######
Emmanuel Iosifovich Rashba
(A Brief Biographical Sketch)

Emmanuel Iosifovich Rashba was born in Kyiv in 1927 (October 30). In 1949 he graduated from the Physics Dept. of Kyiv State University, where he attended lectures by Profs. N.N. Bogolyubov, A.S. Davydov, S.I. Pekar, K.B.Tolpygo. At the university, his scientific work was supervised by A.S. Davydov and S.I. Pekar. After graduating the university, he worked for several years as an engineer and teacher but in his spare time he was engaged in theoretical studies of excitons.

In 1954, E.I. Rashba was admitted to the Dept. of Semiconductors (leaded by Prof. V.E. Lashkarev) at the Institute of Physics (IP) of the Academy of Sciences of the Ukrainian SSR, where he worked closely with experimentalists and developed (with K.B. Tolpygo) the theory of current carrier transport in semiconductors. One of the important results obtained by them was the description of the current-voltage characteristics of rectifying diodes and *p-n* junctions in the limit of large biases (under the dissipative transport the currents are proportional to the square of the applied voltage) [1,2].

At the same time E.I. Rashba continued his research on excitons [3]. In 1956, based on these results, he defended his Ph.D. thesis under supervision of A.S. Davydov. Further research on the theory of molecular excitons was stimulated by new experimental results obtained in the Dept. of Spectroscopy (headed by Prof. A.F. Prikhot’ko) of the IP. One such result is the discovery of spectral bands with anomalous absorption, which ones could not be directly attributed to excitons, however manifested a significant exciton-like polarization picture. E.I. Rashba explained the behavior of these spectra by constructing a theory of weakly coupled localized excitons. He has found that the polarization and intensity of the impurity bands show strong anomalies when they are close to the actual exciton bands [4]. Later, already at the Institute of Semiconductors (IS) of the Academy of Sciences of the UkrSSR founded in 1960, a similar phenomenon was studied by E.I. Rashba for Wannier-Mott excitons. In spectroscopy of crystals this effect – a giant increase in the strength of the oscillator – is called as the *Rashba effect*. Next years E.I. Rashba continued to take an interest in and study exciton phenomena within the IS.

In 1966, for his work on the theory of excitons in crystals, Prof. E.I. Rashba has received the highest in the USSR Award – Lenin’s Prize, which included E.F. Gross, B.P., Zakharchenya, and A.A. Kaplyansky – researchers from S’t Petersburg (former Leningrad) A.F. Ioffe Institute of Physics and Technology) and also A.S. Davydov, A.F. Prikhot’ko, V.L. Broude, A.F. Lubchenko and M.S. Brodyn from IP.

Because of experimental investigations in the IP concentrated mainly on studying the kinetics of photoconductivity in hexagonal A_{2}B_{6} crystals of the CdS type E.I. Rashba focused on the features of the optical spectra of these crystals. For this it was necessary to study and apply the group theory. As a result, a complete analysis of the electron band structure of crystals without an inversion center was given including, particularly, the spin-orbit interaction (SOI) [5, 6].

These – pioneering in all senses – results deserve special description.

Prior to the work of E.I. Rashba, no separate attention was paid to SOI in crystals. There was one work by G. Dresselhaus [7], where the Hamiltonian of the SOI was introduced in the form proportional to the cube of the carrier wave vector. In the work of E.I. Rashba, the term describing this interaction linear in the wave vector was first obtained and substantiated. This result made it possible to predict a new resonance arising under the action of an electric field and leading to a spin flip [8].

The studies of SOI had quickly led to the prediction of the combined resonance, in which the spin-orbit coupling, which results in "entanglement" of motion in the real and spin spaces, makes possible a new type of transition excited by the electric vector of the high-frequency field and accompanied by a change in the effective spin momentum. In the intensity the combined resonance can significantly exceed the paramagnetic one, and the resonance is especially strong in crystals without an inversion symmetry; its frequencies are equal to linear combinations of paramagnetic and cyclotron resonance frequencies.

Having begun at the IP, E.I. Rashba’s work on SOI was continued at the IS. The SOI also leads to the emergence of the unusual quasiparticle (electron or hole) band structure, at which the energy extremum is reached on a circle – a loop of extrema, thus isoenergetic surfaces for small values of energy are toroіds. The electronic properties of such semiconductors are very specific, in particular, a significant number of carriers can have a negative effective mass [9]. Other phenomena associated with the SOI in crystals without an inversion center have also been predicted and have become a standard method for measuring of spin-orbit coupling velue.

The most complete review of experimental and theoretical results on the combined resonance and close effects was given by E.I. Rashba and V.I. Sheka in monograph *“Landau Level Spectroscopy”*, Ed. by G. Landwehr and E.I. Rashba (N.Y., Elsevier, 1991, p. 178). The pioneering work of E.I. Rashba on the combined resonance in semiconductor crystals in crystals was officially recognized as a discovery in the former USSR.

The next step in the theory of SOI was made by E.I. Rashba and Yu.A. Bychkov who generalized this interaction in paper [10]. Their work forms the basis for development of physics of the SOI in low-dimensional systems.

More than 30 years later, the E.I. Rashba theory of the SOI was used in the first experiment on the “spin transistor” [11], where it was proposed to control the spin precession with the help of electrical field. Due to this work the rapid development of a new discipline – *spintronics *– the physics of processes and devices based on the spin control, began. It became possible to expand the functionality of existing electronic devices by the use additional degree of freedom – the spin, to develop principles of new nanosize semiconductor devices, particularly for quantum computations. Without any doubt, the works of E.I. Rashba are now among the most cited in the scientific literature on solids – especially semiconductors and semiconductor devices.

It is necessary to point out a few of size effects, which bears the name of Rashba. The first one is the electric pinch effect in anisotropic bipolar materials – the field-controlled accumulation of electrons and holes near one of the semiconductor surfaces. Another important and unexpected phenomenon is related to manifestation of features of complex band structure in the electron transport. Specifically, for multi-valley crystals E.I. Rashba noted that distinct transport anisotropy of carriers belonging to different valleys facilitates their spatial separation [12] under an electric field in samples of restricted geometries (*multi-valley Rashba-size effect*). In strong electric field this effect leads to formation of spatial domains populated dominantly by the electrons from one of the valleys [13, 14].

It is pertinent to note that, the interest of E.I. Rashba to manifestation of the features of electron band structures in carrier transport has involving by him Ukrainian researchers, in particular from Bogolyubov Institute for theoretical physics National Academy of Sciences (NAS) of Ukraine, to this subject where the SOI is studied relying on the Dirac equation, rather than the Schrödinger or Pauli ones, which made it possible to find out some previously unknown conditions for the manifestation of SOI.

In 1967 E.I. Rashba was invited to the L.D. Landau Institute of Theoretical Physics, where he headed the Dept. of Semiconductor Theory. He continued an active research career, combining it with work in the most prestigious physics journals in the USSR where he worked from 1973 to 1988. He maintained and still maintains active ties with Ukrainian physicists. His contribution to the development of science in Ukraine was appreciated by awarding him in 2007 the S.I. Pekar Prize of the NAS of Ukraine for outstanding achievements in the field of solid state theory. In 1987, he received the prestigious A.F. Ioffe Prize of the USSR Academy of Sciences, Sie Neville Mott Prize (2005), Oliver Buckly Prize (2022)

In 1991, E.I. Rashba moved to the USA, where he continues to work actively as a professor at Harvard University, also being an honorary professor at a number of other prestigious US universities. He is a Fellow of the American Physical Society His scientific authority is enormous, he has been awarded a number of high level international scientific awards, international conferences are held in his honor. Among them Alan Berman Res. Publ. Award of Naval Res. Lab (USA) – 2001; Symposium in Honor of E.I. Rashba (Boston) – 2002; NATO Adv. Res. Workshop on Frontiers of Spintronics & Optics – 2004;; Symposium in Honor of E.I. Rashba, Frontiers of Spintronics, Cambridge (USA) – 2008); Special issue of the “International Journal on Superconductivity and Magnetism” Frontiers of Spintronics and Optics in Semiconductors: In Honor of E.I. Rashba, v. 16, No. 4, (2003); the Sir Nevill Mott Lecture (United Kingdom) – 2005; Arkady Aronov Lectureships (Israel) – 2005; Oliver Buckly Prize (USA) – 2022.

Now Rashba's name became the well-known terms such as *Rashba effect* – a giant increase in the strength of the oscillator of some quantum transitions, *Rashba Hamiltonian, Rashba spin-orbital interaction, size Rashba effects*, etc., which are the parts of the titles of about 4000 scientific papers in which the references on his original papers can be absent. Nevertheless, according to Scopus DB, paper [8] is the most cited and paper [10] is the second most cited of the papers published in these journals, respectively.

###### The most cited E.I. Rashba’s papers

- E.I. Rashba and K.B. Tolpygo. JTF, v. 26. p. 1419 (1956).
- E.I. Rashba and A.I. Nosar. JTF, v. 27. p. 1431 (1957).
- E.I. Rashba. Optics and spektrosk, v. 2, p. 75 (1957).
- E.I. Rashba. Optics and Spektrosk, v. 2, p. 568, (1957).
- E.I. Rashba. Sov. Phys. Solid State, v. 1, p. 368 (1959).
- E.I. Rashba and V.I. Sheka. Sov. Phys. Solid State – Collected Papers, v. II, p. 162 (1959).
- G. Dresselhaus. Phys. Rev., v.100, p. 580 (1955).
- E.I. Rashba. Sov. Phys. Solid State, v. 2, p. 1224 (1960).
- I.I. Boiko and E.I. Rashba. Sov. Phys. Solid State, v. 2, p. 1692 (1960).
- Yu.A. Bychkov and E.I. Rashba. JETP Lett., v. 39, p. 66 (1984).
- S. Datta and B. Das. Appl. Phys. Lett., v. 56, p. 665 (1990).
- E.I. Rashba. Sov. Phys. JETP v. 21(5), p. 954 (1965).
- E.I. Rashba, I.I. Boyko, V.A. Kochelap, Z.S. Gribnikov, and V.A. Zhadko. Journ. Phys.Soc. Japan, v. 21, Supplement, p. 351 (1966).
- Z.S. Gribnikov, V.A. Kochelap, and E.I. Rashba. Sov. Phys. JETP, v. 24(1), p. 178 (1966).