We propose a planar Josephson junction setup to host Majorana modes where the semiconductor is sandwiched between superconductors on both surfaces. While the studied configuration is related to both devices proposed for use with topological insulators as well as other proposals for Majorana modes without applied magnetic fields, we find that placing the superconductor on both surfaces allows us to replace the topological insulator by a wider variety of spin-orbit coupled semiconductors. Application of an electric field in the junction together with appropriate superconducting phase differences allows different Fermi surfaces to be subject to different phase differences. We find that these conditions can drive the system into a class-D topological superconductor with a pair of Majorana modes at the two ends of the junction. Additionally, class-DIII topological superconductors with helical Majorana modes also occur in other parts of the phase diagram. We simulate our setup on HgTe near the valence band edge described by the well-known 8-band Kane model with realistic parameters and find phase diagram can be achieved. The topological gap can remain comparable to the bulk superconducting gap throughout the fermi surface.
In the heterostructure composed of a topological insulator sandwiched by two s-wave superconductors, the time reversal invariant topological superconducting phase, possessing helical Majorana edge modes, is found to exist when the two s-wave superconductors form a Josephson junction with a pi phase shift. Based on such a heterostructure, a helical Dirac-Majorana interferometer is proposed to directly measure a unique transport signature of the helical Majorana modes. Furthermore, we envision how our proposal can be realized on the basis of existing materials such as Bi2Se3 or Bi2Te3 thin films…
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 propose to use an ancilla fluxonium qubit to interact with a Majorana qubit hosted by a topological one-dimensional wire. The coupling is obtained using the Majorana qubit-controlled 4 pi Josephson effect to flux bias the fluxonium qubit. We demonstrate how this coupling can be used to sensitively identify the topological superconductivity, to measure the state of the Majorana qubit, to construct 2-qubit operations, and to implement quantum memories with the topological protection.
We show that elongated magnetic skyrmions can host Majorana bound states in a proximity-coupled two-dimensional electron gas sandwiched between a chiral magnet and an $s$-wave superconductor. Our proposal requires stable skyrmions with unit topological charge, which can be realized in a wide range of multilayer magnets, and allows quantum information transfer by using standard methods in spintronics via skyrmion motion. We also show how braiding operations can be realized in our proposal.
One of the goals of modern spectroscopy is to invent techniques which detect neutral excitations that have been theoretically proposed. For superconductors, two point transport measurements detect the Andreev crossed reflection which confirms the existence of the Majorana fermions. Similar information can be obtained from a measurement using two piezoelectric transducers. One transducer measures the stress tensor response from the strain field generated by the second transducer. The ratio between the stress response and strain velocity determines the dissipative response. We will show that the…
We show that Floquet chiral topological superconductivity arises naturally in Josephson junctions made of magnetic topological insulator-superconductor sandwich structures. The Josephson phase modulation associated with an applied bias voltage across the junction drives the system into the anomalous Floquet chiral topological superconductor hosting chiral Majorana edge modes in the quasienergy spectrum, with the bulk Floquet bands carrying zero Chern numbers. The bias voltage acts as a tuning parameter enabling novel dynamical topological quantum phase transitions driving the system into a myr…
We investigate a heterostructure system with a spin-orbit coupled semiconductor sandwiched by an s-wave superconductor and a ferromagnetic insulator, which supports Majorana fermions (MFs) at the superconducting vortex cores. We propose a scheme of transporting and braiding the MFs, which only requires application of point-like gate voltages in a system with nano-meter patterns. By solving the time-dependent Bogoliubov-de Gennes equation numerically, we monitor the time evolutions of MF wave-functions and show that the braiding of MFs with non-Abelian statistics can be achieved by adiabatic sw…
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,…
Topological Majorana fermion (MF) quasiparticles have been recently suggested to exist in semiconductor quantum wires with proximity induced superconductivity and a Zeeman field. Although the experimentally observed zero bias tunneling peak and a fractional ac-Josephson effect can be taken as necessary signatures of MFs, neither of them constitutes a sufficient "smoking gun" experiment. Since one pair of Majorana fermions share a single conventional fermionic degree of freedom, MFs are in a sense fractionalized excitations. Based on this fractionalization we propose a tunneling experiment that…
Constructing qubits which are suitable for quantum computation remains a notable challenge. Here, we propose a superconducting flux qubit in a dc SQUID structure, formed by a conventional insulator Josephson junction and a topological nanowire Josephson junction with Majorana bound states. The zero energy Majorana bound states transport $4π$ period Josephson currents in the nanowire junction. The interplay between this $4π$ period Josephson effect and the convectional $2π$ period Josephson effect in the insulator junction induces a double-well potential energy landscape in the SQUID. As a resu…
Contrary to the widespread belief that Majorana zero-energy modes, existing as bound edge states in 2D topological insulator (TI)-superconductor (SC) hybrid structures, are unaffected by non-magnetic static disorder by virtue of Anderson's theorem, we show that such a protection against disorder does not exist in realistic multi-channel TI/SC/ferromagnetic insulator (FI) sandwich structures of experimental relevance since the time-reversal symmetry is explicitly broken locally at the SC/FI interface where the end Majorana mode (MM) resides. We find that although the MM itself and the \emph{bul…
Majorana zero modes in condensed matter systems have been the subject of much interest in recent years. Their non-Abelian exchange statistics, making them a unique state of matter, and their potential applications in topological quantum computation, earned them attention from both theorists and experimentalists. It is generally understood that in order to form Majorana zero modes in quasi-one-dimensional topological insulators, time-reversal symmetry must be broken. The straightforward mechanisms for doing so -- applying magnetic fields or coupling to ferromagnets -- turned out to have many un…
Heavy metals, such as Au, Ag, and Pb, often have sharp surface states that are split by strong Rashba spin-orbit coupling. The strong spin-orbit coupling and two-dimensional nature of these surface states make them ideal platforms for realizing topological superconductivity and Majorana fermions. In this paper, we further develop a proposal to realize Majorana fermions at the ends of quasi-one-dimensional metallic wires. We show how superconductivity can be induced on the metallic surface states by a combination of proximity effect, disorder, and interactions. Applying a magnetic field along t…
We study quasiparticle states on a surface of a topological insulator (TI) with proximity-induced superconductivity under an external magnetic field. An applied magnetic field creates two Majorana bound states: a vortex Majorana state localized inside a vortex core and an exterior Majorana state localized along a circle centered at the vortex core. We calculate the spin-resolved local density of states (LDOS) and demonstrate that the shrinking of the radius of the exterior Majorana state, predicted in Ref. [R. S. Akzyanov et al., Phys. Rev. B 94, 125428 (2016)], under a strong magnetic field c…
We propose to realize a one-dimensional chiral topological superconducting state at the magnetic domain walls stripe of a magnetic topological insulator coupled with a conventional $s$-wave superconductor. The localized Majorana zero modes can be constructed in a reconfigurable manner through magnetic domain writing by magnetic force microscopy. This proposal could be further extended to the Majorana zero modes at domain walls on superconducting spin-helical Dirac surface states, and may be applicable to the two-dimensional time-reversal invariant topological superconductor on FeTe$_{0.5}$Se$_…
The pursuit for Majorana fermions is one of the top priorities in condensed matter physics at the moment. In this work we propose a new method of fabricating Majorana Josephson devices in systems with a weak or no spin-orbit coupling and without external magnetic fields. Our proposal is based on curved semiconductor wires in the proximity of superconducting elements and a small number of nanomagnets. With this method it is possible to fabricate devices that are not feasible by employing straight topological wire segments. The proposed method is naturally scalable and opens up a possibility for…
Topological insulators (TIs) have attracted immense interest because they host helical surface states. Protected by time-reversal symmetry, they are robust to non-magnetic disorder. When superconductivity is induced in these helical states, they are predicted to emulate p-wave pairing symmetry, with Majorana states bound to vortices. Majorana bound states possess non-Abelian exchange statistics which can be probed through interferometry. Here, we take a significant step towards Majorana interferometry by observing pronounced Fabry-Perot oscillations in a TI sandwiched between a superconducting…
We propose an experimental scheme to observe non-abelian statistics with cold atoms in a two dimensional optical lattice. We show that the Majorana-Schockley modes associated with line defects obey non-abelian statistics and can be created, braided, and fused, all through adiabatic shift of the local chemical potentials. The detection of the topological qubit is transformed to local measurement of the atom number on a single lattice site. We demonstrate the robustness of the braiding operation by incorporating noise and experiential imperfections in numerical simulations, and show that the req…
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…
Proposals for realizing Majorana fermions in condensed matter systems typically rely on magnetic fields, which degrade the proximitizing superconductor and plague the Majoranas' detection. We propose an alternative scheme to realize Majoranas based only on phase-biased superconductors. The phases (at least three of them) can be biased by a tiny magnetic field threading macroscopic superconducting loops, focusing and enhancing the effect of the magnetic field onto the junction, or by supercurrents. We show how a combination of the superconducting phase winding and the spin-orbit phase induced i…
Magnetic atoms on superconductors induce localized Yu-Shiba-Rusinov (YSR) bound states. The proposal that topological superconductivity and Majorana modes can be engineered in arrays of hybridizing YSR states has led to their intense investigation. Here, we study Majorana modes emerging from bands of hybridized YSR states in artificially constructed Manganese (Mn) chains on superconducting Niobium (Nb). By controlling the chain geometry on the single atom level, we can measure the interaction-induced energy splitting of Majorana modes from both chain's ends with increasing chain length. We fin…
We propose a versatile platform to investigate the existence of Majorana bound states (MBSs) and their non-Abelian statistics through braiding. This implementation combines a two-dimensional electron gas formed in a semiconductor quantum well grown on the surface of an s-wave superconductor with a nearby array of magnetic tunnel junctions (MTJs). The underlying magnetic textures produced by MTJs provide highly controllable topological phase transitions to confine and transport MBSs in two dimensions, overcoming the requirement for a network of wires. Obtained scaling relations confirm that var…
Motivated by recent proposals to realize Majorana bound states in chains and arrays of magnetic atoms deposited on top of a superconductor, we study the topological properties of various chain structures, ladders and two-dimensional arrangements exhibiting magnetic helices. We show that magnetic domain walls where the chirality of a magnetic helix is inverted support two protected Majorana states giving rise to a tunneling conductance peak twice the height of a single Majorana state. The topological properties of coupled chains exhibit nontrivial behaviour as a function of the number of chains…
Majorana zero mode is an exotic quasi-particle excitation with non-Abelian statistics in topological superconductor systems, and can serve as the cornerstone for topological quantum computation, a new type of fault-tolerant quantum computation architecture. This review paper highlights recent progress in realizing Majorana modes in iron-based high-temperature superconductors. We begin with the discussion on topological aspect of electronic band structures in iron-based superconductor compounds. Then we focus on several concrete proposals for Majorana modes, including the Majorana zero modes in…
We present a detailed theoretical study of chiral topological superconductor phases in proximity-superconducting graphene systems based on an effective model inspired by DFT simulations. Inducing s-wave superconductivity to quantum anomalous Hall effect systems leads to chiral topological superconductors. For out-of-plane magnetization we find topological superconducting phases with even numbers of chiral Majorana fermions per edge which is correlated to the opening of a nontrivial gap in the bulk system in the $\mathrm{ K}$-points and their connection under particle-hole symmetry. We show tha…
In this work, we show that a quasi-one-dimensional $d_{x^2-y^2}$-wave superconductor with Rashba spin-orbit coupling is a topological superconductor (TS). This time-reversal invariant DIII class TS supports two topologically protected zero energy Majorana fermions at each end of the system. In contrast to proposals using s-wave superconductors in which a strong magnetic field and the fine tuning of the chemical potential are needed to create Majorana fermions, in our proposal, the topologically non-trivial regime can be reached in the absence of a magnetic field and in a wide range of chemical…
A topological superconductor is characterized by having a pairing gap in the bulk and gapless self-hermitian Majorana modes at its boundary. In one dimension, these are zero-energy modes bound to the ends, while in two dimensions these are chiral gapless modes traveling along the edge. Majorana modes have attracted a lot of interest due to their exotic properties, which include non-abelian exchange statistics. Progress in realizing topological superconductivity has been made by combining spin-orbit coupling, conventional superconductivity, and magnetism. The existence of protected Majorana mod…
Realizing topological superconductivity and Majorana zero modes in the laboratory is one of the major goals in condensed matter physics. We review the current status of this rapidly-developing field, focusing on semiconductor-superconductor proposals for topological superconductivity. Material science progress and robust signatures of Majorana zero modes in recent experiments are discussed. After a brief introduction to the subject, we outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finall…
We show that a film of a semiconductor such as GaAs, in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect, supports zero-energy Majorana fermion modes in the ordinary vortex excitations. The key to the topological order is the existence of spin-orbit coupling, coexisting with proximity-induced s-wave superconductivity. Since time reversal symmetry is explicitly broken, the edge of the film constitutes a chiral Majorana wire. The heterostructure we propose -- a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator -- is…
In a variety of rare-earth based compounds singlet superconductivity coexists with helical magnetism. Here we demonstrate that surfaces of these systems should generically host a finite density of zero-energy Majorana modes. In the limit of vanishing disorder, these modes lead to a divergent contribution to zero-energy density of states and to zero-temperature entropy proportional to the sample surface area. When confined to a wire geometry, a discrete number of Majorana modes can be isolated. The relatively large characteristic energy scales for superconductivity and magnetism, compared to ot…
Supercurrent detection and manipulation of topological phase transitions in Shiba-Majorana hybrid systems
Physical Research Laboratory（物理研究实验室）；Technische Universität Braunschweig（布伦瑞克工业大学）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）；Universität Hamburg（汉堡大学）；International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所磁拓扑国际研究中心）；University of Basel（巴塞尔大学）
One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to …
It has been proposed that a line junction between spiral magnet and superconductor or between ferromagnet and superconductor with Rashba spin-orbital coupling can produce Majorana zero mode (MZM) at the ends of the line. However, a strong magnetic exchange coupling between the magnetic atoms and the superconductor (about half of the bandwidth of the superconductor) is needed to obtain MZM. Here, we design devices to reduce the needed magnetic exchange coupling. In the first proposal, we cover a very narrow $s$-wave superconducting wire formed by a monolayer film or a layered material (such as …
Second-order topological superconductors (SOTSs) host localized Majorana fermions and provide a new platform for topological quantum computation. We propose a remarkable and feasible way to realize networks based on SOTSs which allow to nucleate and braid Majorana bound states (MBSs) in an all-electrical manner without fine-tuning. The proposed setups are scalable in a straightforward way and can accommodate any even number of MBSs. Moreover, the MBSs in the networks allow defining qubits whose states can be initialized and read out by measuring Josephson currents flowing between SOTS islands.…
The nonlocal nature of the fermionic mode spanned by a pair of Majorana bound states in a one-dimensional topological superconductor has inspired many proposals aiming at demonstrating this property in transport. In particular, transport through the mode from a lead attached to the left bound state to a lead attached to the right will result in current cross-correlations. For ideal zero modes on a grounded superconductor, the cross-correlations are however completely suppressed in favor of purely local Andreev reflection. In order to obtain a non-vanishing cross-correlation, previous studies h…
We consider a superconducting film exchange-coupled to a close-by chiral magnetic layer and study how magnetic skyrmions can induce the formation of Majorana bound states (MBS) in the superconductor. Inspired by a proposal by Yang et al. [Phys. Rev. B 93, 224505 (2016)], which suggested MBS in skyrmions of even winding number, we explore whether such skyrmions could result from a merger of ordinary skyrmions. We conclude that the formation of higher-winding skyrmions is not realistic in chiral magnets. Subsequently, we present a possibility to obtain MBS from realistic skyrmions of winding num…
We propose a physical realization of a commuting Hamiltonian of interacting Majorana fermions realizing $Z_{2}$ topological order, using an array of Josephson-coupled topological superconductor islands. The required multi-body interaction Hamiltonian is naturally generated by a combination of charging energy induced quantum phase-slips on the superconducting islands and electron tunneling. Our setup improves on a recent proposal for implementing a Majorana fermion surface code [1], a 'hybrid' approach to fault-tolerant quantum computation that combines (1) the engineering of a stabilizer Hamil…
A fundamental obstacle for achieving quantum computation is local decoherence. One way to circumvent this problem rests on the concepts of topological quantum computation using non-local information storage, for example on pairs of Majorana fermions (MFs). The arguably most promising way to generate MFs relies at present on spin-triplet p-wave states of superconductors (SC), which are not abundant in nature, unfortunately. Thus, proposals for their engineering in devices, usually via proximity effect from a conventional SC into materials with strong spinorbit coupling (SOC), are intensively in…
In this paper we find that confining a second-order topological superconductor with a harmonic potential leads to a proliferation of Majorana corner modes. As a consequence, this results in the formation of Majorana corner flat bands which have a fundamentally different origin from that of the conventional mechanism. This is due to the fact that they arise solely from the one-dimensional gapped boundary states of the hybrid system that become gapless without the bulk gap closing under the increase of the trapping potential magnitude. The Majorana corner states are found to be robust against th…
We introduce two-dimensional topological insulators in proximity to high-temperature cuprate or iron-based superconductors as high-temperature platforms of Majorana Kramers pairs of zero modes. The proximity-induced pairing at the helical edge state of the topological insulator serves as a Dirac mass, whose sign changes at the sample corner because of the pairing symmetry of high-$T_c$ superconductors. This sign changing naturally creates at each corner a pair of Majorana zero modes protected by time-reversal symmetry. Conceptually, this is a topologically trivial superconductor-based approach…
Non-Majorana-origin of the half-integer conductance quantization elucidated by multi-terminal superconductor-quantum anomalous Hall insulator heterostructure
Recently there have been numerous proposals to create Majorana zero modes in solid state heterojunctions, superconducting wires and optical lattices. Putatively the information stored in qubits constructed from these modes is protected from various forms of decoherence. Here we show that this is not the case. We present a generic method to study the effect of external perturbations on these modes. We focus on the case where there are no interactions between different Majorana modes either directly or through intermediary fermions. To quantify the rate of loss of the information stored in the M…
We consider a new model system supporting Majorana zero modes based on semiconductor nanowires with a full superconducting shell. We demonstrate that, in the presence of spin-orbit coupling in the semiconductor induced by a radial electric field, the winding of the superconducting order parameter leads to a topological phase supporting Majorana zero modes. The topological phase persists over a large range of chemical potentials and can be induced by a predictable and weak magnetic field piercing the cylinder. The system can be readily realized in semiconductor nanowires covered by a full super…
We uncover a novel two-particle Berry phase mechanism to realize exotic corner modes in second-order topological insulators (TIs) and topological superconductors (TSCs) with time-reversal symmetry. We show that the nontrivial pseudospin textures of edge states in two different types of two-dimensional TIs give rise to the novel two-particle geometric phases in the particle-hole and particle-particle channels, respectively, for which the edge mass domain walls or intrinsic $π$-junctions emerge across corners when an external magnetic field or $s$-wave superconductivity is considered, hosting Di…
Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as $(i)$ a tool for revealing the nature of correlated insulators and $(ii)$ a platform for Majorana-based topological qubits. In particular, we show that the band structure of a gate-defined wire immersed in an `inter-valley coherent' correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the …
We propose that propagating one-dimensional Majorana fermions will develop in the vortex cores of certain iron-based superconductors, most notably Li(Fe$_{1-x}$Co$_x$)As. A key ingredient of this proposal are the 3D Dirac cones recently observed in ARPES experiments [P. Zhang et al., Nat. Phys. $\textbf{15}$, 41 (2019)]. Using an effective Hamiltonian around the $Γ-Z$ line we demonstrate the development of gapless one-dimensional helical Majorana modes, protected by $C_4$ symmetry. A topological index is derived which links the helical Majorana modes to the presence of monopoles in the Berry c…
We consider a three-dimensional topological insulator (TI) wire with a non-uniform chemical potential induced by gating across the cross-section. This inhomogeneity in chemical potential lifts the degeneracy between two one-dimensional surface state subbands. A magnetic field applied along the wire, due to orbital effects, breaks time-reversal symmetry and lifts the Kramers degeneracy at zero-momentum. If placed in proximity to an $s$-wave superconductor, the system can be brought into a topological phase at relatively weak magnetic fields. Majorana bound states (MBSs), localized at the ends o…
Spin chains proximitized with superconducting condensates have emerged as one of the most promising platforms for the realization of Majorana modes. Here, we craft diluted spin chains atom-by-atom following seminal theoretical proposal suggesting indirect coupling mechanisms as a viable route to trigger topological superconductivity. Starting from single adatoms hosting deep Shiba states, we use the highly anisotropic Fermi surface of the substrate to create spin chains characterized by different magnetic configurations along distinct crystallographic directions. By scrutinizing a large set of…
We find the coexistence of two kinds of non-abelian anyons, Majorana fermion at the geometric ends and Jackiw-Rebbi-type bound state (JRBS)at a domain-wall, in a topological superconducting phase in one-dimensional (1D) systems. Each localized JRBS carries a new fractional quantity, half of the parity of fermion number. This induces a topological protected crossing at the zero energy for its eigen-energy. For a chain embedded with a JRBS, one is possible to switch between the occupied and empty states of Majorana zero energy state (MZES) by varying the strength of external magnetic field acros…
We propose a method utilizing edge current to observe Majorana fermions in the surface Andreev bound state for the superfluid $^3$He A- and B-phases. The proposal is based on self-consistent analytic solutions of quasi-classical Green's function with an edge. The local density of states and edge mass current in the A-phase or edge spin current in the B-phase can be obtained from these solutions. The edge current carried by the Majorana fermions is partially cancelled by quasiparticles (QPs) in the continuum state outside the superfluid gap. QPs contributing to the edge current in the continuum…
