Band Edge Structure of PbS, PbSe, and PbTe

Wright, George B.

doi:10.1103/physrev.135.a821

Cited by 112 publications

(67 citation statements)

References 23 publications

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“…[16][17][18][19] In this model a pair of interband matrix elements P ʈ and P Ќ describe the strong nonspherical anisotropy of the conduction and valence bands at the L point of the Brillouin zone. The dispersion relations for the conduction and valence band energies are given by…”

Section: Discussionmentioning

confidence: 99%

Auger recombination dynamics of lead salts under picosecond free-electron-laser excitation

et al. 1998

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Pump-probe transmission experiments have been performed on PbSe above the fundamental absorption edge near 4 m in the temperature range 30 to 300 K, using the Dutch ps free-electron laser. For temperatures below 200 K and carrier densities above the threshold for stimulated emission, stimulated recombination represents the most efficient recombination mechanism with relatively fast kinetics in the 50-100-ps regime, in good agreement with earlier reports of photoluminescent emission. Above this temperature Auger recombination dominates, and the Auger coefficient C is determined from the pump-probe decay curves. In the lowtemperature regime the Auger coefficient is determined from the decay curves at times beyond 100 ps. The Auger coefficient is approximately constant ͑with a value of about 8ϫ10 Ϫ28 cm 6 s Ϫ1) between 300 and 70 K, and then drops a value of about 1ϫ10 Ϫ28 cm 6 s Ϫ1 at 30 K, in good agreement with the theory for nonparabolic near-mirror bands and nondegenerate statistics. It is found that C for PbSe is between one and two orders of magnitude lower than for Hg 1Ϫx Cd x Te of comparable band gap. ͓S0163-1829͑98͒07243-9͔

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Section: Discussionmentioning

confidence: 99%

Auger recombination dynamics of lead salts under picosecond free-electron-laser excitation

et al. 1998

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“…32 It is strong in PbTe, moderate in PbSe and absent or negligible in PbS. The ratio of the longitudinal component m along the Γ-L direction and the transverse component m ⊥ in the plane perpendicular to Γ-L is reported to be around 1.8 in PbSe.…”

Section: B the Real Part Of The Dielectric Functionmentioning

confidence: 97%

“…The ratio of the longitudinal component m along the Γ-L direction and the transverse component m ⊥ in the plane perpendicular to Γ-L is reported to be around 1.8 in PbSe. 32 This anisotropy is expected to decrease in the heavily doped case.…”

Section: B the Real Part Of The Dielectric Functionmentioning

confidence: 99%

Temperature-driven band inversion inPb0.77Sn0.23Se: Optical and Hall effect studies

et al. 2014

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Optical and Hall-effect measurements have been performed on single crystals of Pb0.77Sn0.23Se, a IV-VI mixed chalcogenide. The temperature dependent (10-300 K) reflectance was measured over 40-7000 cm −1 (5-870 meV) with an extension to 15,500 cm −1 (1.92 eV) at room temperature. The reflectance was fit to the Drude-Lorentz model using a single Drude component and several Lorentz oscillators. The optical properties at the measured temperatures were estimated via KramersKronig analysis as well as by a Drude-Lorentz fit. The carriers were p-type with the carrier density determined by Hall measurements. A signature of valence intraband transition is found in the lowenergy optical spectra. It is found that the valence-conduction band transition energy as well as the free-carrier effective mass reach minimum values at 100 K, suggesting temperature-driven band inversion in the material. Density functional theory calculation for the electronic band structure are also presented.

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“…These properties are very different from the isotropic M ∼ 1 in PbTe, although the T point of rhombohedral Bi has the equivalent symmetries to the L point of rocksalt PbTe [24]. This difference can be interpreted as the difference of the order of the band: the hole band of Bi has the T − 45 symmetry, which is equivalent to L − 45 , whereas that of PbTe has the L + 6 .…”

mentioning

confidence: 91%

“…For PbTe, the matrix elements with the L + 6 top valence band are given as [24] Figure 2. Sn content dependences of (a) the inverse mass, (b) the g-factor, and (c) the ratio of the Zeeman splitting to the cyclotron energy for the longitudinal ( ) and the perpendicular (⊥) direction of the magnetic field.…”

mentioning

confidence: 99%

Crystalline spin–orbit interaction and the Zeeman splitting in Pb_1−xSn_xTe

Hayasaka

Fuseya

2016

J. Phys.: Condens. Matter

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Abstract. The ratio of the Zeeman splitting to the cyclotron energy (M = ∆E Z / ω c ), which characterizes the relative strength of the spin-orbit interaction in crystals, is examined for the narrow gap IV-VI semiconductors PbTe, SnTe, and their alloy Pb 1−x Sn x Te on the basis of the multiband k · p theory. The inverse mass α, the g-factor g, and M are calculated numerically by employing the relativistic empirical tight-binding band calculation. On the other hand, a simple but exact formula of M is obtained for the six-band model based on the group theoretical analysis. It is shown that M < 1 for PbTe and M > 1 for SnTe, which are interpreted in terms of the relevance of the interband couplings due to the crystalline spin-orbit interaction. It is clarified both analytically and numerically that M = 1 just at the band inversion point, where the transition from trivial to nontrivial topological crystalline insulator occurs. By using this property, one can detect the transition point only with the bulk measurements. It is also proposed that M is useful to evaluate quantitatively a degree of the Dirac electrons in solids.The spin-orbit interaction (SOI) affects the eigenstate of electrons in solids in a variety of ways. It strongly depends on the crystal structure and the momentum of the carrier. One of the most fundamental such effects is the modification of the band structure. For example, in semiconductors of the diamond and zincblende structures, the band modification can be characterized by the spin-orbit splitting energy. But this is not the whole information of the crystalline SOI. Another important information can be obtained under a magnetic field, where we cannot attain to only with the band calculations. The one-body Hamiltonian under the magnetic field can be separated into two part in general: the symmetric and the antisymmetric part with respect to the commutation of the kinematical momentum operator [1,2,3,4,5]. The eigenenergy of the symmetric part is given in terms of the cyclotron energy as ω c (n + 1/2) with an anisotropic cyclotron mass. The eigenenergy of the antisymmetric part is given by the Zeeman energy with an anisotropic g-factor. This Zeeman energy does not originate from the bare electron spins, but originates from the orbital motion of electrons. The antisymmetric part is relevant only in the case with the sizable crystalline SOI. Therefore, the effect of the crystalline SOI is clearly reflected by the antisymmetric part, whose relative strength is characterized by the ratio of the Zeeman splitting to

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Band Edge Structure of PbS, PbSe, and PbTe

Cited by 112 publications

References 23 publications

Auger recombination dynamics of lead salts under picosecond free-electron-laser excitation

Auger recombination dynamics of lead salts under picosecond free-electron-laser excitation

Temperature-driven band inversion inPb0.77Sn0.23Se: Optical and Hall effect studies

Crystalline spin–orbit interaction and the Zeeman splitting in Pb_1−xSn_xTe

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Band Edge Structure of PbS, PbSe, and PbTe

Cited by 112 publications

References 23 publications

Auger recombination dynamics of lead salts under picosecond free-electron-laser excitation

Auger recombination dynamics of lead salts under picosecond free-electron-laser excitation

Temperature-driven band inversion inPb0.77Sn0.23Se: Optical and Hall effect studies

Crystalline spin–orbit interaction and the Zeeman splitting in Pb1−xSnxTe

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Crystalline spin–orbit interaction and the Zeeman splitting in Pb_1−xSn_xTe