Magnetoreflection Studies in Bismuth

Maltz, Martin; Dresselhaus, M. S.

doi:10.1103/physrevb.2.2877

Cited by 90 publications

(28 citation statements)

References 10 publications

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“…In fact, the magneto-optical measurements on bismuth already exhibit clear peak structures. 26,[32][33][34] The present proposal of SPEC will be confirmed experimentally, e.g., by the ordinary magneto-optical measurements with the use of the Kerr effect. 115) When we compare the theoretical results for bismuth with the experiments, we need to consider the contribution from the holes at T -point in general.…”

Section: % Spin-polarized Electric Current (Spec)supporting

confidence: 52%

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: % Spin-polarized Electric Current (Spec)supporting

confidence: 52%

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

2015

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“…1b. Quite a few (far)infrared magneto-optical studies have been carried out to study band parameters, Landau level transitions and selection rules in Bi [19][20][21][22][23][24][25][26][27][28][29][30]. However these were limited to selected wavelengths or, when spectroscopy was done, the polarisation dependence was not measured [31,32].…”

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confidence: 99%

Suppressed Magnetic Circular Dichroism and Valley-Selective Magnetoabsorption due to the Effective Mass Anisotropy in Bismuth

et al. 2016

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We have measured the far-infrared reflectivity and Kerr angle spectra on a high-quality crystal of pure semimetallic bismuth as a function of magnetic field, from which we extract the conductivity for left-and right handed circular polarisations. The high spectral resolution allows us to separate the intraband Landau level transitions for electrons and holes. The hole transition exhibits 100% magnetic circular dichroism, it appears only for one polarisation as expected for a circular cyclotron orbit. However the dichroism for electron transitions is reduced to only 13 ± 1%, which is quantitatively explained by the large effective mass anisotropy of the electron pockets of the Fermi surface. This observation is a signature of the mismatch between the metric experienced by the photons and the electrons. It allows for a contactless measurement of the effective mass anisotropy and provides a direction towards valley polarised magneto-optical pumping with elliptically polarised light.Circular dichroism, the property of materials to interact differently with left and right circularly polarised light is associated with symmetry breaking due to e.g. molecular chirality, spontaneous magnetisation or an external magnetic field. A charged particle in a magnetic field moves in a circular orbit perpendicular to that field. Radiation propagating parallel to the field is only absorbed by that particle for right or left circular polarisation, leading to 100% magnetic circular dichroism. In condensed matter, the behaviour of charge carriers in a lattice is described using an effective mass, which can be very different from the free-electron mass, but also strongly anisotropic [1]. In the latter case the cyclotron orbits become elliptical which, as we will show, strongly reduces the magnetic circular dichroism. The reduction of magnetic circular dichroism can thus be regarded as a manifestation of the mismatch between the metric experienced by photons (isotropic) and the electrons (anisotropic), which becomes apparent when they interact [2-4]. As a consequence, elliptically polarised light with the same ellipticity as an electron pocket can cause a 100% valley polarised magneto-optical absorption.Bismuth is a canonical semimetal which possesses a rich electronic structure with strong spin-orbit interaction, low carrier density, long mean-free path and small cyclotron mass [5][6][7][8] (Fig. 1a). A hole pocket is oriented along the trigonal axis, where the bands are almost parabolic.Three electron pockets are tilted 6• from the plane perpendicular to the trigonal axis and have a Dirac-like band dispersion. In this plane the dielectric function is isotropic. A magnetic field parallel to the trigonal axis combined with light propagating along the same axis therefore presents an ideal case to measure the dichroism in relation to the effective mass. For holes the mass is isotropic in the plane whereas for electrons it is strongly anisotropic (a factor > 200 [18]), leading to a strong dichroism contrast between electron and hole transi...

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“…This brings into prominence a light-hole band that is separated from the light-electron band by a direct gap of about 11 meV. The existence of such a band was predicted theoretically by Mase [l], Cohen [ 2 ] , and Golin [3] and has been confirmed experimentally by the magneto-optical work of Engeler [4] and Brown et al [5], by the tunnelling studies of Esaki [6], and by the magneto-reflection studies of Maltz and Dresselhaus [7]. The low-field galvanomagnetic investigations of Morimoto and Takamura We have carried out a number of thermo-galvanomagnetic measurements on single-crystal Bi containing about 0.24 at "/b Sn between liquid helium and room temperature.…”

Section: Introductionmentioning

confidence: 84%

Thermomagnetic effects in tin‐doped bismuth

Uher

Goldsmid

Drabble

1975

Physica Status Solidi (b)

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Several of the thermo-galvanomagnetic phenomena have been studied for bismuth doped with about 0.24 atyo Sn in the temperature range from about 5 to 300 K. The Hall coefficient, magneto-resistance, Seebeck coefficient, Nernst coefficient, and thermal conductivity have been measured in magnetic fields of u p to about 6 T with current flow in the trigonal and bisectrix directions. The most remarkable observation has been that of a negative Seebeck coefficient for a range of temperatures well below that a t which electrons in the main conduction band should be excited. A group of electrons, possibly closely associated with the light hole band, is invoked t o explain the results.Mehrere thermo-galvanische Erscheinungen wurden an Wismut, dem 0,24 At yo Zinn beigefiigt war, im Temperaturbereich yon ungefahr 5 bis 300 K untersucht. Hallkoeffizient, Magnetowiderstand, Seebeckkoeffizient, Nernstkoeffizient und Warmeleitfahigkeit wurden in Magnetfeldern bis zu 6 T bei StromfluB in Richtung der trigonalen Achse und der Bisektrix gemessen. Am bemerkenswertesten ist die Beobachtung cines negativen Seebeckkoeffizienten in einem Temperaturbereich, der betrachtlich unter dem liegt, bei dem Elektronen im Hauptleitungsband angeregt werden sollten. Eine Gruppe von Elektronen, die moglicherweise mit dem Band leichter Locher verknupft ist, wird zur Erklarung der Ergebnisse herangezogen.

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Magnetoreflection Studies in Bismuth

Cited by 90 publications

References 10 publications

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Suppressed Magnetic Circular Dichroism and Valley-Selective Magnetoabsorption due to the Effective Mass Anisotropy in Bismuth

Thermomagnetic effects in tin‐doped bismuth

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