Topological Superconductivity and Majorana Fermions in Metallic Surface-States

Heavy metals, such as Au, Ag, and Pb, often have sharp surface states that are split by strong Rashba spin-orbit coupling. The strong spin-orbit coupling and two-dimensional nature of these surface states make them ideal platforms for realizing topological superconductivity and Majorana fermions. In this paper, we further develop a proposal to realize Majorana fermions at the ends of quasi-one-dimensional metallic wires. We show how superconductivity can be induced on the metallic surface states by a combination of proximity effect, disorder, and interactions. Applying a magnetic field along the wire can drive the wire into a topologically non-trivial state with Majorana end-states. Unlike the case of a perpendicular field, where the chemical potential must be fined tuned near the Rashba-band crossing, the parallel field allows one to realize Majoranas for arbitrarily large chemical potential. We then show that, despite the presence of a large carrier density from the bulk metal, it is still possible to effectively control the chemical potential of the surface states by gating. The simplest version of our proposal, which involves only an Au(111) film deposited on a conventional superconductor, should be readily realizable.Comment: 9 Pages, 6 Figure

Engineering a p+ip Superconductor: Comparison of Topological Insulator and Rashba Spin-Orbit Coupled Materials

We compare topological insulator materials and Rashba coupled surfaces as candidates for engineering p+ip superconductivity. Specifically, in each type of material we examine 1) the limitations to inducing superconductivity by proximity to an ordinary s-wave superconductor, and 2) the robustness of the resulting superconductivity against disorder. We find that topological insulators have strong advantages in both regards: there are no fundamental barriers to inducing superconductivity, and the induced superconductivity is immune to disorder. In contrast, for Rashba coupled quantum wires or surface states, the the achievable gap from induced superconductivity is limited unless the Rashba coupling is large. Furthermore, for small Rashba coupling the induced superconductivity is strongly susceptible to disorder. These features pose serious difficulties for realizing p+ip superconductors in semiconductor materials due to their weak spin-orbit coupling, and suggest the need to seek alternatives. Some candidate materials are discussed.Comment: 10 pages, 4 Figures; Changes for v2: References added, Includes an expanded discussion of surface vs bulk disorder (see Sec. IVc. and Appendix A

Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films

The ends of one-dimensional p+ip superconductors have long been predicted to possess localized Majorana fermion modes. We show that Majorana end states survive beyond the strict 1D single-channel limit so long as the sample width does not exceed the superconducting coherence length, and exist when an odd number of transverse quantization channels are occupied. Consequently we find that the system undergoes a sequence of topological phase transitions driven by changing the chemical potential. These observations make it feasible to implement quasi-1D p+ip superconductors in metallic thin-film microstructures, which offer 3-4 orders of magnitude larger energy scales than semiconductor-based schemes. Some promising candidate materials are described.Comment: 5 pages, 5 figures, final published version, appendix on samples with random edge geometries adde

Majorana End-States in Multi-band Microstructures with Rashba Spin-Orbit Coupling

A recent work [1] demonstrated, for an ideal spinless p+ip superconductor, that Majorana end-states can be realized outside the strict one-dimensional limit, so long as: 1) the sample width does not greatly exceed the superconducting coherence length and 2) an odd number of transverse sub-bands are occupied. Here we extend this analysis to the case of an effective p+ip superconductor engineered from Rashba spin-orbit coupled surface with induced magnetization and superconductivity, and find a number of new features. Specifically, we find that finite size quantization allows Majorana end-states even when the chemical potential is outside of the induced Zeeman gap where the bulk material would not be topological. This is relevant to proposals utilizing semiconducting quantum wires, however, we also find that the bulk energy gap is substantially reduced if the induced magnetization is too large. We next consider a slightly different geometry, and show that Majorana end-states can be created at the ends of ferromagnetic domains. Finally, we consider the case of meandering edges and find, surprisingly, that the existence of well-defined transverse sub-bands is not necessary for the formation of robust Majorana end-states.Comment: 9 pages, 9 figure

Ocean shrimp report 1977 season

Statewide Pacific ocean shrimp, Pandalus jordani, landings totaled 15,639,585 lb, more than triple the 1975 record catch of 4,992,233 lb. Record landings were recorded in Area A (Eureka-Crescent City), Area B-2 (Bodega Ray) with catches totaling 13,025,844 and 2,028,607 lb, respectively. Area B-1 (Fort Bragg) landings totaled 585,133 lb and no landings were reported from Area C (Avila-Morro Bay). In Area A the average catch per hour for the season for single-rig vessels was 1,241 lb and 2,228 lb for double-rig vessels. Area B-2 average catch per hour by the single-rig vessels was 2,536 lb. Two-year-old (1975 year class) shrimp dominated the catches in all areas. The outlook for the 1978 season in all areas is questionable because of the relatively weak showing of the incoming 1977 year class but it might make a significant contribution if abundant and of a marketable slze. (19pp.

Ocean shrimp report 1978 season

Statewide Pacific ocean shrimp, Pandalus jordani, landings totaled 13,163,243 lb, down about 2.5 million lb from the 1977 record catch of 15,639,584 lb. However, the 1978 landings were still the second highest on record. Area A (Eureka-Crescent City) landings were the second highest in history with landings of 11,101,895 lb. Landings of 2,061,348 lb in Area B-1 (Fort Bragg) broke all existing records for the bed. The previous record was 799,722 lb landed in 1961. No landings were reported for Areas B-2 (Bodega Bay) and C (Avila-Morro Bay). In Area A the average catch per hour for the season for single-rig vessels was 581 lb and 862 lb for double-rig vessels. Area B-1 average catch per hour was 819 lb and 1,069 lb per hour for single-rig and double-rig vessels, respectively. Two-year-old (1976 year class) shrimp dominated the catches during the first three months in Area A and throughout the season in Area B-1. One-year-old (1977 year class) shrimp dominated the catches in Area A from July to the end of the season. Catches during the first part of October in Area A fell below the established criteria for keeping the season open. This necessitated closing the season two weeks early. (16pp.

Superconductivity and Ferromagnetism in Oxide Interface Structures: Possibility of Finite Momentum Pairing

We introduce a model to explain the observed ferromagnetism and superconductivity in LAO/STO oxide interface structures. Due to the polar catastrophe mechanism, 1/2 charge per unit cell is transferred to the interface layer. We argue that this charge localizes and orders ferromagnetically via exchange with the conduction electrons. Ordinarily this ferromagnetism would destroy superconductivity, but due to strong spin-orbit coupling near the interface, the magnetism and superconductivity can coexist by forming an FFLO-type condensate of Cooper pairs at finite momentum, which is surprisingly robust in the presence of strong disorder.Comment: 6 pages of Supplementary materials added containing details of calculation and further discussion of the FFLO state with disorder, references added, final version as publishe

Learning probability spaces for classification and recognition of patterns with or without supervision

Learning probability spaces for classification and recognition of patterns with or without supervisio