Rashba Hamiltonian and electron transport

By L. Molenkamp, G. Schmidt, G. Bauer. 2001

140 citations recorded by the source corpus.

The Rashba Hamiltonian describes the splitting of the conduction band as a result of spin-orbit coupling in the presence of an external field and is commonly used to model the electronic structure of confined narrowgap semiconductors. Due to the mixing of spin states some care has to be exercised in the calculation of transport properties. We derive the velocity operator for the Rashba-split conduction band and demonstrate that the transmission of an interface between a ferromagnet and a Rashba-split semiconductor does not depend on the magnetization direction, in contrast with previous assertions in the literature. DOI: 10.1103/PhysRevB.64.121202 PACS number~s!: 71.70.2d Narrow-gap semiconductors, most notably InAs, play an important role in the rapidly evolving field of spintronics. As a nonmagnetic element in hybrid devices, these materials are expected to help control the electron spin states, just like the electron charge is controlled in conventional electronic devices. Part of this potential stems from the natural twodimensional electron gas ~2DEG! on clean InAs surfaces, which allows high-quality ohmic contacts to superconductors and ferromagnets. Another reason is the seminal paper of Datta and Das, 1 which describes how the electrical field of an external gate electrode can be used to manipulate the precession of a conduction electron spin. Essential for this mechanism is the field-dependent spin-orbit coupling, which is relatively large and well-established for the 2DEG on InAs. It is now generally accepted that the spin-orbit interaction in narrow-gap 2DEGs is governed by the Rashba Hamiltonian, 2 which increases linearly with the electron wave vector. The spin-orbit-interaction induced ‘spin-splitting’ is sometimes confused with an exchange or Zeeman splitting. However, the latter require breaking of the time inversion symmetry and are therefore fundamentally different from the former. It is then not surprising that physical properties like exciton spin splittings or, in the present context, spindependent transport properties of narrow-gap hybrid devices are not well understood. In a recent paper, for example, it was argued 3 that the conductance of the interface between a ferromagnet and a spin-orbit spin-split semiconductor should change on a flip of the magnetization direction of the ferromagnet. This obviously cannot be correct because in the absence of an external magnetic field, the spin-quantization axis in the ~isotropic! semiconductor can be rotated with the magnetization direction, which should therefore be without physical consequences. 4 The problem with the calculations of Ref. 3 can be traced to an incorrect treatment of the velocity operator, which in the presence of spin-orbit interaction is not simply given by \k /m, where m is the effective mass of an electron and k W its wave vector. It is the purpose of our communication to clarify the issues mentioned above. First, we will discuss the nature of the eigenstates of the Rashba Hamiltonian in some detail and derive the proper velocity operator. For comparison, we give similar expressions for the eigenstates and velocity operator for a Stoner-Wohlfarth ferromagnet. Finally, we calculate explicitly the transmission coefficient between a ferromagnet and a ‘‘Rashba-split’’ electron gas and show that the contact conductance is invariant with respect to a magnetization reversal of the ferromagnet. The Hamiltonian of an otherwise free electron system, but including the Rashba spin-orbit scattering term reads: 2

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/e3afaa490202321eda7aa633c629d569a602a23d