non-Abelian Majorana Fermions Research Articles

Competitive spin-flipped normal reflection and equal-spin Andreev reflection in heterojunctions of nodal-line superconductors

The superconducting phase of topological semimetals has become a promising route for the implementation of topological superconductivity and non-Abelian Majorana fermions. Here, we investigate quantum transport in the junctions composed of a nodal-line superconductor, i.e., a topological nodal-line semimetal with superconducting pairing. It is shown that two topologically nontrivial regions exist in the surface Brillouin zone of the nodal-line superconductor labeled by the transverse momentum. Specifically, topological regions with topological invariants $\mathcal{N}=1$ and $\mathcal{N}=2$ host a single and a pair of Majorana zero modes at the surface, respectively. We show that the single Majorana zero mode in the $\mathcal{N}=1$ region can induce resonant equal-spin Andreev reflection, while the Majorana pair in the $\mathcal{N}=2$ region can lead to resonant spin-flipped normal reflection. Both reflection processes can give rise to spin currents but with different polarization directions, whose proportions can be adjusted by a Zeeman field. We also study the transport properties of the device with a sandwich structure and predict that strong crossed Andreev reflection can be implemented with a finite bias. Detection schemes for all these novel transport properties, which can be revealed by spin-resolved transport signatures, are proposed. Our work paves the way for the implementation and detection of Majorana fermions in nodal-line superconductors.

Non-Abelian Majorana fermions in topological s-wave Fermi superfluids

By solving the Bogoliubov–de Gennes equations analytically, we derive the fermionic zero-modes satisfying the Majorana property that exist in vortices of a two-dimensional s-wave Fermi superfluid with spin–orbit coupling and Zeeman spin-splitting. The Majorana zero-mode becomes normalisable and exponentially localised to the vicinity of the vortex core when the superfluid is topologically non-trivial. We calculate the energy splitting due to Majorana hybridisation and identify that the s-wave Majorana vortices obey non-Abelian statistics.

Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a NbSe_{2} Superconductor.

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (NbSe_{2}) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

Superconducting proximity effect in semiconductor nanowires

We theoretically consider the proximity effect in semiconductor-superconductor hybrid nanostructures, which are being extensively studied in the context of the ongoing search for non-Abelian Majorana fermions in solid state systems. Specifically, we consider the dependence on the thickness of the semiconductor in the direction normal to the interface, a physical effect that has been uncritically neglected in prior work on the subject. Quite surprisingly, we find the unanticipated result that increasing the semiconductor thickness leads to a suppression of the induced superconducting gap due to proximity-induced interband coupling. As a result, in the limit of strong semiconductor-superconductor coupling, the proximity-induced gap becomes much smaller than the bulk superconductor gap and depends weakly on the interface transparency.

Majorana meets Coxeter: Non-Abelian Majorana fermions and non-Abelian statistics

We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The new non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.

Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures

We show that a film of a semiconductor in which s-wave superconductivity and Zeeman splitting are induced by the proximity effect, supports zero-energy Majorana fermion modes in the ordinary vortex excitations. Since time-reversal symmetry is explicitly broken, the edge of the film constitutes a chiral Majorana wire. The heterostructure we propose-a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator-is a generic system which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.