The transitions between the spin-split bands by spin-orbit interaction are relevant to many novel phenomena such as the resonant dynamical magnetoelectric effect and the spin Hall effect. We perform optical spectroscopy measurements combined with first-principles calculations to study these transitions in the recently discovered giant bulk Rashba spin-splitting system BiTeI. Several novel features are observed in the optical spectra of the material including a sharp edge singularity due to the reduced dimensionality of the joint density of states and a systematic doping dependence of the intraband transitions between the Rashba-split branches. These confirm the bulk nature of the Rashba-type splitting in BiTeI and manifest the relativistic nature of the electron dynamics in a solid.

We study the magneto-optical (MO) response of polar semiconductor BiTeI with giant bulk Rashba spin splitting at various carrier densities. Despite being non-magnetic, the material is found to yield a huge MO activity in the infrared region under moderate magnetic fields (≤ 3 T). By comparison with first-principles calculations, we show that such an enhanced MO response is mainly due to the intraband transitions between the Rashba-split bulk conduction bands in BiTeI, which give rise to distinct novel features and systematic doping dependence of the MO spectra. We further predict an even more pronounced enhancement in the low-energy MO response and dc Hall effect near the crossing (Dirac) point of the conduction bands.PACS numbers: 78.20.Bh,78.20.Ls,71.70.Ej The spin-orbit interaction (SOI) plays a crucial role in the rapidly evolving field of spintronics [1][2][3][4]. The principal importance of SOI is in its ability to intrinsically couple the electron spin with its orbital motion, and hence produce many novel phenomena such as the spin Hall effect [5] and spin Galvanic effect [6]. In the presence of an external magnetic field, SOI can effectively mediate the interaction between photons and electron spins, thereby leading to interesting magneto-optical (MO) effects, e.g. non-linear Kerr rotation [7] whereby the polarization plane of the linearly-polarized light in reflection is rotated as a consequence of SOI.In practice, most materials under magnetic field exhibit a rather complicated MO response. This is because usually too many energy bands are involved in the optical excitations, which, given that SOI is also at work, leads the respective inter-and intraband optical transitions to produce complex spectra. This accordingly prevents a comprehensive understanding of the role of SOI on the MO response of the given materials using the available theoretical models. In contrast, semiconductors with Rashba-split conduction/valence bands appear to be ideal systems for studying MO effects, as they have a rather simple spin-dependent multi-band scheme. However, these systems have rarely been studied up to now, mainly because they usually show a very weak Rashba spin splitting (RSS) which cannot be resolved experimentally, and also because RSS had been found only in the two-dimensional electron-gas or metallic systems formed at the surface or interface where the MO effect is hardly detectable.This situation has been greatly improved recently by the discovery of the giant bulk RSS in the polar semiconductor BiTeI. The angle-resolved photoemission spectroscopy (ARPES) [8] has revealed that the bulk conduction bands in BiTeI are subject to a large RSS (see Fig. 1(a)), well describable by the 2D Rashba Hamiltonian H R = p 2 /2m + λe z · (S × p), near the time-reversal symmetry point A, where e z is the direction of the potential gradient breaking the inversion symmetry, and S and p are the spin and momentum operators, respectively. This leads to a Dirac-like band dispersion near p = 0 and a splitting increasing linearl...