In this work, we investigate the conductance and current correlations properties of a quantum topological inteferometer consisting of a QD coupled to two Majorana Bound States (MBSs) confined at both ends of a 1D topological superconductor ring nanowire. We analyze the ring in its topological non trivial and trivial phases to show that the tunneling conductance, shot noise and fano factor present unique characteristics to distinguish the hallmark of MBSs. We reinforce our findings by taking advantage of the correspondence between the quantum topological interferometer and a dot effectively coupled to a single Majorana state in a straight topological superconductor wire configuration. We show that, besides the characteristic zero-bias conductance $e^{2} /2h$ and the already known shot noise features, the Fano factor provides significant information to distinguish the MBSs presence.
We investigate the spectral and transport properties of a double quantum dot laterally attached to a topological superconducting nanowire, hosting the Majorana zero-energy modes. Specifically, we consider a geometry, in which the outer quantum dot is embedded between the external normal and superconducting leads, forming a circuit. First, we derive analytical expressions for the bound states in the case of an uncorrelated system and discuss their signatures in the tunneling spectroscopy. Then, we explore the case of strongly correlated quantum dots by performing the numerical renormalization g…
We investigate theoretically the features of the Majorana hallmark in the presence of Coulomb repulsion between two quantum dots describing a spinless Aharonov-Bohm-like interferometer, where one of the dots is strongly coupled to a Kitaev wire within the topological phase. Such a system has been originally proposed without Coulomb interaction in J. of Appl. Phys. 116, 173701 (2014). Our findings reveal that for dots in resonance, the ratio between the strength of Coulomb repulsion and the dot-wire coupling changes the width of the Majorana zero-bias peak for both Fano regimes studied, indicat…
We consider an interferometer based on artificially induced topological superconductivity and chiral 1D Majorana fermions. The (non-topological) superconducting island inducing the superconducting correlations in the topological substrate is assumed to be floating. This allows probing the physics of interfering Majorana modes via microwave response, i.e., the frequency dependent impedance between the island and the earth. Namely, charging and discharging of the island is controlled by the time-delayed interference of chiral Majorana excitations in both normal and Andreev channels. We argue tha…
We propose an interferometer for chiral Majorana modes where the interference effect is caused and controlled by a Josephson junction of proximity-induced topological superconductors, hence, a Majorana-Josephson interferometer. This interferometer is based on a two-terminal quantum anomalous Hall bar, and as such its transport observables exhibit interference patterns depending on both the Josephson phase and the junction length. Observing these interference patterns will establish quantum coherent Majorana transport and further provide a powerful characterization tool for the relevant system.
We propose an Aharonov-Bohm interferometer consisted of two topological superconducting chains (TSCs) to generate coherence of Majorana qubits, each qubit is made of two Majorana zero modes (MZMs) with the definite fermion parity. We obtain the generalized exact master equation as well as its solution and study the real-time dynamics of the MZM qubit states under various operations. We demonstrate that by tuning the magnetic flux, the decoherence rates can be modified significantly, and dissipationless MZMs can be generated. By applying the bias voltage to the leads, one can manipulate MZM qub…
We investigate the transport properties through a nanostructure composed of parallel double quantum dots coupled to two normal contacts. Additionally, each quantum dot is connected to a topological superconducting nanowire, hosting Majorana zero modes at its ends. A magnetic flux threading across the area enclosed by the interferometer is considered. First, we investigate the physical quantities of the system employing Green's function formalism. We find that the emergence of bound states appears in symmetric configurations of topological superconducting nanowires, i.e., depending on their len…
Helical Dirac-Majorana interferometer in a superconductor-topological insulator sandwich structure
在拓扑绝缘体与两个s波超导体构成的异质结构中，当两个s波超导体形成具有π相移的约瑟夫森结时，存在具有螺旋Majorana边缘模的时反不变性拓扑超导相.基于这样的异质结构，螺旋Dirac-Majorana干涉仪被提出来直接测量螺旋Majorana模式的独特输运特征。此外，我们设想如何在现有材料如Bi 2 Se 3或Bi 2 Te 3薄膜的基础上实现我们的提议。
Majorana zero modes are leading candidates for topological quantum computation due to non-local qubit encoding and non-abelian exchange statistics. Spatially separated Majorana modes are expected to allow phase-coherent single-electron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAs-Al island embedded in an Aharonov-Bohm interferometer. With increasing parallel magnetic field, a discrete sub-gap state in the island is lowered to zero energy yielding pe…
We study the full counting statistics of interferometers for chiral Majorana fermions with two incoming and two outgoing Dirac fermion channels. In the absence of interactions, the FCS can be obtained from the $4\times4$ scattering matrix $S$ that relates the outgoing Dirac fermions to the incoming Dirac fermions. After presenting explicit expressions for the higher-order current correlations for a modified Hanbury Brown-Twiss interferometer, we note that the cumulant-generating function can be interpreted such that unit-charge transfer processes correspond to two independent half-charge trans…
We study the transport properties of an interferometer composed by a quantum dot (QD) coupled with two normal leads and two one-dimensional topological superconductor nanowires (TNWs) hosting Majorana bound states (MBS) at their ends. The geometry considered is such that one TNW has both ends connected with the QD, forming an Aharonov-Bohm (AB) interferometer threaded by an external magnetic flux, while the other TNW is placed near the interferometer TNW. This geometry can alternatively be seen as a long wire contacted across a local defect, with possible coupling between independent-MBS. We u…
Motivated by the need of quantum measurement of Majorana qubits and surface-code stabilizers, we analyze the performance of a double-dot interferometer under the influence of environment noise. The double-dot setup design allows accounting for the full multiple tunneling process between the dots through the Majorana island, within a master equation approach. In the co-tunneling regime, which results in a Majorana-mediated effective coupling between the dots, the master equation approach allows us to obtain analytic solutions for the measurement currents. The measurement quality, characterized …
Shot noise signatures of Majorana-assisted transport in an Aharonov-Bohm interferometer
Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）；Pontificia Universidad Católica de Valparaíso（瓦爾帕萊索天主教宗座大學）；Universidad de Antofagasta（安托法加斯塔大學）
DC Conductance of X-shaped Majorana Interferometer reveals Non-Abelian Anyon Statistics
Heinrich-Heine-Universität（海因里希·海涅大学）；I.N.F.N., Gruppo collegato di Cosenza（意大利国家核物理研究所，科森扎协作组）；Università della Calabria（卡塔尼亚大学）；RWTH Aachen University（亚琛工业大学）
该研究提出四端 X 形手性马约拉纳干涉仪，利用线性响应直流电导张量检测伊辛任意子非阿贝尔统计。通过手征玻色化理论发现其电导张量各向同性，能产生非零电导，可直接证明非阿贝尔统计，补充了双臂干涉仪研究。
We introduce a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory, which is based on a $SO(7)_1/(G_2)_1$ coset factorization, leads to a solvable one dimensional model that is extended to two dimensions using a network construction. In addition to providing a description of the Fibonacci phase without parafermions, our theory predicts a closely related "anti-Fibonacci" phase, whose topological order is characterized by the tricritical Ising model. We show that Majorana fermio…
In modern experiments with hybrid superconducting (SC)/semiconducting nanowires the presence of zero-energy Andreev bound states (ABSs), characterized by a partial overlap of the Majorana wave functions, is a common problem that significantly complicates the detection of a genuine Majorana bound state (MBS). In this article, taking into account spatial inhomogeneity of experimentally investigated nanowire samples, we study interference transport features of a curved heterostructure in which two normal wires (or arms) are separated by a superconducting wire. Since Andreev reflection on the two …
The Majorana zero mode (MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in (Li0.84Fe0.16)OHFeSe. Here using scanning tunneling spectroscopy (STS), we demonstrate that Majorana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state, and consequent…
We investigate the conductance of an Aharonov-Bohm (AB) interferometer coupled to a quantum dot and two Majorana bound states on the edge of the topological superconductor with finite length. When the tunnel couplings between the Majorana bound states and the Aharonov-Bohm interferometer are fixed to the specific phase, the differential conductance becomes zero irrespective of all the parameters as long as the hoppings to the two Majorana fermions on the opposite side are equal. The conductance at the zero bias voltage does not change with the magnetic flux penetrating the ring for all cases. …
We study the temperature dependence of Coulomb Blockade peak conductance based on a Majorana-hosted superconducting island. In the low-temperature regime, we discover a coherent double Fu-teleportation (FT) process, where any independent tunneling process always involves two coherent FTs; and we also find an anomalous universal scaling behavior, which shows a transition from a [max(T,eV)]^6 to a [max(T,eV)]^3 conductance behavior as increasing energy scale. In the high-temperature regime, using the familiar rate equation method, we find that the conductance is proportional to the reciprocal of…
Majorana 'zero-modes' are expected to be immune to decoherence. The primary method for their characterization in a 1D topological superconductor, is measuring the tunneling current into the edge of the superconductor. Presently, the hallmark of a localized Majorana edge-state is an emergent quantized zero-bias conductance peak (ZBCP). However, such a conductance peak can also result from other mechanisms; e.g., crossing (and sticking) of two branches of a standard Andreev bound state, or a soft potential at the edge of the superconductor. Since the emergence of a 'Majorana-ZBCP' must be accomp…
We predict conductance oscillations in a quantum-anomalous Hall 2d strip having a superconducting region of length $L_x$ with a chiral Majorana mode. These oscillations require a finite transverse extension of the strip $L_y$ of a few microns or less. Measuring the conductance periodicity with $L_x$ and a fixed bias, or with bias and a fixed $L_x$, yields the speed of the chiral Majorana mode. The physical mechanism behind the oscillations is the interference between backscattered chiral modes from second to first interface of the NSN double junction. The interferometer effect is enhanced by t…
We present a new measurement-based scheme for performing braiding operations on Majorana zero modes and for detecting their non-Abelian statistics without moving or hybridizing them. In our scheme, the topological qubit encoded in any pair of well-separated Majorana zero modes in a mesoscopic superconductor island is read out from the transmission phase shift in electron teleportation through the island in the Coulomb blockade regime. We propose experimental setups to measure the teleportation phase shift via conductance in an electron interferometer or persistent current in a closed loop.
We investigate a paradigmatic case of topological superconductivity in a one-dimensional nanowire with $d-$orbitals and a strong interplay of spin-orbital degrees of freedom due to the competition of orbital Rashba interaction, atomic spin-orbit coupling, and structural distortions. We demonstrate that the resulting electronic structure exhibits an orbital dependent magnetic anisotropy which affects the topological phase diagram and the character of the Majorana bound states (MBSs). The inspection of the electronic component of the MBSs reveals that the spin-orbital polarization generally occu…
We calculate the current noise power spectrum in a nanoscopic interferometer consisting of a Majorana bound state (MBS) and a localized spin. We show that for large voltage (though less than the superconducting gap) several strong resonance peaks appear at frequencies that depend on the Zeeman splitting of the localized spin and on its tunneling to the localized spin. We also evaluate the differential conductance and find the unitary limit peak $2e^2/h$ at zero voltage as well as peaks at voltages corresponding to the resonances. We propose that detection of the resonances and related peaks in…
Majorana Zero Modes (MZMs) are prime candidates for robust topological quantum bits, holding a great promise for quantum computing. Semiconducting nanowires with strong spin orbit coupling offers a promising platform to harness one-dimensional electron transport for Majorana physics. Demonstrating the topological nature of MZMs relies on braiding, accomplished by moving MZMs around each other in a certain sequence. Most of the proposed Majorana braiding circuits require nanowire networks with minimal disorder. Here, the electronic transport across a junction between two merged InSb nanowires i…
We propose a theoretical approach based on an interferometer composed by two quantum dots asymmetrically coupled to isolated Majorana quasiparticles (MQPs), lying on the edges of two topological Kitaev chains, respectively via couplings $(t+Δ)$ and $(Δ-t)$. This setup enables us to probe MQPs in a quite distinct way from the zero-bias peak feature. Most importantly, the system behaves as a current switch made by two distinct paths: (i) for the upper dot connected to both chains, the device perceives both MQPs as an ordinary fermion and the current crosses solely the lower dot, since current in…
By tuning the magnetic flux, the two ends of a 1D topological superconductor weakly coupled to a normal metal as a ring-shaped junction can host split Majorana zero modes (MZMs). When this ring geometry becomes Coulomb blockaded, and the two leads come into contact with the two wire ends, the current moves through the superconductor or the normal metal as an interferometer. The two-terminal interference conductance can be experimentally measured as a function of gate voltage and magnetic flux through the ring. However, a $4π$ periodicity in the conductance-phase relation (often considered the …
Theoretically, a pair of Majorana bound states in a topological superconductor forms a single fermionic level even at large separations, implying that the parity information is stored nonlocally. The nonlocality leads to a long-distance coherence for electrons tunneling through a Coulomb blockaded Majorana wire [Fu, Phys. Rev. Lett. 104, 056402 (2010)], an effect that can be observed, e.g., in an interferometer. Here, we examine theoretically the coherent electron transfer, taking into account that tunneling implies the long-distance transfer of charge, which is carried by one-dimensional plas…
We consider the surface states of a spherical topological insulator piecewise-terminated by superconductivity or ferromagnetism over various regions of the spherical surface. Such terminations gap the surface states by breaking U(1) particle-number symmetry or time-reversal symmetry, respectively. Interfaces and trijunctions between differently terminated surface regions can host propagating and bound Majorana modes, and the finite size of the spherical system makes it easily amenable to numerical analysis via exact diagonalization of the Bogoliubov-de Gennes Hamiltonian within a truncated Hil…
Kitaev chain (KC) is a prototypical model for the study of Majorana fermions (MFs). In the topological phase, a KC hosts two MFs at its ends. Being separated in space, these two MFs are nonlocal. The nonlocal transport in a KC biased between two normal metal leads is mediated by electron tunneling (ET) and crossed Andreev reflection (CAR). ET contributes positively while CAR contributes negatively to the nonlocal conductance. Enhanced CAR and hence a negative nonlocal conductance is a hallmark of nonlocality of MFs. But simple conductance measurements in the above setup cannot probe the nonloc…
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…
Proposed as a fundamental symmetry describing our universe, spacetime supersymmetry (SUSY) has not been discovered yet in nature. Nonetheless, it has been predicted that SUSY may emerge in low-energy physics of quantum materials such as topological superconductors and Weyl semimetals. Here, by performing state-of-the-art sign-problem-free Majorana quantum Monte Carlo (QMC) simulations of an interacting 2D topological superconductor, we show convincing evidences that the N=1 SUSY emerges at its edge quantum critical point (EQCP) while its bulk remains gapped and topologically nontrivial. Remark…
Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所马格托国际研究中心）；CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris（巴黎理工学院综合理工学院中心）；Department of Physics, University of Basel（巴塞尔大学物理系）
We consider a Josephson contact mediated by 1D chiral modes on a surface of a 3D topological insulator with superimposed superconducting and magnetic layers. The system represents an interferometer in which 1D chiral Majorana modes on the boundaries of superconducting electrodes are linked by ballistic chiral Dirac channels. We investigate the noise of the Josephson current as a function of the dc phase bias and the Aharonov-Bohm flux. Starting from the scattering formalism, a Majorana representation of the Keldysh generating action for cumulants of the transmitted charge is found. At temperat…
A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demons…
We propose multi-particle interference protocols in the time-energy domain which are able to probe localized topological quasiparticles. Using a set of quantum dots tunnel-coupled to a topologically nontrivial system, the time dependence of the dot level energies defines a many-body interferometry platform which (to some extent) is similar to the Hong-Ou-Mandel (HOM) interferometer. We demonstrate that for a superconducting island harboring at least four Majorana bound states, the probability distribution of the final dot occupation numbers will exhibit a characteristic interferometric pattern…
Noncentrosymmetric superconductors (NCSs), characterized by antisymmetric spin-orbit coupling and a mixture of spin-singlet and spin-triplet pairing components, are promising candidate materials for topological superconductivity. An important hallmark of topological superconductors is the existence of protected zero-energy states at surfaces or in vortex cores. Here we investigate Majorana vortex-bound states in three-dimensional nodal and fully gapped NCSs by combining analytical solutions of Bogoliubov-de Gennes (BdG) equations in the continuum with exact diagonalization of BdG Hamiltonians.…
