Tailoring spin and magnetism in systems of reduced dimensionality
Final Report Abstract
Topological states in systems of reduced dimensionality offer many intriguing possibilities, both for fundamental research as well as for potential applications. In this project, we present properties of two different such systems in reduced dimensionalities, in both of which strong spin-orbit coupling plays a crucial role in the formation of exotic states and excitation modes: magneto-optical properties of HgTe/CdTe quantum wells and topological superconductivity in quantum dots and quantum rings. In two-dimensional topological insulators, such as inverted HgTe/CdTe quantum wells, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field Bc, above which only quantum Hall (QH) states can be found. Using linear response theory, we theoretically investigate the magneto-optical properties of inverted HgTe/CdTe quantum wells, both for infinite two-dimensional and finite-strip geometries, and possible signatures of the transition between the QSH and QH regimes. In the QSH regime, we find an additional absorption peak at low energies for the finite-strip geometry. This peak arises due to the presence of edge states in this geometry and persists for any Fermi level in the QSH regime, while in the QH regime the peak vanishes if the Fermi level is situated in the bulk gap. Thus, by sweeping the gate voltage, it is potentially possible to distinguish between the QSH and QH regimes due to this signature. Moreover, we investigate the effect of additional spin-orbit coupling due to bulk or structure-inversion asymmetry and finite temperature on this measurement scheme. Engineering topological superconductivity in semiconductor structures provides fascinating ways to obtain and study Majorana modes in a condensed matter context. Here, we theoretically investigate topological superconductivity in quantum dots (QDs) and quantum rings (QRs), both for chiral p-wave superconductors as well as experimentally more realistic hybrid structures. By applying a magnetic field which is expelled from a QR, but which creates a flux that is an odd integer multiple of Φ0 /2 = 𝜋ℏ/𝑒, Majorana modes, that is, degenerate quasiparticle edge modes with zero energy and zero charge density, become possible in the topological regime. Finite-size effects result in a splitting of these degenerate edge modes, leading to approximate Majorana modes in the sense that they have only approximately zero energy and zero charge density and are only approximately degenerate. This small, but finite charge distribution is then spread over the entire QR which is in stark contrast to other chiral quasiparticle edge modes found in the system whose significantly larger charge distributions follow the probability densities and thus are localized at a given edge. Even if a magnetic field penetrates into the superconducting region, the system can under certain circumstances still support such edge modes with approximately zero energy and charge. Based on these findings, we propose measuring the local charge density of quasiparticle excitations as a way to supplement conductance-based measurements to confirm the presence of notoriously elusive Majorana fermions. Finally, electrostatic and ferromagnetic tunnel junctions based on the surfaces of threedimensional topological insulators are presented. These junctions can exhibit giant transverse Hall currents as well as – in certain regimes – a negative differential conductance, which makes them an attractive and versatile system for spintronic applications.
Publications
- Probing Majorana-like states in quantum dots and quantum rings, Phys. Rev. B 91, 144505 (2015)
B. Scharf and I. Žutić
(See online at https://doi.org/10.1103/PhysRevB.91.144505) - Probing topological transitions in HgTe/CdTe quantum wells by magneto-optical measurements, Phys. Rev. B 91, 235433 (2015)
B. Scharf, A. Matos-Abiague, I. Žutić, and J. Fabian
(See online at https://doi.org/10.1103/PhysRevB.91.235433)
