A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle-hole symmetry. Tunneling of Majorana quasi-particle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with $4π$-periodicity.
Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting `fractional Josephson currents'. Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity---even when noise spoils parity conservation.
For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide analogous relations for Josephson junctions involving one-dimensional time-reversal-invariant topological superconductors supporting Majorana-Kramers pairs, considering both topological-topological and s-wave-topological junctions. Working in the regime where the junction is much shorter than the superconducting coherence length, we obtain a number of analytical …
Planar Josephson junctions provide a versatile platform, alternative to the nanowire-based geometry, for the generation of the Majorana bound states, due to the additional phase tunability of the topological superconductivity. The proximity induction of chiral magnetism and superconductivity in a two-dimensional electron gas showed remarkable promises to manipulate topological superconductivity. Here, we consider a Josephson junction involving a skyrmion crystal and show that the chiral magnetism of the skyrmions can create and control the Majorana bound states without the requirement of an in…
We consider recent experiments on wide superconductor-quantum spin Hall insulator (QSHI)-superconductor Josephson junctions, which have shown preliminary evidence of proximity-induced superconductivity at the edge-modes of the QSHI system based on an approximate analysis of the observed Fraunhofer spectra of the Josephson critical current as a function of the applied magnetic field. Using a completely independent exact numerical method involving a non-linear constrained numerical optimization, we calculate the supercurrent profiles, comparing our results quantitatively with the experimental Fr…
The fractional Josephson effect has been observed in many instances as a signature of a topological superconducting state containing zero-energy Majorana modes. We present a nontopological scenario which can produce a fractional Josephson effect generically in semiconductor-based Josephson junctions, namely, a resonant impurity bound state weakly coupled to a highly transparent channel. We show that the fractional ac Josephson effect can be generated by the Landau-Zener processes which flip the electron occupancy of the impurity bound state. The Josephson effect signature for Majorana modes be…
Josephson junctions and superconducting wires when probed with current pulses exhibit stochastic switching from superconducting to a stable non-zero voltage state. Electrical current dependence of the switching probability (so called S-curve) or switching current distribution is a fingerprint of the physics governing the escape process. This work addresses the criterion of independent switching event in a series of switching experiments. Treating Josephson junction as an electrical coin with current-tuned switching probability we investigate effect of correlation between switching events on th…
Twisted interfaces between stacked van der Waals cuprate crystals enable tunable Josephson coupling between in-plane anisotropic superconducting order parameters. Employing a novel cryogenic assembly technique, we fabricate Josephson junctions with an atomically sharp twisted interface between Bi2Sr2CaCu2O8+x crystals. The Josephson critical current density sensitively depends on the twist angle, reaching the maximum value comparable to that of the intrinsic junctions at small twisting angles, and is suppressed by almost 2 orders of magnitude yet remains finite close to 45 degree twist angle. …
WTe2, as a type-II Weyl semimetal, has 2D Fermi arcs on the (001) surface in the bulk and 1D helical edge states in its monolayer. These features have recently attracted wide attention in condensed matter physics. However, in the intermediate regime between the bulk and monolayer, the edge states have not been resolved owing to its closed band gap which makes the bulk states dominant. Here, we report the signatures of the edge superconductivity by superconducting quantum interference measurements in multilayer WTe2 Josephson junctions and we directly map the localized supercurrent. In thick WT…
We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanishes in such an i-Josephson junction, the second order coupling from tunneling always generates chiral superconductivity orders with broken time reversal symmetry. Josephson frequency in the i-junction is doubled, namely $ω= 4eV /h$. The result provides a way to engineer topological superconductivity such as the d + id' -wave superconducting state ch…
Theory of reentrant superconductivity in Corbino Josephson junctions
Cornell University（康奈尔大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Harvard University（哈佛大学）；Sungkyunkwan University (SKKU)（成均馆大学）；Institute for Basic Science (IBS)（基础科学研究院）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Columbia University（哥伦比亚大学）
The interplay of superconductivity, magnetic fields, and spin-orbit interaction lies at the heart of topological superconductivity. Remarkably, the recent experimental discovery of $φ_{0}$ Josephson junctions by Szombati et al., Nat. Phys. 12, 568 (2016), characterized by a finite phase offset in the supercurrent, require the same ingredients as topological superconductors, which suggests a profound connection between these two distinct phenomena. Here, we theoretically show that a quantum dot $φ_{0}$ Josephson junction can serve as a new qualitative indicator for topological superconductivity…
We consider a Josephson bijunction consisting of a thin $SIS$ $π$-Josephson junction sandwiched between two-dimensional semiconducting layers with strong Rashba spin-orbit interaction. Each of these layers forms an $SNS$ junction due to proximity-induced superconductivity. The $SIS$ junction is assumed to be thin enough such that the two Rashba layers are tunnel-coupled. We show that, by tuning external gates, this system can be controllably brought into a time-reversal invariant topological superconducting phase with a Kramers pair of Majorana bound states being localized at the end of the no…
Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity in a short Josephson junction at an edge of a 2D topological insulator subject to a perpendicular magnetic field. The magnetic field effect is entirely orbital, coming from a gradient of the order parameter phase at the edge, which results in a soliton defect at the junction with a pair of gapless Andreev bound states. The latter are reducible to Majorana z…
We consider a heterostructure of semiconductor layers sandwiched between two superconductors, forming a two-dimensional Josephson junction. Applying a Zeeman field perpendicular to the junction can render a topological superconducting phase with chiral Majorana edge mode. We show that the phase difference between two superconductors can efficiently reduce the magnetic field required to achieve the chiral topological superconductivity, providing an experimentally feasible setup to realize chiral Majorana edge modes. We also construct a lattice Hamiltonian of the setup to demonstrate the chiral …
Molecule-intercalated van der Waals Josephson junctions uncover complex multiband superconductivity
CIC nanoGUNE（CIC纳米技术研究中心）；Centro de Física de Materiales – Materials Physics Center (CFM-MPC) CSIC-EHU（材料物理中心（CFM-MPC）西班牙国家研究委员会-巴斯克大学）；Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Facultad de Químicas (EHU)（巴斯克大学化学学院先进聚合物与材料系：物理、化学与技术）；Instituto de Nanociencia y Materiales de Aragón (INMA) CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所（INMA）西班牙国家研究委员会-萨拉戈萨大学）；Laboratorio de Microscopías Avanzadas (LMA), Universidad de Zaragoza（萨拉戈萨大学高级显微镜实验室）；Ikerbasque, Basque Foundation for Science（伊克尔巴斯科科学基金会）
Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for fault-tolerant quantum computing. Several observations of zero-bias conductance peaks measured in tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference ϕ between t…
The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in wh…
We trace the historical fate of experiment and theory of microwave-stimulated superconductivity as originally reported for constriction-type superconducting weak links. It is shown that the observed effect disappeared by improving weak links to obtain the desired Josephson-properties. Separate experiments were carried out to evaluate the validity of the proposed theory of Eliash'berg for $\textit{energy-gap-enhancement}$ in superconducting films in a microwave field, without reaching a full quantitatively reliable measurement of the stimulated energy gap in a microwave-field, but convincing en…
We study the spectrum of Andreev bound states and Josephson currents across a junction of $N$ superconducting wires which may have $s$- or $p$-wave pairing symmetries and develop a scattering matrix based formalism which allows us to address transport across such junctions. For $N \ge 3$, it is well known that Berry curvature terms contribute to the Josephson currents; we chart out situations where such terms can have relatively large effects. For a system of three $s$- or three $p$-wave superconductors, we provide analytic expressions for the Andreev bound state energies and study the Josephs…
Electron density oscillations with acoustic dispersions and sustained at boundaries between different media provide information about surface and interface properties of hetero-structures. In ultra-thin metallic films these plasmonic excitations are heavily damped. Superconductivity is predicted to reduce dissipation allowing detection of these resonances. Emerging low-loss interface Cooper-pair waves have been studied before, however, the observation of surface-confined Josephson plasmons has remained elusive. Here, we report on generation and coupling to these excitations in an ultrathin sin…
We study all the possible different two terminal configurations of Josephson junctions containing wires of time-reversal invariant topological superconductors (TRITOPS) and ordinary superconductors, including combinations with an interacting quantum dot between both wires in the junction. We introduce simple effective Hamiltonians which explain the different qualitative behaviors obtained. We analyze a wide range of phenomena, including occurrence and quenching of the so called $0-π$ transition, anomalous periodicity and jumps of the Josephson current as a function of the phase difference, and…
We investigate the Josephson current in a Fano-Josephson junction formed by the direct coupling between two topological superconducting wires and their indirect coupling via a quantum dot. It is found that when two Majorana zero modes respectively appear in the wires, the Fano interference causes abundant Josephson phase transition processes. What is notable is that in the presence of appropriate direct and indirect inter-wire couplings, the fractional Josephson effect disappears and then such a structure transforms into a $0$-phase normal Josephson junction. On the other hand, if finite coupl…
The $4π$ Josephson Effect is a distinguishing feature of a topological Josephson junction. However, stringent conditions make it hard to observe in experiments. Here we numerically study the transient transport properties in a topological Josephson junction. We show that the $4π$ Josephson current can be sustained for a significant time (around several $μs$ with suitable conditions). Furthermore, we compare the behaviors of Josephson current in different conditions, identifying three main regimes: First, when both the superconducting wires of the Josephson junction lie in the topologically non…
We propose a semiconductor-superconductor hybrid device for realizing topological superconductivity and Majorana zero modes consisting of a planar Josephson junction structure with periodically modulated junction width. By performing a numerical analysis of the effective model describing the low-energy physics of the hybrid structure, we demonstrate that the modulation of the junction width results in a substantial enhancement of the topological gap and, consequently, of the robustness of the topological superconducting phase and associated Majorana zero modes. This enhancement is due to the f…
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 the effects of magnetic and crystalline anisotropies on the topological superconducting state of planar Josephson junctions (JJs). In junctions where only Rashba spin-orbit coupling (SOC) is present, the topological phase diagram is insensitive to the supercurrent direction, but exhibits a strong dependence on the magnetic field orientation. However, when both Rashba and Dresselhaus SOCs coexist, the topological phase diagram strongly depends on both the magnetic field and junction crystallographic orientations. We examine the impact of the magnetic and crystalline anisotropy on…
We theoretically study topological planar Josephson junctions (JJs) formed from spin-orbit-coupled two-dimensional electron gases (2DEGs) proximitized by two superconductors and subjected to an in-plane magnetic field $B_\parallel$. Compared to previous studies of topological superconductivity in these junctions, here we consider the case where the superconducting leads are narrower than the superconducting coherence length. In this limit the system may be viewed as a proximitized multiband wire, with an additional knob being the phase difference $ϕ$ between the superconducting leads. A combin…
We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field the quasi-one-dimensional region between the two superconductors can support a topological superconducting phase hosting Majorana bound states at its ends. We study the phase diagram of the system as a function of the Zeeman field and the phase difference between the two superconductors (treated as an externally controlled parameter). Remarkably, at a phase difference of $π$, the topological pha…
Wires made of topological insulators (TI) are a promising platform for searching for Majorana bound states. These states can be probed by analyzing the fractional ac Josephson effect in Josephson junctions with the TI wire as a weak link. An axial magnetic field can be used to tune the system from trivial to topologically nontrivial. Here we investigate the oscillations of the supercurrent in such wire Josephson junctions as a function of the axial magnetic field strength and different contact transparencies. Although the current flows on average parallel to the magnetic field we observe $h/2e…
One of the salient signatures of Majorana zero modes and topological superconductivity is a $4π$-periodic Josephson effect due to the combination of fermion parity conservation and the presence of a topologically protected odd number of zero energy crossings in the Andreev spectrum. In this paper, we study this effect in Josephson junctions composed of two semiconducting nanowires with Rashba spin-orbit coupling and induced superconductivity from the proximity effect. For certain orientations of the external magnetic field, such junctions possess a chiral symmetry and we show how this symmetry…
