Motion of Electrons and Holes in Perturbed Periodic Fields

Luttinger, J. M.; Kohn, W.

doi:10.1103/physrev.97.869

Cited by 2,947 publications

(1,476 citation statements)

References 19 publications

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“…Here we introduce the method of Luttinger and Kohn, 75) which clearly represents the essence of the k · p theory. Let H be the Hamiltonian of the electron in a periodic potential with spin-orbit interaction as…”

Section: K · P Theory In the Luttinger-kohn Representationmentioning

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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Section: K · P Theory In the Luttinger-kohn Representationmentioning

confidence: 99%

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

2015

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“…Further insight of these results can be obtained within the so called effective mass description, that can be formally derived from the kp theory of the energy bands. This technique had tremendous importance in the description of semiconductors 74 . In practical matters, it amounts to replace q in equation (4) by the momentum operator.…”

Section: A Electronic Statesmentioning

confidence: 99%

Edge states in graphene-like systems

2015

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The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional Quantum Hall effect, the Quantum Anomalous Hall (QAH) and the Quantum Spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.

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“…For systems with spin-orbit coupling the KohnLuttinger Hamiltonian [9] is derived in the basis of total angular momentum eigenstates with j = 3/2 and 1/2, and m j = −j, −j + 1, ..., j. The manybody interaction Hamiltonian in this basis can be written as…”

Section: Exchange and Correlations In Realistic Valence Bandsmentioning

confidence: 99%

Hole–hole correlation effects on magnetic properties of Mn III1−V diluted magnetic semiconductors

Jungwirth

Lee

MacDonald

2001

Physica E: Low-dimensional Systems and Nanostructures

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The mean-field theory represents a useful starting point for studying carrier-induced ferromagnetism in MnxIII1−xV diluted magnetic semiconductors. A detail description of these systems requires to include correlations in the many-body hole system. We discuss the effects of correlations among itinerant carriers on magnetic properties of bulk MnxIII1−xV and magnetic semiconductor quantum wells. Presented results were obtained using parabolic band approximation and we also derive a many-body perturbation technique that allows to account for hole-hole correlations in realistic semiconductor valence bands.

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Motion of Electrons and Holes in Perturbed Periodic Fields

Cited by 2,947 publications

References 19 publications

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Edge states in graphene-like systems

Hole–hole correlation effects on magnetic properties of Mn III1−V diluted magnetic semiconductors

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