We show that an ordinary semiconducting thin film with spin-orbit coupling can, under ap- propriate circumstances, be in a quantum topologically ordered state supporting exotic Majorana excitations which follow non-Abelian statistics. The key to the quantum topological order is the coexistence of spin-orbit coupling with proximity-induced s-wave superconductivity and an externally-induced Zeeman coupling of the spins. For the Zeeman coupling below a critical value, the system is a non-topological (proximity-induced) s-wave superconductor. However, for a range of Zeeman coupling above the critical value, the lowest energy excited state inside a vortex is a zero-energy Majorana fermion state. The system, thus, has entered into a non-Abelian s-wave superconducting state via a topological quantum phase transition (TQPT) tuned by the Zeeman coupling. In the one-dimensional version of the same structure and for the Zeeman coupling above the critical value, there are localized Majorana zero-energy modes at the two ends of a semiconducting quantum nanowire. In this case, the Zeeman coupling can be induced more easily by an external magnetic field parallel to the wire, obviating the need for a magnetic insulator. We show that, despite the fact that the superconducting pair potential in the nanowire is explicitly s-wave, tunneling of electrons to the ends of the wire reveals a pronounced zero-bias peak. Such a peak is absent when the Zeeman coupling is below its critical value, i.e., the nanowire is in the non-topological s-wave superconducting state. We argue that the observation of this zero-bias tunneling peak in the semiconductor nanowire is possibly the simplest and clearest experiment proposed so far to unambiguously detect a Majorana fermion mode in a condensed matter system.
Digital Commons Citation
Sau, Jay D.; Tewari, Sumanta; Lutchyn, Roman M.; Stanescu, Tudor D.; and Das Sarma, S., "Non-Abelian Quantum Order In Spin-Orbit-Coupled Semiconductors: Search For Topological Majorana Particles In Solid-State Systems" (2010). Faculty & Staff Scholarship. 616.
Sau, Jay D., Tewari, Sumanta., Lutchyn, Roman M., Stanescu, Tudor D., & Das Sarma, S. (2010). Non-Abelian Quantum Order In Spin-Orbit-Coupled Semiconductors: Search For Topological Majorana Particles In Solid-State Systems. Physical Review B - Condensed Matter And Materials Physics, 82(21). http://doi.org/10.1103/Physrevb.82.214509