The Excitonic State at the Semiconductor-Semimetal Transition
10.1016/s0081-1947(08)60740-7
Crossref book-chapter
Elsevier
Solid State Physics (78)
Bibliography

Halperin, B. I., & Rice, T. M. (1968). The Excitonic State at the Semiconductor-Semimetal Transition. Solid State Physics, 115–192.

Authors 2
  1. B.I. Halperin (first)
  2. T.M. Rice (additional)
References 74 Referenced 277
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  15. The exciton binding energy should vary as e−2, and e is expected to be roughly proportional to Ed−2 (see Penn12). The decrease in effective mass often associated with small Ed may decrease tho exciton binding energy still further.
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  21. A semiconductor-semimetal transition, with an intermediate excitonic distorted phase, may also be possible for a direct band-gap semiconductor, if the bands have proper symmetry (see des Cloizeaux3). The distorted phase in such a system would involve a change in crystal symmetry but not a discontinuous change in the crystal period. We shall not discuss the direct gap case here.
  22. The possibilities of charge-density oscillation and spin-density oscillation were first suggested by des Cloizeaux3 and by Kozlov and Maksimov,4 respectively.
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  37. The transport of spin, which is conserved in the absence of spin-orbit and magnetic forces, will be considered in Part IX, Section 20.
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  40. Equation (12) of Kozlov and Maksimov31 actually yields zero energy current when properly summed over the Brillouin zone, because the summand is the gradient of a periodic function of wave vector.
  41. Furthermore, as was pointed out by Jérome et al.9 true heat transport requires the transport of entropy, and entropy is never carried by a supercurrent.
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  51. In particular, wo note that the transformation (13.1) treats the electron pocket index (± w) on a footing different from the conduction electron spin index. In the dominant-term approximation, however, these two indices are completely equivalent, as is discussed at the end of Part IX, Section 19.
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  61. Binding can occur only if the electron pair and the positron pair both form spin singlets, so that there is no Pauli exclusion principle repulsion between the atoms.
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  63. The paper of Keldysh and Kozlov57 on the low-density exciton gas cannot be correct in the true low-density limit because it neglects this binding.
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  66. According to Hylleraas and Ore,53 we have EBB/EB ≤ 0.02 for the equal mass case.
  67. If the interaction between exciton molecules is essentially repulsive, the interaction between a free exciton and a sea of molecules is probably also repulsive. The energy necessary to place an exciton in the lowest momentum state is therefore increased by the fluid and will still be positive at ETG = EB Note also that EG, the minimum energy for addition of two free; charged carriers, will be less than ETG in the neighborhood of the transition. An electron e and a hole h can combine with an exciton molecule e2h2 to form two charged species e2h and h2e with a net reduction in energy.
  68. Because a pressure-induced first-order transition in a real (compressible) crystal is always accompanied by a discontinuous change of lattice parameter, there will be a range of values of ETG about EB + μL for which the lattice is unstable. The possibility for the crystal under pressure to gain free energy by a lattice contraction will increase the tendency toward first-order transitions and will also increase the size of any discontinuities as compared with transitions in the electron-hole gas in a hypothetical crystal of fixed lattice constant.
  69. The possibility that such a state might occur near the semimetal-semiconductor transition of a crystal such as Bi, whirh hits heavy holes and light electrons, was suggested to us by C. Herring.
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  71. The relative phases are fixed in aecord with (11.7), i.e., ratios of the quantities i (A0), (A1), (A2) and (A3) must all be real.
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  74. A discussion of antiferromagnetic spin waves from a hydrodynamic point of view will be found in B. I. Halperin and P. C. Hobenberg (to be published).
Dates
Type When
Created 17 years, 2 months ago (May 30, 2008, 4:45 a.m.)
Deposited 6 years, 7 months ago (Dec. 28, 2018, 1:25 a.m.)
Indexed 2 weeks, 6 days ago (Aug. 2, 2025, 1:22 a.m.)
Issued 57 years, 7 months ago (Jan. 1, 1968)
Published 57 years, 7 months ago (Jan. 1, 1968)
Published Print 57 years, 7 months ago (Jan. 1, 1968)
Funders 0

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@inbook{Halperin_1968, title={The Excitonic State at the Semiconductor-Semimetal Transition}, ISSN={0081-1947}, url={http://dx.doi.org/10.1016/s0081-1947(08)60740-7}, DOI={10.1016/s0081-1947(08)60740-7}, booktitle={Solid State Physics}, publisher={Elsevier}, author={Halperin, B.I. and Rice, T.M.}, year={1968}, pages={115–192} }