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Basics of Semiconductor and Spin Physics

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Spin Physics in Semiconductors

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 157))

Abstract

This introductory chapter is mainly addressed to readers new to the field.

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Notes

  1. 1.

    A special care is taken to indicate who has done what and when, since there exists much confusion on these matters in the current literature.

  2. 2.

    It is often stated that the origin of spin-orbit interaction is relativistic and quantum-mechanical. This is true in the sense that it can be derived from the relativistic Dirac equation by keeping terms on the order of \(1/c^2\). However, the above formula \(\varvec{B} = (1/c)\varvec{E} \times \varvec{v}\) is not relativistic: one does not need the theory of relativity to understand that, when moving with respect to a stationary charge, a current, and hence a magnetic field will be seen. Given, that the electron has a magnetic moment, the spin-orbit interaction follows directly. It is also not really quantum-mechanical: a classical object having a magnetic moment would experience the same interaction. The only place where quantum mechanics enters, is the value of the electron magnetic moment and, of course, the fact that the electron spin is 1/2.

  3. 3.

    In fact the interaction energy derived in this simple-minded way should be cut into half (the “Thomas’s one half” [6]) if one takes properly into account that, because of the electron acceleration in the electric field of the nucleus, its moving frame is not inertial. This finding, made in 1926, resolved the factor of 2 discrepancy between the measured and previously calculated fine structure splittings.

  4. 4.

    Interestingly, General Relativity predicts spin-orbit effects (on the order of \((v/c)^2\)) in the motion of planets. Thus the “spin” of the Earth should make a slow precession around its orbital angular momentum.

  5. 5.

    A small part of the excited electrons can emit photons before loosing their energy by thermalization. The studies of the spectrum and polarization properties of this so-called hot luminescence reveal interesting and unusual physics, see [10, 11].

  6. 6.

    More accurately, one should use the Hamiltonian in (1.3), which takes care of the warping of iso-energetic surfaces. In fact, the energy spectrum depends on the growth direction, and on the orientation of the vector \(\varvec{p}\) in the xy plane with respect to the crystal axes. However the general properties of the spectrum are the same.

  7. 7.

    In most of the current literature (as well as in some chapters of this book) this expression is called “Rashba term” or “Rashba interaction”. Rather, it should be referred to as Rashba-Sheka term. There is no good reason for ignoring one of the authors, it is unfair and incorrect.

  8. 8.

    In many publications [28, 29] are erroneously cited as the origin of the “Rashba term” in 2D. Meanwhile, in [28] (but not in the better known [29]) the authors correctly attribute this result to Vasko [25], although do not mention the work of Ohkawa and Uemura [24].

  9. 9.

    It has become a bad habit to label the two terms as “Rashba” and “Dresselhaus” terms, without any good reason or justification: the results given by (1.9 - 1.11), for 2D structures were not known prior to the publications in [24, 25, 30] and neither Rashba, nor Dresselhaus have introduced any linear in \(\varvec{p}\) terms for the 2D case (Rashba and Sheka have derived such terms in bulk wurtzite-type crystals, Dresselhaus had no linear terms at all). The normal practice is to give credit to those who have in fact obtained previously unknown results.

  10. 10.

    The reason is that the z projection of the spin is rotated by both x and y components of the random field, while the x spin projection is influenced by the y component only, since the z component of the random field is zero.

  11. 11.

    In fact, the normal spin component will slowly decay because of the small cubic in \(\varvec{p}\) Dresselhaus terms, which were neglected in deriving (1.12). Experimentally, a \(\sim 20\) times suppression of the relaxation rate for the z spin component in \(\langle 110\rangle \) quantum wells was observed by Ohno et al. [42].

  12. 12.

    Bernevig et al. [31] have explained their result as a consequence of the exact SU(2) symmetry in special cases and used the Keldysh formalism. Here a more pedestrian qualitative explanation is given.

  13. 13.

    I thank S. Ganichev and E. Ivchenko for an illuminating discussion of this issue.

  14. 14.

    Probably, because announcing a new effect is more exciting than digging into literature to find out that it is already known.

  15. 15.

    Some of the labels used are: current-induced spin polarization (CISP), inverse spin-galvanic effect (ISGE), current-induced spin accumulation (CISA), magneto-electric effect (MEE), kinetic magneto-electric effect (KMEE), Edelstein effect (EE), inverse Edelstein effect (IEE), and even Rashba-Edelstein effect (REE).

  16. 16.

    The concept of a mean nuclear magnetic field is well justified for electrons in semiconductors, either moving freely in the conduction band or localized on a shallow donor. Thus, for a shallow donor in GaAs the Bohr radius is around 10 nm, so that about \(10^5\) lattice nuclei are simultaneously seen by a localized electron.

  17. 17.

    As it was pointed out in Sect. 1.2, the magnetic dipole-dipole interaction between electron spins can be usually neglected. Given that a similar interaction between nuclear spins is about a million times smaller, it may seem strange that this interaction may be of any importance. The answer comes when we consider the extremely long time scale in the nuclear spin system (seconds or more) compared to the characteristic times for the electron spin system (nanoseconds or less).

  18. 18.

    It should be noticed that obtaining a high degree of nuclear polarization in solids is a very desirable goal for experimental nuclear and particle physics.

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Dyakonov, M.I. (2017). Basics of Semiconductor and Spin Physics. In: Dyakonov, M. (eds) Spin Physics in Semiconductors. Springer Series in Solid-State Sciences, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-65436-2_1

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