Radiation-induced resistance oscillations in 2D electron systems with strong Rashba coupling

www.nature.com/scientificreports OPEN Received: 28 July 2017 Accepted: 4 October 2017 Published: xx xx xxxx Radiation-induced resistance oscillations in 2D electron systems with strong Rashba coupling Jesús Iñarrea1,2 We present a theoretical study on the effect of radiation on the mangetoresistance of two-dimensional electron systems with strong Rashba spint-orbit coupling. We want to study the interplay between two well-known effects in these electron systems: the radiation-induced resistance oscillations and the typical beating pattern of systems with intense Rashba interaction. We analytically derive an exact solution for the electron wave function corresponding to a total Hamiltonian with Rashba and radiation terms. We consider a perturbation treatment for elastic scattering due to charged impurities to finally obtain the magnetoresistance of the system. Without radiation we recover a beating pattern in the amplitude of the Shubnikov de Hass oscillations: a set of nodes and antinodes in the magnetoresistance. In the presence of radiation this beating pattern is strongly modified following the profile of radiation-induced magnetoresistance oscillations. We study their dependence on intensity and frequency of radiation, including the teraherzt regime. The obtained results could be of interest for magnetotransport of nonideal Dirac fermions in 3D topological insulators subjected to radiation. Radiation-induced resistance oscillations (RIRO) and zero resistance states (ZRS)1,2 are remarkable phenomena in condensed matter physics that reveal a novel scenario in radiation-matter coupling. Those effects rise up when a high-mobility, typically above 106 cm2/Vs, two dimensional electron system under a moderate magnetic field (B) is illuminated with microwave (MW) or terahertz (TH) radiation. The mangetoresistance (Rxx) of such systems (2DES) shows oscillations with peaks and valleys at a certain radiation power. When increasing power, the Rxx oscillations increase in turn and at high enough intensity the valleys turn into ZRS. The radiation-induced resistance oscillations show characteristic traits such as periodicity in the inverse of B1,2, a 1/4 cycle shift in the oscillations minima3, sensitivity to temperature4,5 and radiation power6. For the latter case, a sublinear law is obtained for the dependence of RIRO on the radiation power, Rxx ∝ Pα, where P is the radiation power and, interestingly, the exponent is around 0.5. This clearly indicates a squared root dependence7–16. A great number of experiments and theoretical models have been presented to date to try to explain such striking effects. From a theoretical standpoint, we can cite for instance the displacement model17 based on radiation-assisted inter Landau level scattering, the inelastic model based on the effect of radiation on the nonequilibrium electron distribution function18. Being these two models the most cited to date, other models are also very successful explaining the basic features of RIRO, such as the one by Lei et al.19, or the radiation-driven electron orbit model20–24. We have to admit that to date there is no universally accepted theoretical approach among the people devoted to this field. The current or future theoretical models dealing with RIRO or ZRS have to confront with the available experimental results to prove how good and accurate they are. Another approach to prove theories is to check out if they are able to predict results on novel scenarios where there are no experiments carried out yet. For instance RIRO and ZRS obtained on different semiconductor platforms other than GaAs, the most extensively platform used in this kind of experiments. The main reason for using GaAs is that this platform offers the highest mobility25 to date, (~3.0×107 cm2/Vs), among different semiconductor heterostructures. In this article we present a theoretical study on the effect of radiation on the magnetotransport in samples with strong Rashba26–28 spin-orbit interaction (RSOI), such as InAs. The interest by heterostructures with InAs is increasing very fast in the last years, on the one hand for their technological impact being part of new electronic devices. On the other hand from basic research standpoint in fields such as spintronics transistors and the realisation of Majorana fermions29. Usually, the electron mobility in InAs has been always below 1.0 × 106 cm2/Vs and 1 Escuela Politécnica Superior, Universidad Carlos III, Leganes, Madrid, Spain. 2Unidad Asociada al Instituto de Ciencia de Materiales, CSIC Cantoblanco, Madrid, 28049, Spain. Correspondence and requests for materials should be addressed to J.I. (email: ) SCIEntIfIC REPOrts | 7: 13573 | DOI:10.1038/s41598-017-14125-1 1 www.nature.com/scientificreports/ RIRO can hardly be seen. Yet, there have been published very recently experimental results demonstrating that improving MBE growth techniques in quantum wells of InAs electron mobilities can be dramatically increased30. They claimed a mobility close to 3.0 × 106 cm2/Vs. Therefore, samples of InAs, with strong RSOI, can now become reasonable candidates to observe RIRO. Then, we could study the interplay of Rashba interaction and radiation in these kind of systems. We could also predict that with samples with even higher mobilities and at high enough radiation intensity, 2DES systems with RSOI can give rise to ZRS. Thus, we start off based on the previous theory of the radiation-driven electron orbit20–24. This theory stems from the displacement model17 and shares with it the interplay between charged impurity scattering and radiation to be at the heart of RIRO. As a further evolution of the displacement model, our theory proceeds in an alternative approach starting from the exact solution of the time-dependent Schrodinger equation for an electron under magnetic field and radiation. The obtained exact wave function represents a Landau state where the guiding center is harmonically driven back and forth by radiation at the same frequency. Interestingly, the Landau states guiding center follows a classical trajectory given by the solution of the driven classical oscillator. According to this theory, the interaction of the driven Landau states with charged impurities ends up giving rise to shorter and longer average advanced distances by the scattered electrons. These distances are reflected on irradiated Rxx as valleys and peaks respectively. We have added to the same total Hamiltonian of the radiation-driven electron orbit theory the Rashba interaction, solving exactly the corresponding time-dependent Schrodinger equation. Then, applying a Boltzmann transport model we are able to obtain an expression for Rxx with radiation and RSOI. In the simulations we obtain, first without radiation, the well-known beating pattern with the system of nodes and antinodes of the Rashba magnetoresistance31–43. Then, we switched on light obtaining Rxx that shows a strong deformation of the previous beati (...truncated)