Measuring the Majorana entropy $S_M=k_B\log(2^\frac{1}{2})$ may uniquely reveal whether an initial equilibrium state of a nanoscale device is of Majorana nature and subsequent operations deal with an essentially nonlocal pair of non-Abelian Majorana bound states and not with trivial or other accidental non-Abelian states. However, in realistic setups both Majorana modes are inevitably involved in tunneling processes. We show that even when the tunneling amplitude of one Majorana mode is significantly suppressed, the Majorana entropy ruins and straightforward experiments will in general detect entropy $S\ll S_M$. To avoid this general problem we present a mechanism of the Majorana entropy revival via the tunneling phases of the Majorana modes and demonstrate that to successfully observe the universal Majorana plateau $S=S_M$ one should intelligently tune the tunneling phases instead of leaving them uncontrolled. Practical feasibility of appropriate Majorana entropy measurements is supported by an example with parameters well achievable in modern labs.
We study the quantum dynamics of Majorana and regular fermion bound states coupled to a quasi-one-dimensional metallic lead. The dynamics following the quench in the coupling to the lead exhibits a series of dynamical revivals as the bound state propagates in the lead and reflects from the boundaries. We show that the nature of revivals for a single Majorana bound state depends uniquely on the presence of a resonant level in the lead. When two spatially separated Majorana modes are coupled to the lead, the revivals depend only on the phase difference between their host superconductors. Remarka…
We consider a two-dimensional px+i py superconductor in the presence of multiple vortices, which support zero-energy Majorana fermion states in their cores. Intervortex tunnelings of the Majorana fermions lift the topological state degeneracy. Using the Bogoliubov-de Gennes equation, we calculate splitting of the zero-energy modes due to these tunneling events. We also discuss superconducting fluctuations and, in particular, their effect on the energy splitting.
Universal fractionalization of quantum transport characteristics in Majorana quantum dot devices is expected to emerge for well separated Majorana bound states. We show that the Majorana universality of the differential shot noise $\partial S^>/\partial V$ and conductance $\partial I/\partial V$ at low bias voltages $V$ arises only in ideal setups with only one Majorana mode entangled with the quantum dot. In realistic devices, where both Majorana modes are entangled with the quantum dot, $\partial S^>/\partial V$ and $\partial I/\partial V$ become very sensitive to tunneling phases and their …
We propose a scheme to distinguish zero-energy peaks due to Majorana from those due to other effects at finite temperature by simply replacing the normal metallic lead with a resistive lead (large R kΩ) in the tunneling spectroscopy. The dissipation effects due to the large resistance change the tunneling conductance significantly in different ways. The Majorana peak remains increase as temperature decreases G T^(2r-1) for r=e^2 R/h<1/2. The zero-energy peak due to other effects splits into two peaks at finite temperature and the conductance at zero voltage bias varies with temperature by a po…
We propose a scheme to detect the Majorana-zero-mode-induced crossed Andreev reflection by measuring tunneling current directly. In this scheme a metallic ring structure is utilized to separate electron and hole signals. Since tunneling electrons and holes have different propagating wave vectors, the conditions for them to be constructively coherent in the ring differ. We find that when the magnetic flux threading the ring varies, it is possible to observe adjacent positive and negative current peaks of almost equal amplitudes.
We consider theoretically tunneling characteristic of a junction between a normal metal and a chain of coupled Majorana bound states generated at crossings between topological and non-topological superconducting sections, as a result of, for example, disorder in nanowires. While an isolated Majorana state supports a resonant Andreev process, yielding a zero bias differential conductance peak of height 2e^2/h, the situation with more coupled Majorana states is distinctively different with both zeros and 2e^2/h peaks in the differential conductance. We derive a general expression for the current…
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…
Recent tunneling experiments on InSb hybrid superconductor-semiconductor devices have provided hope for a stabilization of Majorana edge modes in a spin-orbit quantum wire subject to a magnetic field and superconducting proximity effect. Connecting the experimental scenario with a microscopic description poses challenges of different kind, such as accounting for the effect of interactions on the tunneling properties of the wire. We develop a density matrix renormalization group (DMRG) analysis of the tunneling spectra of interacting Majorana chains, which we explicate for the Kitaev chain mode…
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…
The image of a Majorana mode located on the focus of an elliptical corral of free electrons is studied. The Majorana mode may be taken at the edge of a topological wire superimposed on the two-dimensional electron gas. At low energies the states of the wire are ignored except for the Majorana mode. Usual tunneling to a fermionic mode is compared. In the favorable cases, tunneling to a Majorana mode leads to an enhanced mirage effect and a spectral weight mainly confined around the foci, in comparison to the tunneling to a fermionic mode. The Majorana character of the image is shown computing t…
The zero-energy bound states at the edges or vortex cores of chiral p-wave superconductors should behave like majorana fermions. We introduce a model Hamiltonian that describes the tunnelling process when electrons are injected into such states. Using a non-equilibrium green function formalism, we find exact analytic expressions for the tunnelling current and noise and identify experimental signatures of the majorana nature of the bound states to be found in the shot noise. We discuss the results in the context of different candidate materials that support triplet superconductivity. Experiment…
Majorana fermions are promising building blocks of forthcoming technology in quantum computing. However, their non-ambiguous identification has remained a difficult issue because of the concomitant competition with other topologically trivial fermionic states, which poison their detection in most spectroscopic probes. By employing numerical and analytical methods, here we show that the Fano factor tomography is a key distinctive feature of a Majorana bound state, displaying a spatially constant Poissonian value equal to one. In contrast, the Fano factor of other trivial fermionic states, like …
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 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 theoretically consider transport properties of a normal metal (N)- superconducting semiconductor nanowire (S)-normal metal (N) structure (NSN) in the context of the possible existence of Majorana bound states in disordered semiconductor-superconductor hybrid systems in the presence of spin-orbit coupling and Zeeman splitting induced by an external magnetic field. We study in details the transport signatures of the topological quantum phase transition as well as the existence of the Majorana bound states in the electrical transport properties of the NSN structure. Our theory includes the rea…
A one-dimensional semiconductor nanowire proximitized by a nearby superconductor may become a topological superconductor hosting localized Majorana zero modes at the two wire ends in the presence of spin-orbit coupling and Zeeman spin splitting (arising from an external magnetic field). The hallmark of the presence of such Majorana zero modes is the appearance of a zero-temperature quantized zero-bias conductance peak in the tunneling spectroscopy of the Majorana nanowire. We theoretically study the temperature and the tunnel coupling dependence of the tunneling conductance in such nanowires t…
In thermodynamics a macroscopic state of a system results from a number of its microscopic states. This number is given by the exponent of the system's entropy $\exp(S)$. In non-interacting systems with discrete energy spectra, such as large scale quantum dots, $S$ as a function of the temperature has usually a plateau shape with integer values of $\exp(S)$ on these plateaus. Plateaus with non-integer values of $\exp(S)$ are fundamentally forbidden and would be thermodynamically infeasible. Here we investigate the entropy of a non-interacting quantum dot coupled via tunneling to normal metals …
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…
Experimental evidence for Majorana bound states largely relies on measurements of the tunneling conductance. While the conductance into a Majorana state is in principle quantized to $2e^2/h$, observation of this quantization has been elusive, presumably due to temperature broadening in the normal-metal lead. Here, we propose to use a superconducting lead instead, whose gap strongly suppresses thermal excitations. For a wide range of tunneling strengths and temperatures, a Majorana state is then signaled by symmetric conductance peaks at $eV=\pmΔ$ with quantized height $G=(4-π)2e^2/h$. For a su…
We consider a model of a Josephson junction of two topological superconducting wires mediated by an interacting quantum dot. An additional normal electrode coupled to the dot from the top allows to probe its density of states. The Majorana states adjacent to the dot hybridize across the junction and from a bound state in the dot. The dot is subjected to the effective magnetic field arising from the superposition of the fields driving each wire into topological states, which, dependent on the angle between the fields, introduces variable Zeeman splitting of the dot active level. We show that el…
We have modeled SQUIDs with topologically non-trivial superconducting junctions and performed an optimization study on the Majorana fermion detection. We find that the SQUID parameters beta_L, and beta_C can be used to increase the ratio of Majorana tunneling to standard Cooper pair tunneling by more than two orders of magnitude. Most importantly, we show that dc SQUIDs including topologically trivial components can still host strong signatures of the Majorana fermion. This paves the way towards the experimental verification of the theoretically predicted Majorana fermion.
A semiconducting nanowire with strong Rashba coupling and in proximity of a superconductor hosts Majorana edge modes. An array of such nanowires with inter-wire coupling gives an approximate description of a two-dimensional topological superconductor, where depending on the strength of the magnetic field and the chemical potential, a rich phase diagram hosting trivial and different types of non-trivial phases can be achieved. Here, we theoretically consider such a two-dimensional assembly of spin-orbit coupled superconducting nanowires and calculate the collective tunneling conductance between…
Electron transport through Majorana nanowire with strongly asymmetric couplings to normal metal leads is considered. In three terminal geometry (electrically grounded nanowire) it is shown that the presence of unbiased electrode restores zero-bias anomaly even for strong Majorana energy splitting. For effectively two-terminal geometry we show that electrical current through asymmetric Majorana junction is qualitatively different from the analogous current through a resonant (Breit-Wigner) level.
Photon-assisted tunneling frequently provides detailed information on the underlying charge-transfer process. In particular, the Tien-Gordon approach and its extensions predict that the sideband spacing in bias voltage is a direct fingerprint of the number of electrons transferred in a single tunneling event. Here, we analyze photon-assisted tunneling into subgap states in superconductors in the limit of small temperatures and bias voltages where tunneling is dominated by resonant Andreev processes and does not conform to the predictions of simple Tien-Gordon theory. Our analysis is based on a…
Braiding of non-Abelian Majorana anyons is a first step towards using them in quantum computing. We propose a protocol for braiding Majorana zero modes formed at the edges of nanowires with strong spin orbit coupling and proximity induced superconductivity. Our protocol uses high frequency virtual tunneling between the ends of the nanowires in a tri-junction, which leads to an effective low frequency coarse grained dynamics for the system, to perform the braid. The braiding operation is immune to amplitude noise in the drives, and depends only on relative phase between the drives, which can be…
We investigate a system of multiple Majorana states at the end of a topological superconducting wire coupled to a normal lead. For a minimum of three Majorana fermions at the interface, we find nontrivial renormalization physics. Interface tunneling processes can be classified in terms of spin-1/2 and spin-3/2 irreducible representations of the SU(2) group. We show that the renormalization of the tunneling amplitudes belonging to different representations is completely different in that one type is suppressed, whereas the other is enhanced, depending on the sign of the interaction coupling. Th…
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…
We study the thermoelectric effect between a conducting lead and a Majorana edge state. In the tunneling limit, we first use the Landuaer-Buttiker formalism to derive the Mott formula relating the thermopower and the differential conductance between a conducting lead and a superconductor. When the tunneling takes place between a conducting lead and a Majorana edge state, we show that a non-vanishing thermopower can exist. Combining measurements of the differential conductance and the voltage difference induced by the temperature difference between the conducting lead and the edge state, the Mo…
Potter and Lee have demonstrated the presence of Majorana zero modes at the ends of quasi one-dimensional (1-D) p+ip superconductors. We use conformal field theory (CFT) methods to show that inter-edge tunneling of the vortex excitations along the length of the channel is crucial for such localization. We show that localization of Majorana modes occurs also in quasi 1-D channels of the 5/2 fractional quantum Hall (FQH) systems when modeled, following Moore and Read, as the p+ip paired state of composite fermions. We propose a tunnel-interferometry experiment to detect these modes, which should…
We consider a quantum dot coupled to a topological superconductor and two normal leads and study transport properties of the system. Using Keldysh path-integral approach, we study current fluctuations (shot noise) within the low-energy effective theory. We argue that the combination of the tunneling conductance and the shot noise through a quantum dot allows one to distinguish between the topological (Majorana) and non-topological (e.g., Kondo) origin of the zero-bias conduction peak. Specifically, we show that, while the tunneling conductance might exhibit zero-bias anomaly due to Majorana or…
In the presence of Rashba spin-orbit coupling, magnetic field can drive a proximitized nanowire into a topological superconducting phase. We study transport properties of such nanowires in the Coulomb blockade regime. The associated with the topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire - a non-local signature of topological superconductivity. In this work, we focus on the case of strong hybridization of the Majorana modes with the normal leads. The induced by hybridization broadening of the Ma…
Hybrid nanowires with proximity-induced superconductivity in the topological regime host Majorana zero modes (MZMs) at their ends, and networks of such structures can produce topologically protected qubits. In a double-island geometry where each segment hosts a pair of MZMs, inter-pair coupling mixes the charge parity of the islands and opens an energy gap between the even and odd charge states at the inter-island charge degeneracy. Here, we report on the spectroscopic measurement of such an energy gap in an InAs/Al double-island device by tracking the position of the microwave-induced quasipa…
We study the local density of states (LDOS) in systems of Luttinger-liquid nanowires connected to a common mesoscopic superconducting island, in which Majorana bound states give rise to different types of topological Kondo effects. We show that electron interactions enhance the low-energy LDOS in the leads close to the island, with unusual exponents due to Kondo physics that can be probed in tunneling experiments.
Quantum thermodynamics is a promising route to unambiguous detections of Majorana bound states. Being fundamentally different from quantum transport, this approach reveals unique Majorana thermodynamic behavior and deepens our insight into Majorana quantum transport itself. Here we demonstrate that a nanoscopic system with topological superconductors produces a remarkable accumulation of Majorana thermodynamic states in wide ranges of Majorana tunneling phases by means of increasing its temperature $T$. Revealing this physical behavior is twofold beneficial. First, it significantly reduces the…
Trivial Andreev bound states arising from chemical potential variations could lead to zero-bias tunneling conductance peaks at finite magnetic fields in class $D$ nanowires, precisely mimicking the predicted zero-bias conductance peaks arising from the topological Majorana bound states. This finding raises a serious question on the efficacy of using zero-bias tunneling conductance peaks, by themselves, as evidence supporting the existence of topological Majorana bound states in nanowires. In the current work, we provide specific experimental protocols for tunneling spectroscopy measure- ments …
We investigate the dynamics of a charge qubit consisting of two Coulomb-blockaded islands hosting Majorana zero modes. The frequency of the qubit is determined by coherent single-electron tunneling between two islands originating from the hybridization of two Majorana zero modes localized at the junction. We calculate the sequential tunneling current $I$ through the double-island device coupled to normal metal leads. We demonstrate that the $I\!-\!V$ characteristics in the large-bias regime can be used as a measurement of the coherent Majorana coupling $E_M$. We propose dc and ac transport exp…
Current state of the art devices for detecting and manipulating Majorana fermions commonly consist of networks of Majorana wires and tunnel junctions. We study a key ingredient of these networks - a topological Josephson junction with charging energy - and pinpoint crucial features for device implementation. The phase dependent tunneling term contains both the usual 2pi-periodic Josephson term and a 4pi-periodic Majorana tunneling term representing the coupling between Majoranas on both sides of the junction. In non-topological junctions when the charging energy is small compared to the Joseph…
Thermodynamic measurements of magnetic fluxes and I-V characteristics in SQUIDs offer promising paths to the characterization of topological superconducting phases. We consider the problem of macroscopic quantum tunneling in an rf-SQUID in a topological superconducting phase. We show that the topological order shifts the tunneling rates and quantum levels, both in the parity conserving and fluctuating cases. The latter case is argued to actually enhance the signatures in the slowly fluctuating limit, which is expected to take place in the quantum regime of the circuit. In view of recent advanc…
Majorana zero modes can appear at the wire ends of a 1D topological superconductor and manifest themselves as a quantized zero-bias conductance peak in the tunneling spectroscopy of normal-superconductor junctions. However, in superconductor-semiconductor hybrid nanowires, zero-bias conductance peaks may arise owing to topologically trivial mechanisms as well, mimicking the Majorana-induced topological peak in many aspects. In this work, we systematically investigate the characteristics of zero-bias conductance peaks for topological Majorana bound states, trivial quasi-Majorana bound states an…
We develop a theory for the proximity effect in superconductor-semiconductor-normal metal tunneling structures, which have recently been extensively studied experimentally, leading to the observation of transport signatures consistent with the predicted zero-energy Majorana bound states. We show that our model for the semiconductor nanowire having multiple occupied subbands with different transmission probabilities through the barrier reproduces the observed "soft-gap" behavior associated with substantial subgap tunneling conductance. We study the manifestations of the soft gap phenomenon both…
It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of coherent electron transport from a tunneling tip into a Corbino geometry Josephson junction where four Majorana bound states (MBSs) rotate. While the MBSs rotate, electron tunneling happens from the tip to one of the MBSs thereby changing the fermion parity of the MBSs. The tunneling events in combination with the rotation allow us to identify a novel braiding op…
One of the simplest proposed experimental probes of a Majorana bound-state is a quantized (2e^2/h) value of zero-bias tunneling conductance. When temperature is somewhat larger than the intrinsic width of the Majorana peak, conductance is no longer quantized, but a zero-bias peak can remain. Such a non-quantized zero-bias peak has been recently reported for semiconducting nanowires with proximity induced superconductivity. In this paper we analyze the relation of the zero-bias peak to the presence of Majorana end-states, by simulating the tunneling conductance for multi-band wires with realist…
We consider a simple conceptual question with respect to Majorana zero modes in semiconductor nanowires: Can the measured non-ideal values of the zero-bias-conductance-peak in the tunneling experiments be used as a characteristic to predict the underlying topological nature of the proximity induced nanowire superconductivity? In particular, we define and calculate the topological visibility, which is a variation of the topological invariant associated with the scattering matrix of the system as well as the zero-bias-conductance-peak heights in the tunneling measurements, in the presence of dis…
We study transport properties of a quantum dot coupled to a Majorana zero mode and two normal leads. We investigate the full counting statistics of charge tunneling events which allows one to extract complete information about current fluctuations. Using a Keldysh path-integral approach, we compute the cumulant generating function. We first consider a noninteracting spinless regime, and find that for the symmetric dot-lead couplings, the zero-frequency cumulants exhibit a universal pattern of Euler numbers, independent of the microscopic parameters. For a spinful case, the Coulomb interaction …
The magnetopolaronic generalization of a Majorana-resonant-level (MRL) model is considered for a single-level vibrating quantum dot coupled to two half-infinite $g=1/2$ Tomonaga-Luttinger liquid (TLL) leads. A qualitatively new non-trivial formula for the effective transmission coefficient and differential conductance for resonant magnetopolaron-assisted tunneling is obtained under the assumption about a fermion-boson factorization of corresponding averages. This approach is valid for the case of weak magnetopolaronic coupling in a system. Surprisingly, it is found that despite a supposed weak…
The Floquet topological superconducting state is a nonequilibrium time-periodic state hosting Majorana fermions. We study its transport properties by using the Kitaev model with time-periodic incommensurate potentials, which experiences phase transition from the Floquet topological superconducting phase to the Anderson localized phase with increasing driving strength. We study both the real time dynamics of the current and the non-analytic behavior of the tunneling conductance at the transition. Especially, we find that the tunneling conductance changes continuously at the transition, being a …
We study a planar Josephson junction under an applied DC voltage bias in the presence of an in-plane magnetic field. Upon tuning the bias voltage across the junction, $V_{\rm J}$, the two ends of the junction are shown to simultaneously host both $0$- and $π$-Majorana modes. These modes can be probed using either a Scanning-Tunneling-Microscopy measurement or through resonant Andreev tunneling from a lead coupled to the junction. While these modes are mostly bound to the junction's ends, they can hybridize with the bulk by absorbing or emitting photons. We analyze this process both numerically…
We study the differential conductance for charge tunneling into a semiconductor wire--superconductor hybrid structure, which is actively investigated as a possible scheme for realizing topological superconductivity and Majorana zero modes. The calculations are done based on a tight-binding model of the heterostructure using both a Blonder-Tinkham-Klapwijk approach and a Keldysh non-equilibrium Green's function method. The dependence of various tunneling conductance features on the coupling strength between the semiconductor and the superconductor, the tunnel barrier height, and temperature is …
The magnetopolaronic generalization of a Majorana-resonant-level (-MRL) model is considered for a single-level vibrating quantum dot symmetrically coupled to two half-infinite $g=1/2$- Tomonaga-Luttinger liquid (-TLL) leads at the Toulouse point. At the resonance by gate voltage the exact solution for the effective transmission coefficient is obtained in the whole range of magnetopolaronic coupling constant values. The obtained exact solution exists due to special Majorana-like symmetry of tunnel Hamiltonian and gives rise to nontrivial interference between different virtual vibronic channels …
Inspired by a recent experimental observation of the zero-bias tunneling conductance in superconductor-semiconductor nanowire devices, we consider here transport properties of the junctions consisting of a nanowire (Luttinger liquid) coupled to a topological superconductor characterized by the presence of Majorana zero-energy end states. The presence of the Majorana modes leads to a quantization of the zero-bias tunneling conductance at zero temperature. In order to understand this phenomenon, we have developed a framework, based on real-time Keldysh technique, which allows one to compute tunn…
We study the transport through the Kitaev's chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of $e^2/h$, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate disorder suppresses the current at finite voltage bias, and then narrows the linear response regime of the $I-V$ curve which exhibits two plateaus corresponding to the superconducting gap and the band edge respectively. The linear conductance abruptly drops to…
Considering Rashba quantum wires with a proximity-induced superconducting gap as physical realizations of Majorana fermions and quantum dots, we calculate the overlap of the Majorana wave functions with the local wave functions on the dot. We determine the spin-dependent tunneling amplitudes between these two localized states and show that we can tune into a fully spin polarized tunneling regime by changing the distance between dot and Majorana fermion. Upon directly applying this to the tunneling model Hamiltonian, we calculate the effective magnetic field on the quantum dot flanked by two Ma…
A vortex in an s-wave superconductor with a surface Dirac cone can trap a Majorana bound state with zero energy leading to a zero-bias peak (ZBP) of tunneling conductance. The iron-based superconductor FeTe$_x$Se$_{1-x}$ is one of the material candidates hosting these Majorana vortex modes. It has been observed by recent scanning tunneling spectroscopy measurement that the fraction of vortex cores possessing ZBPs decreases with increasing magnetic field on the surface of this iron-based superconductor. We construct a three-dimensional tight-binding model simulating the physics of over a hundre…
We propose and study the charge transport through single and double quantum point contacts setup between helical Majorana modes and an interacting helical Luttinger liquid. We show that the differential conductance decreases for stronger repulsive interactions and that the point contacts become insulating above a critical interaction strength. For a single point contact, the differential conductance as a function of bias voltage shows a series of peaks due to Andreev reflection of electrons in the Majorana modes. In the case of two point contacts, interference phenomena make the structure of t…
