Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor

Top-transmon: hybrid superconducting qubit for parity-protected quantum computation

Qubits constructed from uncoupled Majorana fermions are protected from decoherence, but to perform a quantum computation this topological protection needs to be broken. Parity-protected quantum computation breaks the protection in a minimally invasive way, by coupling directly to the fermion parity of the system --- irrespective of any quasiparticle excitations. Here we propose to use a superconducting charge qubit in a transmission line resonator (a socalled transmon) to perform parity-protected rotations and read-out of a topological (top) qubit. The advantage over an earlier proposal using a flux qubit is that the coupling can be switched on and off with exponential accuracy, promising a reduced sensitivity to charge noise.Comment: 7 pages, 5 figure

Ballistic Josephson junctions in edge-contacted graphene

Hybrid graphene-superconductor devices have attracted much attention since the early days of graphene research. So far, these studies have been limited to the case of diffusive transport through graphene with poorly defined and modest quality graphene-superconductor interfaces, usually combined with small critical magnetic fields of the superconducting electrodes. Here we report graphene based Josephson junctions with one-dimensional edge contacts of Molybdenum Rhenium. The contacts exhibit a well defined, transparent interface to the graphene, have a critical magnetic field of 8 Tesla at 4 Kelvin and the graphene has a high quality due to its encapsulation in hexagonal boron nitride. This allows us to study and exploit graphene Josephson junctions in a new regime, characterized by ballistic transport. We find that the critical current oscillates with the carrier density due to phase coherent interference of the electrons and holes that carry the supercurrent caused by the formation of a Fabry-P\'{e}rot cavity. Furthermore, relatively large supercurrents are observed over unprecedented long distances of up to 1.5 $\mu$m. Finally, in the quantum Hall regime we observe broken symmetry states while the contacts remain superconducting. These achievements open up new avenues to exploit the Dirac nature of graphene in interaction with the superconducting state.Comment: Updated version after peer review. Includes supplementary material and ancillary file with source code for tight binding simulation

The Aharonov-Bohm effect for massless Dirac fermions and the spectral flow of Dirac type operators with classical boundary conditions

We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by a bundle automorphism. This result is used to study conditions for the existence of nonzero spectral flow of a family of self-adjoint Dirac type operators with local boundary conditions in a two-dimensional domain with nontrivial topology. Possible physical realizations of nonzero spectral flow are discussed.Comment: 15 pages, 6 figures. Submitted to Theoretical and Mathematical Physics. v2: A change has been made to the paragraph describing the previous work of M. Prokhorov

How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions, which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermions is the supression of topological superconductivity by disorder. We show that Majorana fermions protected by a robust topological gap can occur at the ends of a chain of quantum dots connected by s-wave superconductors. In the appropriate parameter regime, we establish that the quantum dot/superconductor system is equivalent to a 1D Kitaev chain, which can be tuned to be in a robust topological phase with Majorana end modes even in the case where the quantum dots and superconductors are both strongly disordered. Such a spin-orbit coupled quantum dot - s-wave superconductor array provides an ideal experimental platform for the observation of non-Abelian Majorana modes.Comment: 8 pages; 3 figures; version 2: Supplementary material updated to include more general proof for localized Majorana fermion

Strained graphene structures: from valleytronics to pressure sensing

Due to its strong bonds graphene can stretch up to 25% of its original size without breaking. Furthermore, mechanical deformations lead to the generation of pseudo-magnetic fields (PMF) that can exceed 300 T. The generated PMF has opposite direction for electrons originating from different valleys. We show that valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudo-magnetic field created by a Gaussian-like deformation allows electrons from only one valley to transmit and a current of electrons from a single valley is generated at the opposite side of the locally strained region. Furthermore, applying a pressure difference between the two sides of a graphene membrane causes it to bend/bulge resulting in a resistance change. We find that the resistance changes linearly with pressure for bubbles of small radius while the response becomes non-linear for bubbles that stretch almost to the edges of the sample. This is explained as due to the strong interference of propagating electronic modes inside the bubble. Our calculations show that high gauge factors can be obtained in this way which makes graphene a good candidate for pressure sensing.Comment: to appear in proceedings of the NATO Advanced Research Worksho

Edge States of Monolayer and Bilayer Graphene Nanoribbons

On the basis of tight-binding lattice model, the edge states of monolayer and bilayer graphene nanoribbons (GNRs) with different edge terminations are studied. The effects of edge-hopping modulation, spin-orbital coupling (SOC), and bias voltage on bilayer GNRs are discussed. We observe the following: (i) Some new extra edge states can be created by edge-hopping modulation for monolayer GNRs. (ii) Intralayer Rashba SOC plays a role in depressing the band energy gap $E_g$ opened by intrinsic SOC for both monolayer and bilayer GNRs. An almost linear dependent relation, i.e., $E_g\sim \lambda_R$, is found. (iii) Although the bias voltage favors a bulk energy gap for bilayer graphene without intrinsic SOC, it tends to reduce the gap induced by intrinsic SOC. (iv) The topological phase of the quantum spin Hall effect can be destroyed completely by interlayer Rashba SOC for bilayer GNRs.Comment: 6 pages, 6 figure

Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks

We propose a scheme in semiconducting quantum nanowires structure to demonstrate the non-Abelian statistics for Majorana fermions in terms of braid group. The Majorana fermions are localized at the endpoints of semiconducting wires, which are deposited on an \emph{s}-wave superconductor. The non-Abelian nature of Majorana fermion is manifested by the fact that the output of the different applied orders of two operations, constructed by the braid group elements, are different. In particular, the difference can be unambiguously imprinted on the quantum states of a superconducting flux qubit.Comment: V1, accepted for publication at JETP Letters; v2, typos correcte

Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire

We show that weak antilocalization by disorder competes with resonant Andreev reflection from a Majorana zero-mode to produce a zero-voltage conductance peak of order e^2/h in a superconducting nanowire. The phase conjugation needed for quantum interference to survive a disorder average is provided by particle-hole symmetry - in the absence of time-reversal symmetry and without requiring a topologically nontrivial phase. We identify methods to distinguish the Majorana resonance from the weak antilocalization effect.Comment: 13 pages, 8 figures. Addendum, February 2014: Appendix B shows results for weak antilocalization in the circular ensemble. (This appendix is not in the published version.

Long-term follow-up of a female patient with Weber–Christian panniculitis

Weber–Christian disease is a rare form of lobular panniculitis characterized by painful subcutaneous nodules on the trunk and limbs commonly concurrent with systemic manifestations and a tendency to relapse. Known are only sporadic cases of a long-term (more than 5-year) followup of patients with Weber–Christian disease. For this reason, there are neither prognostic criteria for the disease no proven conventional treatment option now. The paper describes a clinical case of a female patient with a verified diagnosis of Weber–Christian disease who has a sustained subclinical remission due to low-dose prednisone use and basic antirecurrent therapy