The<i>g</i>-factor and de haas-van alphen effect of electrons in bismuth

Cohen, Morrel H.; Blount, E. I.

doi:10.1080/14786436008243294

Cited by 260 publications

(108 citation statements)

References 18 publications

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“…The spin-orbit coupling introduces an interaction energy of λL⋅S, leading to an effective g-factor of g eff = g (1±λL⋅S/Δ) where Δ is the crystal field splitting and λ is the spin-orbital coupling constant [84]. Spin-orbit coupling is predicted to play a more important role in Dirac materials [85][86][87]. When the spin-orbit coupling and non-relativistic approximation are taken into account, the cyclotron energy is found to be equal to the Zeeman splitting energy derived from the Dirac equation [85][86][87], from which the g-factor is determined to be 2m 0 /m D where m 0 and m D represent free electron mass and Dirac electron mass respectively.…”

Section: Discussionmentioning

confidence: 99%

Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations

et al. 2017

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Section: Discussionmentioning

confidence: 99%

Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations

et al. 2017

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“…Since g * is quite large in bismuth, 20,71) the spin magneticmoment is also quite large, µ s ∼ 10 3 µ B . This large spin magnetic-moment can generate large spin responses such as in spin Hall effect and spin-polarized electric current.…”

Section: Anomalous Magnetic-momentmentioning

confidence: 99%

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

2015

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Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikovde 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 spinpolarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.

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“…50) To address the unusual electronic properties of Bi, an effective two-band model was constructed by Cohen and Blount in 1960. 51) In 1964, Wolff recognized that this two-band model can be transformed into the four-component massive Dirac Hamiltonian, and he presented an elegant analysis of the selection rules using the Dirac theory. 47) This was the beginning of the notion of Dirac fermions in solid states, although some of the peculiar physics of massless Dirac fermions were recognized in as early as 1956 by McClure in the context of graphite.…”

Section: Dirac Materialsmentioning

confidence: 99%

Topological Insulator Materials

2013

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Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on topological insulator materials with an emphasis on basic theory and materials properties. After presenting a historical perspective and basic theories of topological insulators, it discusses all the topological insulator materials discovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in which the author was involved. A summary is given for possible ways to confirm the topological nature in a candidate material. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulating samples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transport properties. In particular, the Dirac fermion physics and the resulting peculiar quantum oscillation patterns are discussed in detail. It is emphasized that proper analyses of quantum oscillations make it possible to unambiguously identify surface Dirac fermions through transport measurements. The prospects of topological insulator materials for elucidating novel quantum phenomena that await discovery conclude the review.

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Theg-factor and de haas-van alphen effect of electrons in bismuth

Cited by 260 publications

References 18 publications

Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations

Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Topological Insulator Materials

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