Heterostructures of spin-orbit coupled materials with s-wave superconductors are thought to be capable of supporting zero-energy Majorana bound states. Such excitations are known to obey non-Abelian statistics in two dimensions, and are thus relevant to topological quantum computation (TQC). In a one-dimensional system, Majorana states are localized to phase boundaries. In order to bypass the constraints of one-dimension, a wire network may be created, allowing the exchange of Majoranas by way of junctions in the network. Alicea et al. have proposed such a network as a platform for TQC, showing that the Majorana bound states obey non-Abelian exchange statistics even in quasi-one-dimensional systems. Here we show that the particular realization of non- Abelian statistics produced in a Majorana wire network is highly dependent on the local properties of individual wire junctions. For a simply connected network, the possible realizations can be characterized by the chirality of individual junctions. There is in general no requirement for junction chiralities to remain consistent across a wire network. We show how the chiralities of different junctions may be compared experimentally and discuss the implications for TQC in Majorana wire networks.
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 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…
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…
A phase from an adiabatic exchange of Majorana bound states (MBS) reveals their exotic anyonic nature. For detecting this exchange phase, we propose an experimental setup consisting of a Corbino-geometry Josephson junction on the surface of a topological insulator, in which two MBS at zero energy can be created and rotated. We find that if a metallic tip is weakly coupled to a point on the junction, the time-averaged differential conductance of the tip-Majorana coupling shows peaks at the tip voltages $eV = \pm (α- 2πl) \hbar/ T_J$, where $α= π/2$ is the exchange phase of the two circulating M…
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…
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 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 …
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…
The Majorana fermion can be described by a real wave function with only two phases (0 and π) which provide a controllable degree of freedom. We propose a strategy to regulate the phase of the chiral Majorana state by coupling with a scanning tunneling microscope tip in a system consisting of quantum anomalous Hall insulator coupled with a superconductor. With the change of the chemical potential, the chiral Majorana state can be tuned alternately between 0 and π, in which, correspondingly, the perfect normal tunneling and perfect crossed Andreev reflection appear. The perfect crossed Andreev r…
Signatures of Majorana fermion bound states in one-dimensional topological insulator (TI) nanowires with proximity effect induced superconductivity are studied. The phase diagram and energy spectra are calculated for single TI nanowires and it is shown that the nanowires can be in the topological invariant phases of winding numbers $W=0, \pm 1$, and $\pm 2$ corresponding to the cases with zero, one and two pairs of Majorana fermions in the single TI nanowires. It is also shown that the topological winding numbers, i.e., the numbers of pairs of Majorana fermions in the TI nanowires can be extra…
Demonstration of non-Abelian anyon statistics often requires dynamical controls of a complicated device that are challenging in realistic situations. We propose a {\it single} Josephson junction to detect a non-Abelian statistics effect of Majorana fermions, formed by two finite-size $s$-wave superconductors on a topological insulator under a magnetic field. At certain field strengths, a train of three localized Majorana fermions appears along the junction, while an extended chiral Majorana fermion encircles the train and the superconductors. A DC voltage bias across the junction causes the tr…
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 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.
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 $π$ 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 …
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…
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.
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 find that Majorana fermions induce selective equal spin Andreev reflections (SESARs), in which incoming electrons with certain spin polarization in the lead are reflected as counter propagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin-polarized. Therefore, a topological superconductor which supports Majorana fermions…
Kitaev's Pfaffian formula equates the ground-state fermion parity of a closed system to the sign of the Pfaffian of the Hamiltonian in the Majorana basis. Using Klich's theory of full counting statistics for paired fermions we generalize the Pfaffian formula to account for quantum fluctuations in the fermion parity of an open subsystem. A statistical description in the framework of random-matrix theory is used to answer the question when a vanishing fermion parity in a superconductor fusion experiment becomes a distinctive signature of an isolated Majorana zero-mode.
Unambiguous identification of Majorana physics presents an outstanding problem whose solution could render topological quantum computing feasible. We develop a numerical approach to treat finite-size superconducting chains supporting Majorana fermions, which is based on iterative application of a two-site Bogoliubov transformation. We demonstrate the applicability of the method by studying a resonant level attached to the superconductor subject to external perturbations. In the topological phase, we show that the spectrum of a single resonant level allows to distinguish peak coming from Majora…
It is shown in previous works that the coupling between two Majorana end states in superconducting quantum wires leads to fractional Josephson effect. However, in realistic experimental conditions, multiple bands of the wires are occupied and the Majorana end states are accompanied by other fermionic end states. This raises the question concerning the robustness of fractional Josephson effect in these situations. In this work, we show that the absence of the avoided energy crossing which gives rise to the fractional Josephson effect is robust, even when the Majorana fermions are coupled with a…
We describe experimental signatures of Majorana fermion edge states, which form at the interface between a superconductor and the surface of a topological insulator. If a lead couples to the Majorana fermions through electron tunneling, the Majorana fermions induce \textit{resonant} Andreev reflections from the lead to the grounded superconductor. The linear tunneling conductance is $0 $ ($2 e^2/h$) if there is an even (odd) number of vortices in the superconductor. Similar resonance occurs for tunneling into the zero mode in the vortex core. We also study the current and noise of a two-lead d…
We consider different configurations of ac driven quantum dots coupled to superconductor leads where Majorana fermions can exist as collective quasiparticles. The main goal is to tune the existence, localization and properties of these zero energy quasiparticles by means of periodically driven external gates. In particular, we analyze the relevance of the system and driving symmetry. We predict the existence of different sweet spots with Floquet Majorana fermions in configurations where they are not present in the undriven system.
Majorana billiards are finitely sized, arbitrarily shaped superconducting islands that host Majorana bound states. We study the fermion-parity switches of the ground state of Majorana billiards. In particular, we study the density and statistics of these fermion-parity switches as a function of applied magnetic field and chemical potential. We derive formulae that specify how the average density of fermion-parity switches depends on the geometrical shape the billiard. Moreover, we show how oscillations around this average value is determined by the classical periodic orbits of the billiard. Fi…
We consider an experimentally feasible setup to demonstrate the existence and coherent dynamics of Majorana fermion. The transport setup consists of a quantum dot and a tunnel-coupled semiconductor nanowire which is anticipated to generate Majorana excitations under some conditions. For transport under finite bias voltage, we find that a subtraction of the source and drain currents can expose the essential feature of the Majorana fermion, including the zero-energy nature by gate-voltage modulating the dot level. Moreover, coherent oscillating dynamics of the Majorana fermion between the nanowi…
Recently, Majorana Fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation (TQC). They are proposed to exist in various two-dimensional (2D) topological systems, such as px+ipy topological superconductor and nanowire-superconducting hybridization system. In this paper, two types of Majorana Fermions with different polygon sign rules are pointed out. A "smoking gun" numerical evidence to identify MF's classification is presented through looking for the signature of a first order topological quantum phase trans…
