Superconductivity and the quantum Hall effect are considered to be two cornerstones of condensed matter physics. The realization of hybrid structures where these two effects coexist has recently become an active field of research. In this work, we study a Josephson junction where a central region in the quantum Hall regime is proximitized with superconductors that can be driven to a topological phase with an external Zeeman field. In this regime, the Majorana modes that emerge at the ends of each superconducting lead couple to the chiral quantum Hall edge states. This produces distinguishable features in the Andreev levels and Fraunhofer patterns that could help in detecting not only the topological phase transition but also the spin degree of freedom of these exotic quasiparticles. The current phase relation and the spectral properties of the junction throughout the topological transition are fully described by a numerical tight-binding calculation. In pursuance of the understanding of these results, we develop a low-energy spinful model that captures the main features of the numerical transport simulations in the topological phase.
We study a realization of a 1d chain of Majorana bound states at the interfaces between alternating ferromagnetic and superconducting regions at a quantum spin Hall insulator edge. In the limit of well separated Majoranas, the system can be mapped to the transverse field Ising model. The disordered critical point can be reached by tuning the relative magnitude or phases of the ferromagnetic and superconducting order parameters. We compute the voltage dependence of the tunneling current from a metallic tip into the Majorana chain as a direct probe of the random critical state.
We show that quasi-one-dimensional (1D) quantum wires can be written onto the surface of magnetic topological insulator (MTI) thin films by gate arrays. When the MTI is in a quantum anomalous Hall (QAH) state, MTI$/$superconductor quantum wires have especially broad stability regions for both topological and non-topological states, facilitating creation and manipulation of Majorana particles on the MTI surface.
Higher-order topological superconductors and superfluids host lower-dimensional Majorana corner and hinge states since novel topology exhibitions on boundaries. While such topological nontrivial phases have been explored extensively, more possible schemes are necessary for engineering Majorana states. In this paper we propose Majorana corner states could be realized in a two-dimensional attractive quantum spin-Hall insulator with opposite in-plane Zeeman energy at two sublattice sites. The appropriate Zeeman field leads to the opposite Dirac mass for adjacent edges of a square sample, and natu…
We propose two experiments to probe the Majorana fermion edge states that occur at a junction between a superconductor and a magnet deposited on the surface of a topological insulator. Combining two Majorana fermions into a single Dirac fermion on a magnetic domain wall allows the neutral Majorana fermions to be probed with charge transport. We will discuss a novel interferometer for Majorana fermions, which probes their Z_2 phase. This setup also allows the transmission of neutral Majorana fermions through a point contact to be measured. We introduce a point contact formed by a superconductin…
The non-Abelian braiding of Majorana fermions is one of the most promising operations providing a key building block for the realization of topological quantum computation. Recently, the chiral Majorana fermions were observed in a hybrid junction btween a quantum anomalous Hall insulator and an s-wave superconductor. Here we show that if a quantum dot or Majorana zero mode couples to the chiral Majorana fermions, the resulting resonant exchange of chiral Majorana fermions can lead to the non-Abelian braiding. Remarkably, any operation in the braid group can be achieved by this scheme. We furth…
We investigate the properties of electron states localized at the edge of a superconducting island placed on the surface of a topological insulator in a magnetic field. In such systems, Majorana fermions emerge if an odd number of vortices (or odd multivortex vorticity) is hosted by the island; otherwise, no Majorana states exist. Majorana states emerge in pairs: one state is localized near the vortex core, and another at the island edge. We analyze in detail the robustness of Majorana fermions at the edge of the island threaded by a single vortex. If the system parameters are optimized, the e…
We propose a novel optical method to detect the existence of Majorana fermions at the ends of the semiconductor nanowire via the coupling to an electron spin trapped on a carbon nanotube resonator under the control of a strong pump field and a weak probe field. The coupling strength of Majorana fermion to the spin in the carbon nanotube and the decay rate of the Majorana fermion can be easily measured from the probe absorption spectrum via manipulating the spin-mechanical coupling in the suspended\ carbon nanotube. The scheme proposed here will open a good perspective for its applications in a…
Chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain two-dimensonal topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions lead to the same unitary transformation as that in the braiding of Majorana zer…
We study the formation of Majorana fermions in honeycomb-lattice structures in the presence of a Zeeman field, Rashba spin-orbit coupling, and in the proximity of an s-wave superconductor. We show that an exact mapping exists between an anisotropic hexagonal-lattice nanoribbon at k = 0 and a one-dimensional chain, for which the existence of Majorana fermions has been extensively discussed. Consequently we can predict the conditions for the emergence of Majorana fermions at the edges of such ribbon, and relate the existence of Majoranas to a band inversion in the bulk band structure. Moreover w…
We calculate density and current spatial distributions of a 2D model junction between a normal QAH contact and a superconducting QAH region hosting propagating (chiral) Majorana modes. We use a simplified Hamiltonian describing the spatial coupling of the modes on each side of the junction, as well as the related junction conductance. We study how this coupling is affected by orbital effects caused by an external magnetic field.
Commencing with the composite fermion description of the $ν=5/2$ fractional quantum Hall effect, we study the dynamics of the edge neutral Majorana fermions. We confirm that these neutral modes are chiral and show that a conventional p-wave pairing interaction between CFs does not contribute to the dynamics of the edge neutral fermions. We find an important bilinear coupling between the charged and neutral modes. We show that owing to this coupling, the dispersion of the neutral modes is linear and their velocities are proportional to the wave vector of the charged mode. This dynamic origin of…
We predict conductance oscillations in a quantum-anomalous Hall 2d strip having a superconducting region of length $L_x$ with a chiral Majorana mode. These oscillations require a finite transverse extension of the strip $L_y$ of a few microns or less. Measuring the conductance periodicity with $L_x$ and a fixed bias, or with bias and a fixed $L_x$, yields the speed of the chiral Majorana mode. The physical mechanism behind the oscillations is the interference between backscattered chiral modes from second to first interface of the NSN double junction. The interferometer effect is enhanced by t…
We propose a new approach to create Majorana fermions at the edge of a periodically driven semiconductor-superconductor Heterostructure. We calculate the quasi-energy spectrum of the periodically driven Heterostructure by using the Floquet's theory. When the interaction between different Brillouin zones of quasi-energy is neglected, one Majorana fermion can be created at each edge of the Heterostructure when the ratio of driven amplitude and driven frequency is larger than a minimum. Furthermore, when the interaction between the nearest Brillouin zones of quasi-energy is considered, we restric…
Chiral Majorana edge modes are theoretically proposed to perform braiding operations for the potential quantum computation. Here, we suggest a scheme to regulate trajectories of the chiral Majorana fermion based on a quantum anomalous Hall insulator (QAHI)-topological superconductor heterostructure. An applied external gate voltage to the QAHI region introduces a dynamical phase so that the outgoing Majorana fermions can be prominently tuned to different leads. The trajectory is mechanically analyzed and the electrical manipulation is represented by the oscillating transmission coefficients ve…
We have investigated the possible presence of Majorana fermions in a semiconductor quantum ring containing a few interacting electrons, and a strong spin-orbit interaction, proximity coupled to an s-wave superconductor. We have found that for rings with sizes of a few hundred angstroms and for certain values of the chemical potential and the entire range of the magnetic field, there are strong indications of the presence of Majorana fermions. In particular, the ground state energies and the average electron numbers for the states with even and odd electron numbers are almost identical. We have…
The physics of Majorana fermion occurs at the edge and interface of many one-dimensional quantum many body system with gapped excitation spectrum. We present the renormalization group equations for strongly interacting helical liquid. We present the results of both Majorana- Ising topological quantum phase transition and also Berezinskii-Kosterlitz-Thouless topological phase transition. We show that the Majorana-Ising topological quantum phase transition for non-interacting case is an exactly solvable line but in presence of interaction the system has no exactly solvable line. We study the eff…
Majorana fermions in a superconductor hybrid system are charge neutral zero-energy states. For the detection of this unique feature, we propose an interferometry of a chiral Majorana edge channel, formed along the interface between a superconductor and a topological insulator under an external magnetic field. The superconductor is of a ring shape and has a Josephson junction that allows the Majorana state to enclose continuously tunable magnetic flux. Zero-bias differential electron conductance between the Majorana state and a normal lead is found to be independent of the flux at zero temperat…
We show that confined Majorana fermions can exist in nanowires with proximity induced s-wave superconducting pairing if the direction of an external magnetic field rotates along the wire. The system is equivalent to nanowires with Rashba-type spin-orbit coupling, with strength proportional to the derivative of the field angle. For realistic parameters, we demonstrate that a set of permanent magnets can bring a nearby nanowire into the topologically non-trivial phase with localized Majorana modes at its ends. Without the requirement of spin-orbit coupling this opens up for a new route for demon…
We analyze the current-biased Shapiro experiment in a Josephson junction formed by two one-dimensional nanowires featuring Majorana fermions. Ideally, these junctions are predicted to have an unconventional $4π$-periodic Josephson effect and thus only Shapiro steps at even multiples of the driving frequency. Taking additionally into account overlap between the Majorana fermions, due to the finite length of the wire, renders the Josephson junction conventional for any dc-experiments. We show that probing the current-phase relation in a current biased setup dynamically decouples the Majorana fer…
Majorana bound states exist inside a core of half-quantum vortex in spin-triplet superconductors. Despite intense efforts, they have not been discovered in any spin-triplet superconductor candidate materials. After the success of topological insulator, another route to achieve Majorana fermions has been suggested: heterostructures of s-wave superconductors and topological insulator or semimetal with strong spin-orbit coupling provide an effective spinless $p+ip$ pairing which supports Majorana bound states in a single vortex. This theoretical observation has stimulated both experimental and th…
We study the generation of Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic field B. A topological insulator/superconductor heterostructure and a two-dimensional p-wave superconductor are discussed. It is demonstrated that in these systems a single vortex creates two Majorana fermions, one hosted at the vortex core. The wave function of the second Majorana state is localized in the superconductor volume along a circle of radius $r^* \propto B^{-1}$ centered at the vortex core. In the case of many vortices, the sensitivity of $r^*$ to the magneti…
A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field…
We investigate persistent currents in metallic rings interrupted by a Coulomb blockaded topological superconducting segment. We show that the presence of Majorana bound states in the superconductor is reflected in the emergence of an h/e harmonics in the persistent current, whose sign is determined by the fermion parity of the superconductor. The Majorana bound states further render the current finite at zero flux, nevertheless the resulting peculiar symmetry of the persistent current is compatible with a free energy that is even in time-reversal symmetry breaking fields. These unique features…
We show that the interplay of cyclotron motion and Andreev reflection experienced by massless-Dirac-like charge carriers in topological-insulator surface states generates a Majorana-particle excitation. Based on an envelope-function description of the Dirac-Andreev edge states, we discuss the kinematic properties of the Majorana mode and find them to be possible to be tuned by changing the superconductor's chemical potential and/or the magnitude of the perpendicular magnetic field. Our proposal opens up new possibilities for studying Majorana fermions in a controllable setup.
Motivated by recent proposals for the generation of Majorana fermions in semiconducting hybrid structures, we examine possible experimental fingerprints of such excitations. Whereas previous works mainly have focused on zero-energy states in vortex cores in this context, we demonstrate analytically an alternative route to detection of Majorana excitations in semiconducting hybrid structures: interface-bound states that may be probed directly via conductance spectroscopy or STM-measurements. We estimate the necessary experimental parameters required for observation of our predictions.
We investigate the mesoscopic resistor-capacitor circuit consisting of a quantum dot coupled to spatially separated Majorana fermion modes in a chiral topological superconductor. We find substantially enhanced relaxation resistance due to the nature of Majorana fermions, which are their own anti-particles and composed of particle and hole excitations in the same abundance. Further, if only a single Majorana mode is involved, the zero-frequency relaxation resistance is completely suppressed due to a destructive interference. As a result, the Majorana mode opens an exotic dissipative channel on …
Can Majorana zero modes in quantum Hall edges survive edge reconstruction?
Aix Marseille Univ, Université de Toulon, CNRS, CPT（艾克斯马赛大学，土伦大学，法国国家科学研究中心，理论物理中心）；Department of Physics, Indian Institute of Science Education and Research (IISER) Kolkata（印度科学与教育研究所加尔各答分校物理系）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）
We propose Floquet chiral topological superconducting systems hosting Floquet Majorana fermions, which consist of hexagonal lattices in proximity to superconductors with shining circularly polarized light. Specially for bilayer graphene system, we demonstrate that there exist three topological phases determined by certain parameters, namely, the amplitude and frequency of the induced light. The number of chiral Floquet Majorana edge states is confirmed by calculating Chern number analytically and energy spectrum in ribbon geometry. Moreover, this proposal is generalized to other hexagonal latt…
Exploiting the peculiar properties of proximity-induced superconductivity on the surface of a topological insulator, we propose a device which allows the creation of a Majorana fermion inside the core of a pinned Abrikosov vortex. The relevant Bogolyubov-de Gennes equations are studied analytically. We demonstrate that in this system the zero-energy Majorana fermion state is separated by a large energy gap, of the order of the zero-temperature superconducting gap $Δ$, from a band of single-particle non-topological excitations. In other words, the Majorana fermion remains robust against thermal…
Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. While elementary particles of the Majorana type were not identified yet, quasi-particles with Majorana like properties, born from interacting electrons in the solid, were predicted to exist. Here, we present thorough experimental studies, backed by numerical simulations, of a system composed of an aluminum superconductor in proximity to an indium arsenide nanowire, with the latter possessing strong spin-orbit coupling. An induced 1d topological superconductor - supporting Majorana fermions at bo…
Chiral superconductors have the ability to host topologically protected Majorana zero modes which have been proposed as future qubits for topological quantum computing. The recently introduced magnet--superconductor hybrid (MSH) systems consisting of magnetic adatoms deposited on the surface of conventional $s$-wave superconductors represent a promising candidate for the creation, detection, and manipulation of Majorana modes via scanning tunneling microscopy techniques. Here, we present four examples demonstrating the ability to engineer Majorana fermions in nanoscopic MSH systems by using at…
We propose the concept of birefringent Majorana fermions as collective excitations of quantum interacting many-body states motivated by the already known quasiparticles including Dirac fermions, birefringent Dirac fermions and Majorana fermions. Low energy effective models are constructed to understand the basic mathematical structures of equations of motion and physical properties. We find that the equation of motion, with two different "speed of light", describing birefringent Majorana fermions in condensed matter physics is the birefringence version of the original Majorana equation of real…
Quantum simulation aims to simulate a quantum system using a controble laboratory system that underline the same mathematical model. Cavity QED lattice system is that prescribe system to simulate the relativistic quantum effect. We quantum simulate the Dirac fermion mode, Majorana fermion mode and Majorana-Weyl fermion mode and a crossover between them in cavity QED lattice. We also present the different analytical relations between the field operators for different mode excitations.
Under appropriate external conditions a semiconductor nanowire in proximity to an s-wave superconductor can be in a topological superconducting (TS) phase. This phase supports localized zero-energy Majorana fermions at the ends of the wire. However, the non-Abelian exchange statistics of Majorana fermions is difficult verify because of the one-dimensional topology of such wires. In this paper we propose a scheme to transport Majorana fermions between the ends of different wires using tunneling, which is shown to be controllable by gate voltages. Such tunneling-generated hops of Majorana fermio…
We propose a novel realization for a topologically superconducting phase hosting Majorana zero-modes on the basis of quantum spin Hall systems. Remarkably, our proposal is completely free of ferromagnets. Instead, we confine helical edge states around a narrow defect line of finite length in a two-dimensional topological insulator. We demonstrate the formation of a new topological regime, hosting protected Majorana modes in the presence of s-wave superconductivity and Zeeman coupling. Interestingly, when the system is weakly tunnel-coupled to helical edge state reservoirs, a particular transpo…
We propose a system of coupled quantum dots in proximity to a superconductor and driven by separate ac potentials to realize and detect Floquet Majorana fermions. We show that the appearance of Floquet Majorana fermions can be finely controlled in the expanded parameter space of the drive frequency, amplitude, and phase difference across the two dots. While these Majorana fermions are not topologically protected, the highly tunable setup provides a realistic system for observing the exotic physics associated with Majorana fermions as well as their dynamical generation and manipulation.
Each end of a Kitaev chain in topological phase hosts a Majorana fermion. Zero bias conductance peak is an evidence of Majorana fermion when the two Majorana fermions are decoupled. These two Majorana fermions are separated in space and this nonlocal aspect can be probed when the two are coupled. Crossed Andreev reflection is the evidence of the nonlocality of Majorana fermions. Nonlocality of Majorana fermions has been proposed to be probed by noise measurements since simple conductance measurements cannot probe it due to the almost cancellation of currents from electron tunneling and crossed…
We propose using a mobile magnetic domain wall as a host of zero-energy Majorana fermions in a spin-orbit coupled nanowire sandwiched by two ferromagnetic strips and deposited on an $s$-wave superconductor. The ability to control domain walls by thermal means allows to braid Majorana fermions nonintrusively, which obey non-Abelian statistics. The analytical solutions of Majorana fermions inside domain walls are obtained in the strong spin-orbit regime.
We study theoretically the role of topological invariants to protect the Majorana fermions in a model of two-dimensional chiral superconductors which belong to class D of topological periodic table. A rich phase diagram is revealed. Each phase is characterized by the topological invariants for 2d (Z) and 1d (Z2), which lead to the Majorana fermion at the edge of the dislocation and the core of the vortex. Interference of the Majorana fermions originated from the different topological invariants is studied. The stability of the Majorana fermion with respect to the interlayer coupling, i.e., in …
We introduce error-correcting codes that can correct for fermion parity-violating (quasiparticle poisoning) and parity-conserving errors in systems of complex fermions and of Majorana fermions. After establishing properties of fermion codes, we introduce a generic construction of fermion codes from weakly self-dual classical, binary error-correcting codes. We use this method to construct (i) the shortest fermion code to correct for quasiparticle poisoning errors, (ii) translationally-invariant fermion codes and (iii) other codes that correct higher-weight errors. We conclude by discussing a po…
We establish a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero time overhead. This is done by introducing a protocol for Pauli product measurements with tetrons and hexons which only requires local 4-Majorana parity measurements. An analogous protocol is used in the fault-tolerant setting, where tetrons and hexons are replaced by Majorana surface code patches, and parity measurements are replaced by lattice surgery, still only requiring local few-Majorana parity me…
In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this result with the Ivanov braiding associated with Majorana operators. The paper generalizes observations of Kauffman and Lomonaco and of Mo-Lin Ge to show that certain strings of Majorana operators give rise to extraspecial 2-groups and to braiding representations of the Ivanov type.
We study theoretically a strongly type-II s-wave superconducting state of two-dimensional Dirac fermions in proximity to a ferromagnet having in-plane magnetization. It is shown that a magnetic domain wall can host a chain of equally spaced vortices in the superconducting order parameter, each of which binds a Majorana fermion state. The overlap integral of neighboring Majorana states is sensitive to the position of the chemical potential of the Dirac fermions. This leads to a characteristic V-shaped dependence of thermal conductivity of Majorana fermions on the chemical potential.
We consider Majorana fermions tunneling among an array of vortices in a 2D chiral p-wave superconductor or equivalent material. The amplitude for Majorana fermions to tunnel between a pair of vortices is found to necessarily depend on the background superconducting phase profile; it is found to be proportional to the sine of half the difference between the phases at the two vortices. Using this result we study tight-binding models of Majorana fermions in vortices arranged in triangular or square lattices. In both cases we find that the aforementioned phase-tunneling relationship leads to the c…
We study the quantum anomalous thermal Hall effect in a topological superconductor which possesses an integer bulk topological number, and supports Majorana excitations on the surface. To realize the quantum thermal Hall effect, a finite gap at the surface is induced by applying an external magnetic field or by the proximity effects with magnetic materials or $s$-wave superconductors with complex pair-potentials. Basing on the lattice model Hamiltonian for superconducting states in Cu-doped Bi$_2$Se$_3$, we compute the thermal Hall conductivity as a function of various parameters such as the c…
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.
We establish that Majorana fermions on the boundary of topological superconductors have only spin-triplet superconducting correlations independent of whether the bulk superconducting gap is spin singlet or triplet. This is universal for time-reversal broken (respected) topological superconductors (TSCs) with an odd number of (pairs of) Majorana fermions on the boundary. Consequently, resonant Andreev reflection induced by Majorana fermions only occurs in spin-triplet channels and always injects spin-triplet Cooper pairs into the leads. This spin-triplet condensate results in a spin-orbit coupl…
Using scattering theory, we investigate interferometers composed of chiral Majorana fermion modes coupled to normal metal leads. We advance an approach in which also the basis states in the normal leads are written in terms of Majorana modes. Thus each pair of electron-hole states is associated with a pair of Majorana modes. Only one lead Majorana mode couples to the intrinsic Majorana mode whereas its partner is completely reflected. Similarly the remaining Majorana modes are completely reflected but in general mix pair-wise. We demonstrate that the charge current can also be expressed in ter…
Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundary. In conventional topological superconductors, Majorana in-gap states appear in the form of either localized zero-dimensional modes or propagating spin-1/2 fermions with a quasi-relativistic dispersion relation. Here we show that unconventional propagating Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states fall into three different categories: a spin-$S$ Majorana fermi…
We analyse the linear confinement of a Majorana fermion in $\left(1+1\right)$-dimensions. We show that the Dirac equation can be solved analytically. Besides, we show that the spectrum of energy is discrete, however, the energy levels are not equally spaced.
We investigate the interplay between ferromagnetic and superconducting order at the edge of a quantum spin Hall insulator. Using complementary analytical and self-consistent numerical approaches, we study a ferromagnetic Josephson junction and show how the direct coupling between magnetism and the superconducting U(1) phase gives rise to several unusual phenomena which distinguishes the present system from its non-topological equivalent. In particular, we demonstrate how the anomalous current-phase relation triggers supercurrent-induced magnetization dynamics and also study the spatial localiz…
Majorana quasiparticles localized in vortex cores of a chiral p-wave superconductor hybridize with one another to form bands in a vortex lattice. We begin by solving a fully microscopic theory describing all quasiparticle bands in a chiral p-wave superconductor in magnetic field, then use this solution to build localized Wannier wavefunctions corresponding to Majorana quasiparticles. A low-energy tight-binding theory describing the intervortex hopping of these is then derived, and its topological properties---which depend crucially on the signs of the imaginary intervortex hopping parameters--…
We show that the $ν=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a…
In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions on the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana-representation and spin-representation are presented. The degenerate ground states of a symmetry protected spin chain therefore previde a promising platform for topological quantum…
We found parity-violating Majorana fermions in a chiral superconductor Sr2RuO4. The current-voltage curves show an anomalous behavior: The induced voltage is an even function of the bias current. The magnetic field dependent results suggest the excitation of the Majorana fermions along the closed chiral edge current of the single domain under bias current. We also discuss the relationship between a change of the chirality and spontaneous magnetization of the single domain Sr2RuO4.
In this work, we investigate the conductance and current correlations properties of a quantum topological inteferometer consisting of a QD coupled to two Majorana Bound States (MBSs) confined at both ends of a 1D topological superconductor ring nanowire. We analyze the ring in its topological non trivial and trivial phases to show that the tunneling conductance, shot noise and fano factor present unique characteristics to distinguish the hallmark of MBSs. We reinforce our findings by taking advantage of the correspondence between the quantum topological interferometer and a dot effectively cou…
We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic field traps a Majorana zero-mode, so that it can be observed in the gate-voltage-averaged differential conductance <dI/dV> as a 4e^2/h zero-bias peak above a (2/3π^2 - 4)e^2/h background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction,…
