Infrared Magnetoreflection in Bismuth. I. High Fields

Thermoelectric power in carbon nanotubes and quantum wires of nonlinear optical, optoelectronic, and related materials under strong magnetic field: Simplified theory and relative comparison

“…109 Also under the condition E g → ϱ, the above equation gets simplified to the well-known form of parabolic energy bands as E = ប 2 k 2 / 2m * . The TPM has been studied for QWs of II-VI, IV-VI, stressed materials, n-GaP, p-PtSb 2 , and n-GaSb compounds in accordance with the models of Hopfield, 93 Dimmock, 94 Seiler, 95 Rees, 96 99 and the ellipsoidal parabolic model, 98 respectively. It is important to note that under certain limiting conditions, all the results for all the models derived here have transformed into the well-known classical TPM equation valid for nondegenerate semiconductors having parabolic energy bands.…”

“…The corresponding results for the QWs of III-V, ternary, and quaternary compounds form a special case of our generalized analysis. The TPM has also been studied for QWs of II-VI, IV-VI, stressed materials, n-GaP, p-PtSb 2 , and n-GaSb compounds by using the models of Hopfield, 93 Dimmock, 94 Seiler, 95 Rees, 96 99 and the parabolic ellipsoidal model, 98 respectively. The well-known expression of the TPM of wide gap materials has been obtained as a special case of our generalized analysis under certain limiting conditions from all the results.…”

“…Shoenberg 97 indicated that the de Haas-Van Alphen and cyclotron resonance experiments supported the one-band model, although the latter work showed that Bi could be described by the two-band nonparabolic ellipsoidal Lax model since the magnetic field dependence of many physical parameters of Bi supports the above model. 99 The magnetooptical results 100 and the ultrasonic quantum oscillation data 101 107 presented a new model of Bi that fits the data for a large number of magneto-oscillatory and resonance experiments. In Sec.…”

Magneto-optical Kramers-Kronig analysis

“…These properties, combined with a strong spin-orbit interaction, give rise to spectacular magneto-optical effects [27][28][29][30][31] . While some classical phenomena, such as quantum oscillations 32,33 , were first discovered in bismuth, a number of new phenomena were recently found in it and in related compounds, such as a transition to a 3D topological insulating state upon Sb substitution 34 , a valley-ferromagnetic state 36 , a valleynematic Fermi liquid state 37 and avoided Lifshitz-type semimetal-semiconductor transition 35 .…”

Finite- and Quantum-Size Effects of Bismuth Nanowires

“…Note that the valence and the conduction band at the L-point are strongly coupled leading to an increasing electron effective mass with increasing band gap. The dispersion relation for the L-point bands is described by the Lax two-band model (Lax et al, 1960) (see equation (5)). For interband transitions, transitions between the n-th valence subband to the n-th conduction subband are allowed, where |<v|p|c>| is the coupling between the valence subband v and conduction subband c, and m e is the free electron mass.…”