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

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

Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states

One of the simplest proposed experimental probes of a Majorana bound-state is a quantized (2e^2/h) value of zero-bias tunneling conductance. When temperature is somewhat larger than the intrinsic width of the Majorana peak, conductance is no longer quantized, but a zero-bias peak can remain. Such a non-quantized zero-bias peak has been recently reported for semiconducting nanowires with proximity induced superconductivity. In this paper we analyze the relation of the zero-bias peak to the presence of Majorana end-states, by simulating the tunneling conductance for multi-band wires with realistic amounts of disorder. We show that this system generically exhibits a (non-quantized) zero-bias peak even when the wire is topologically trivial and does not possess Majorana end-states. We make comparisons to recent experiments, and discuss the necessary requirements for confirming the existence of a Majorana state.Comment: 5 pages, 4 Figure

Edge-Ferromagnetism from Majorana Flat-Bands: Application to Split Tunneling-Conductance Peaks in the High-Tc Cuprates

In mean-field descriptions of nodal d-wave superconductors, generic edges exhibit dispersionless Majorana fermion bands at zero-energy. These states give rise to an extensive ground-state degeneracy, and are protected by time-reversal (TR) symmetry. We argue that the infinite density of states of these flat-bands make them inherently unstable to interactions, and show that repulsive interactions lead to edge FM which splits the flat bands. This edge FM offers an explanation for the observation of splitting of zero-bias peaks in edge tunneling in High-Tc cuprate superconductors. We argue that this mechanism for splitting is more likely than previously proposed scenarios, and describe its experimental consequences.Comment: 10 pages, 5 figure

Convolutional Framework for Accelerated Magnetic Resonance Imaging

Magnetic Resonance Imaging (MRI) is a noninvasive imaging technique that provides exquisite soft-tissue contrast without using ionizing radiation. The clinical application of MRI may be limited by long data acquisition times; therefore, MR image reconstruction from highly undersampled k-space data has been an active area of research. Many works exploit rank deficiency in a Hankel data matrix to recover unobserved k-space samples; the resulting problem is non-convex, so the choice of numerical algorithm can significantly affect performance, computation, and memory. We present a simple, scalable approach called Convolutional Framework (CF). We demonstrate the feasibility and versatility of CF using measured data from 2D, 3D, and dynamic applications.Comment: IEEE ISBI 2020, International Symposium on Biomedical Imagin