals based on the semiclassical Boltzmann theory, with particular focus on the detailed energy dispersion structure. The negative off-diagonal effective-mass was found to induce negative transverse MR owing to the energy dispersion effect. The impact of the off-diagonal mass was more prominent in case of a linear energy dispersion. Further, Dirac electron systems could realize negative MR even if the Fermi surface was perfectly spherical. The obtained negative MR in the DKK model may explain the long-standing mystery in p-type Si.

The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons

We have studied the charge to spin conversion in Bi_1-x Sb _x /CoFeB heterostructures. The spin Hall conductivity (SHC) of the sputter-deposited heterostructures exhibits a high plateau at Bi-rich compositions, corresponding to the topological insulator phase, followed by a decrease of SHC for Sb-richer alloys, in agreement with the calculated intrinsic spin Hall effect of Bi_1-x Sb _x . The SHC increases with increasing Bi_1-x Sb _x thickness before it saturates, indicating that it is the bulk of the alloy that predominantly contributes to the generation of spin current; the topological surface states, if present, play little role. Unexpectedly, the SHC is found to increase with increasing temperature, following the trend of carrier density. These results suggest that the large SHC at room temperature, with a spin Hall efficiency exceeding 1 and an extremely large spin current mobility, is due to increased number of thermally excited Dirac-like electrons in the L valley of the narrow gap Bi_1-x Sb _x alloy.

Nonperturbative Matrix Mechanics Approach to Spin-Split Landau Levels and the g Factor in Spin-Orbit Coupled Solids

We propose a fully quantum approach to nonperturbatively calculate the spin-split Landau levels and g factor of various spin-orbit coupled solids based on the k·p theory in the matrix mechanics representation. The new method considers the detailed band structure and the multiband effect of spin-orbit coupling irrespective of the magnetic-field strength. We show an application of this method to PbTe, a typical Dirac electron system. Contrary to popular belief, we show that the spin-splitting parameter M, which is the ratio of the Zeeman to cyclotron energy, exhibits a remarkable magnetic-field dependence. This field dependence can rectify the existing discrepancy between experimental and theoretical results. We also show that M evaluated from the fan diagram plot is different from that determined as the ratio of the Zeeman to cyclotron energy, which also overturns common belief.

Thermodynamic evidence of magnetic-field-induced complete valley polarization in bismuth

We investigated the fundamental physical properties in the ultra-quantum limit state of bismuth through measurements of magnetoresistance, magnetization, magnetostriction, and ultrasound attenuation in magnetic fields up to 60T. For magnetic fields applied along the bisectrix direction of a single crystal, a drastic sign reversal in magnetostriction was observed at approximately 39T, which could be ascribed to the complete valley polarization in the electron Fermi pockets. The application of magnetic fields along the binary direction presented an anomalous feature at approximately 50T only in the magnetoresistance. The emergence of a field-induced splitting of a valley was proposed as a possible origin of this anomaly.