Majorana fermion exchange in strictly one dimensional structures

It is generally thought that adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. The exchange relies on the concept of "Majorana shuttle" whereby a $\pi$ domain wall in the superconducting order parameter which hosts a pair of ancillary Majoranas delivers one zero mode across the wire while the other one tunnels in the opposite direction. The method requires some tuning of parameters and does not, therefore, enjoy the full topological protection. The resulting exchange statistics, however, remains non-Abelian for a wide range of parameters that characterize the exchange.Comment: 5 pages, 4 figures, supplemental material is include

Quantization and 2π2\pi Periodicity of the Axion Action in Topological Insulators

The Lagrangian describing the bulk electromagnetic response of a three-dimensional strong topological insulator contains a topological `axion' term of the form '\theta E dot B'. It is often stated (without proof) that the corresponding action is quantized on periodic space-time and therefore invariant under '\theta -> \theta +2\pi'. Here we provide a simple, physically motivated proof of the axion action quantization on the periodic space-time, assuming only that the vector potential is consistent with single-valuedness of the electron wavefunctions in the underlying insulator.Comment: 4 pages, 1 figure, version2 (section on axion action quantization of non-periodic systems added

Stability of Majorana Fermions in Proximity-Coupled Topological Insulator Nanowires

It has been shown previously that a finite-length topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, realizes a one-dimensional topological superconductor with an unpaired Majorana fermion (MF) localized at each end of the nanowire. Here, we study the stability of these MFs with respect to various perturbations that are likely to occur in a physical realization of the proposed device. We show that the unpaired Majorana fermions persist in this system for any value of the chemical potential inside the bulk band gap of order 300 meV in Bi$_2$Se$_3$ by computing the Majorana number. From this calculation, we also show that the unpaired Majorana fermions persist when the magnetic flux through the nanowire cross-section deviates significantly from half flux quantum. Lastly, we demonstrate that the unpaired Majorana fermions persist in strongly disordered wires with fluctuations in the on-site potential ranging in magnitude up to several times the size of the bulk band gap. These results suggest this solid-state system should exhibit unpaired Majorana fermions under accessible conditions likely important for experimental study or future applications.Comment: 17 pages, 13 figure

Finite-temperature Screening and the Specific Heat of Doped Graphene Sheets

At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work we present a semi-analytical expression for the dynamical density-density linear-response function of noninteracting massless Dirac fermions (the so-called "Lindhard" function) at finite temperature. This result is crucial to describe finite-temperature screening of interacting massless Dirac fermions within the Random Phase Approximation. In particular, we use it to make quantitative predictions for the specific heat and the compressibility of doped graphene sheets. We find that, at low temperatures, the specific heat has the usual normal-Fermi-liquid linear-in-temperature behavior, with a slope that is solely controlled by the renormalized quasiparticle velocity.Comment: 9 pages, 5 figures, Submitted to J. Phys.

Effect of disorder on the ground-state properties of graphene

We calculate the ground-state energy of Dirac electrons in graphene in the presence of disorder. We take randomly distributed charged impurities at a fixed distance from the graphene sheet and surface fluctuations (ripples) as the main scattering mechanisms. Mode-coupling approach to scattering rate and random-phase approximation for ground-state energy incorporating the many-body interactions and the disorder effects yields good agreement with experimental inverse compressibility.Comment: Extended introduction and discussion. To appear in Phys. Rev.

AMoDSim: An Efficient and Modular Simulation Framework for Autonomous Mobility on Demand

Urban transportation of next decade is expected to be disrupted by Autonomous Mobility on Demand (AMoD): AMoD providers will collect ride requests from users and will dispatch a fleet of autonomous vehicles to satisfy requests in the most efficient way. Differently from current ride sharing systems, in which driver behavior has a clear impact on the system, AMoD systems will be exclusively determined by the dispatching logic. As a consequence, a recent interest in the Operations Research and Computer Science communities has focused on this control logic. The new propositions and methodologies are generally evaluated via simulation. Unfortunately, there is no simulation platform that has emerged as reference, with the consequence that each author uses her own custom-made simulator, applicable only in her specific study, with no aim of generalization and without public release. This slows down the progress in the area as researchers cannot build on each other's work and cannot share, reproduce and verify the results. The goal of this paper is to present AMoDSim, an open-source simulation platform aimed to fill this gap and accelerate research in future ride sharing systems