Significance Majorana zero modes (MZMs) have been proposed as the building blocks for fault-tolerant topological quantum computation. Recent experiments found both spin and charge signatures of MZMs at ends chains on superconducting surfaces. However, properties such not reliably controlled experimentally. Here, we present a platform in which long-range spin–spin interactions hybridization spin-induced in-gap states surface superconductor can be tuned with unprecedented precision by changing...

We study the spectrum of Andreev bound states and Josephson currents across a junction $N$ superconducting wires which may have $s$- or $p$-wave pairing symmetries develop scattering matrix based formalism allows us to address transport such junctions. For $N \ge 3$, it is well known that Berry curvature terms contribute currents; we chart out situations where can relatively large effects. system three superconductors, provide analytic expressions for state energies in response constant...

We study the properties of a line junction which separates surfaces two three-dimensional topological insulators. The velocities Dirac electrons on may be unequal and even have opposite signs. For time-reversal invariant system, we show that is characterized by an arbitrary parameter $\ensuremath{\alpha}$ determines scattering from junction. If surface same sign, there can edge states propagate along with velocity spin orientation depend ratio velocities. Next, what happens if are at angle...

We demonstrate experimentally that a macroscopic topological insulator (TI) phase can emerge in granular conductor composed of an assembly tunnel coupled TI nanocrystals dimension ∼10 nm × 10 2 nm. Electrical transport measurements on thin films Bi2Se3 reveal the presence decoupled top and bottom surface states exhibit large state penetration depths (∼30 at K). By tuning size couplings between them, this new class TIs may be readily tuned from non-topological to phase, too with designer...

We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi2 Se3 to study states which appear on its various surfaces and along edge between two surfaces. both analytical methods based surface Hamiltonians (which are derived from Hamiltonian) numerical lattice discretization of Hamiltonian. find that application potential barrier an can give rise localized at edge. These have unusual energy-momentum dispersion be controlled by applying edge; in particular, velocity...

We study Majorana modes and transport in one-dimensional systems with a p-wave superconductor (SC) normal metal leads. For system an SC lying between two leads, it is known that there mode at the junction each lead. If pairing Δ changes sign or if strong impurity present some point inside SC, additional appear near point. effect of all these on sub-gap conductance leads SC. derive analytical expression as function length L for energy shifts junctions due to hybridization them; oscillate...

We study transport across a line junction lying between two orthogonal topological insulator surfaces and superconductor which can have either $s$-wave (spin-singlet) or $p$-wave (spin-triplet) pairing symmetry. The three time-reversal invariant barriers on sides. compute the charge spin conductance such their behaviors as function of bias voltage applied parameters used to characterize barrier. find that presence insulators leads both Dirac- Schr\"odinger-like features in conductances....

We show that the application of circularly polarized electromagnetic radiation on surface a Weyl semi-metal can generate states at surface. These be characterized by their momentum. The Floquet eigenvalues these come in complex conjugate pairs rather than being equal to $\pm 1$. If amplitude is small, we find some unusual bulk-boundary relations: lie extrema bulk system, and peaks Fourier transforms state wave functions momenta where have extrema. For case zero momentum, analytically derive...

We theoretically study the spectrum induced by one and two magnetic impurities near boundary of a one-dimensional nanowire in proximity to conventional $s$-wave superconductor extract ground-state configuration. show that energies subgap states, supported impurities, are strongly affected for distances less than superconducting coherence length. In particular, when impurity is moved towards boundary, multiple quantum phase transitions periodically occur which parity condensate oscillates...

We analyze the confinement of electronic surface states in a model topological insulator nanowire. Spin-momentum locking reduces unwanted backscattering presence non-magnetic disorder and is known to counteract localization for certain values magnetic flux threading wire. show that intentional can be induced range conditions nanowire constriction. propose geometry involves two constrictions these regions form effective barriers allow formation quantum dot. zero-temperature non-interacting...

We study Majorana modes and transport in one-dimensional systems with a $p$-wave superconductor (SC) normal metal leads. For system SC lying between two leads, it is known that there mode at the junction each lead. If pairing $\Delta$ changes sign or if strong impurity present some point inside SC, additional appear near point. effect of all these on sub-gap conductance leads SC. derive an analytical expression as function length $L$ for energy shifts junctions due to hybridization them;...

Granular conductors form an artificially engineered class of solid state materials wherein the microstructure can be tuned to mimic a wide range otherwise inaccessible physical systems. At same time, topological insulators (TIs) have become cornerstone modern condensed matter physics as hosting metallic states on surface and insulating in bulk. However it remains understood how granularity affects this new exotic phase matter. We perform electrical transport experiments highly granular...

Consensus protocols play an important role in the study of distributed algorithms. In this paper, we effect bias on two popular consensus protocols, namely, {\em voter rule} and 2-choices with binary opinions. We assume that agents opinion $1$ update their a probability $q_1$ strictly less than $q_0$ which occurs for $0$. call as superior our interest is to conditions under network reaches opinion. are located vertices regular expander graph $n$ vertices. show rule, achieved $O(\log n)$ time...