Physical Review B

The Rashba effect is the cornerstone of fascinating quantum phenomena like spin-charge conversion via the Edelstein effect and its inverse, the spin-Hall effect and its inverse, etc. These have proved to be the foundation for spintronics. However, much of these effects focused on the diffusive regime of electron motion. In spin-orbit coupled systems of the Rashba type, there is a special type of collective spin excitations, known as chiral-spin modes (CSMs). Here, the authors demonstrate that if such systems are probed close to the frequency of the CSMs, the spin-charge conversion effects exhibit a resonant enhancement. Using the polarization properties of the CSMs, the authors also suggest an architecture for spin pumping using THz pulses without the use of magnetic materials that offers control over the polarization of the injected spins. This work offers an avenue to push spintronics to the THz regime.

Emmanuel Rashba was an innovator throughout his long and industrious career, which spanned seven decades from the 1950s to the 2010s. Here, the author reviews the physics of spin-deflection coupling and recounts the state of the field that led Rashba to propose this new form of spin-orbit coupling in 2010. Through this mechanism, electron spins in low-dimensional materials couple directly to local deflections, rather than to deformations as in previously studied spin-orbit coupling mechanisms. This feature yields stronger coupling of spin to lattice vibrations at long wavelengths, and was invoked to explain a pronounced maximum of the spin relaxation rate observed near a narrow avoided crossing in the spectrum of single electron carbon nanotube quantum dots.

The authors have developed a six-band k·p model of chiral (1, 1/2)-fermions in semimetals of the $T$ cubic point group symmetry. Here, the model is used to describe the electronic structure, optical absorption, and photocurrent in chiral multifold silicides like RhSi. The effective Hamiltonian incorporates spin-orbit coupling between the orbital momentum $L$ = 1 and spin 1/2 as well as the linear-in-wavevector Rashba term, which is essential for the circular photogalvanic effect. Parameterized using tight-binding calculations, the model accurately reproduces the low-energy band structure. The authors also compute the intersubband absorption spectrum and the circular photocurrent, demonstrating a quantized low-frequency response governed by a topological charge of four and revealing deviations from the universal value with increasing the light frequency.

A current of spin polarized electrons is injected into a Rashba two-dimensional system at the source electrode. Carriers move with ballistic trajectories and weakly relativistic velocity along the channel and the spin orientation is detected at the drain. The carriers precess coherently under the influence of an electric field $\mathbf{\text{E}}$ provided by a gate voltage. The precession is demonstrated in two ways. 1) Record the drain voltage as $\mathbf{\text{E}}$ varies from zero to values resulting in precession more than a full wavelength. 2) Keep $\mathbf{\text{E}}$ constant and record the drain voltage for multiple values of channel length L, concluding with L greater than $\lambda$. This unique precession occurs because of a special relativistic transformation of E, providing a magnetic field ${\mathbf{\text{H}}}^{*}$.

Rashba spin–orbit coupling (SOC), introduced in seminal works by Emmanuel Rashba, plays a central role in engineered topological superconductivity. In this Perspective, the authors review how Rashba SOC enables the realization of low-dimensional topological superconductors supporting Majorana zero modes, the key building blocks for topological quantum computation. They highlight how tuning the Rashba SOC can enhance the topological gap, and survey material platforms and design strategies where Rashba SOC is leveraged to create and control topological superconducting phases.

An important part of Professor Emmanuel Rashba’s scientific activity belongs to the period from 1954 until 1966, when he lived in Kiev (Ukraine) and worked at the Theoretical Department (headed by Professor S. I. Pekar) of the Institute of Semiconductors, NAS of Ukraine. In addition to the well-known results obtained by him that are currently widely cited, regarding the symmetry of electron bands, spin states, and various associated effects, Rashba also investigated electron transport in semiconductors. These studies show that even then Rashba had a clear understanding that future development of electronics would be directly related to the miniaturization of semiconductor devices, where the influence of sample sizes and physical boundaries significantly affect their electrical properties. Here, the authors briefly review Rashba’s pioneering works on size effects with emphasis on their strong influence on further development of the physics and theory of this interesting and important research area. In particular, his early works on the formation of electron concentration domains with different valley indices in multivalley semiconductors anticipated the emergence of a new direction in electronics, currently called valleytronics and tightly related to spintronics and other booming fields of study.

Symmetries play a crucial role in band structure theory of semiconductor materials, including well-known topological insulators like HgTe. In heterostructure devices, the electrostatic potential from the gate electrode breaks structural inversion symmetry, i.e., the reflection symmetry between the top and bottom of the device. Here, the authors explore structural inversion symmetry breaking in two-dimensional effective models like the Bernevig-Hughes-Zhang model and the Dirac model for surface states in three-dimensional topological insulators. By means of dimensional reduction, these effective models inherit the symmetry properties from k·p theory in three dimensions. In the end, the extra terms induced by the electric field are similar to Rashba spin-orbit coupling.

Broken inversion symmetry together with Rashba spin-orbit coupling fundamentally alters how superconductivity withstands applied magnetic fields. This work constructs a symmetry-respecting Ginzburg–Landau framework for Rashba superconductors and demonstrates that the upper critical field $H_{c2}(T)$ exhibits a distinctly concave temperature dependence in contrast to the usual saturationlike behavior of conventional superconductors. Within this theory, the interplay between Rashba coupling and the effective mass of Cooper pairs is shown to control the superconducting phase boundary, yielding a compact analytic tool for interpreting and fitting unusually high critical fields in noncentrosymmetric systems. The approach further reveals that parity-mixed, multicomponent order parameters can host soft relative-phase modes with axionlike properties, thereby connecting the physics of the phase boundary to topological superconductivity, spintronics, axion dark matter, and the targeted design of future quantum materials.

An account is given of the intense research collaborations and scientific output of Rashba at the Landau Institute for Theoretical Physics over a period spanning a quarter of a century (1966-1991).

Emmanuel Rashba’s pioneering theory of giant oscillator strength (GOS) has proven foundational to modern quantum photonics. When excitons are weakly confined, they coherently explore their entire localization volume. This yields oscillator strengths that scale as the ratio of the exciton localization volume (area) to the cube (square) of the exciton radius in three-dimensional (two-dimensional) systems, dramatically exceeding those of free excitons. GOS directly reduces radiative decay times by the same factor, enabling subnanosecond emission. Landmark experimental confirmation in CuCl nanocrystals demonstrated that size-dependent radiative decay times match Rashba’s predictions exactly. Now unified with the concept of single-photon superradiance, GOS underpins ultrafast light emission across quantum-confined systems, enabling advances in high-speed optical communications, LEDs, nanolasers, and quantum information processing.

Here, an overview is provided of the development of the invariant method in semiconductor physics, starting from the its origins and highlighting the role of Emmanuel I. Rashba in developing it. The author examines the application of the invariant method to construct an appropriate effective-mass Hamiltonian. The key effects of the spin-orbit interaction are discussed, including not only classical Rashba and Dresselhaus splitting but also a new kind of magnetic spin splitting which has been predicted and experimentally verified recently. It is demonstrated that the invariant method has become a universal tool in modern solid-state physics, widely applied not only to three-dimensional but also to two-dimensional crystals, including graphene, silicene, and transition metal dichalcogenide monolayers, all of which play an important role in modern spintronics.

E. I. Rashba predicted that an electric field can drive spin resonance—the electric dipole spin resonance (EDSR) effect which is extensively studied in conventional semiconductors. Here, the authors extend this concept to transition metal dichalcogenide heterobilayers. They demonstrate that the electric dipole inter-spin-subband transitions, symmetry-forbidden in monolayers, become allowed once two distinct layers are stacked. Through symmetry analysis and a microscopic spin-orbit mixing model, they derive selection rules for all six high-symmetry stackings and show that the EDSR rate exceeds that of magnetic-dipole transitions by orders of magnitude. The effect naturally gives rise to a Rashba-type Hamiltonian, opening a pathway for efficient THz control of spin and valley degrees of freedom.

Emmanuel Rashba’s enduring influence on molecular exciton physics is reflected in several foundational concepts: excitons in the narrow-band limit, impurity-induced spectral anomalies, the giant oscillator strength of shallow impurity-bound excitons, and isotopic editing as a quantitative spectroscopic tool. Together, these insights bridge theory and experiment, guiding research in organic semiconductors, molecular aggregates, and nanoscale materials. Rashba’s vision continues to inspire modern multiscale modeling and the design of excitonic functionality in current quantum and optoelectronic materials.

When molecular aggregates absorb light, the resulting exciton is shaped by a local phonon bath, which causes fluctuation, dephasing, and can eventually trap the excitation. This exciton-phonon coupling leads to exciton-polaron formation, transforming the coherent excitonic motion into the incoherent polaronic behavior. Here, the authors compare complementary time-dependent descriptions of this process. In the Heisenberg representation, the mean-field approximation treats phonons as classical fluctuating fields, while the one-quantum approximation retains one-phonon-assisted correlations and captures phonon sidebands in optical spectra. In parallel, a time-dependent variational polaron approach follows relaxation and self-trapping in the excited-state manifold. Together, these methods clarify how excitons evolve, decohere, and become coupled to vibrations.

Emmanuel Rashba is responsible for a body of theory that demonstrates the profound effects of spin-orbit interaction on charge carriers in semiconductors. This notably includes the discovery of important effects on confined carriers in the presence of structural inversion asymmetry. The present article describes, from a personal perspective, experimental discovery and studies of electric-field-excited spin-flip resonances in semiconductors motivated by these theoretical predictions. Initial experiments in 1960 focused on electric-dipole excited spin resonance (EDSR) and combined cyclotron plus spin resonance (in 1967). Recent experiments on quasi-two-dimensional electrons in the quantum Hall effect regime in an asymmetric quantum-well structure have revealed unusual multiline EDSR spectra attributed to effects of Rashba spin-orbit effective fields of electrons in quantum Hall edge channels.