We show that the topology of the Fermi sea of a two-dimensional electron gas (2DEG) is reflected in the ballistic Landauer transport along a long and narrow Josephson $π$-junction that proximitizes the 2DEG. The low-energy Andreev states bound to the junction are shown to exhibit a dispersion that is sensitive to the Euler characteristic of the Fermi sea ($χ_F$). We highlight two important relations: one connects the electron/hole nature of Andreev states to the convex/concave nature of Fermi surface critical points, and one relates these critical points to $χ_F$. We then argue that the transport of Andreev states leads to a quantized conductance that probes $χ_F$. An experiment is proposed to measure this effect, from which we predict an $I$-$V$ characteristic that not only captures the topology of Fermi sea in metals, but also resembles the rectification effect in diodes. Finally, we evaluate the feasibility of measuring this quantized response in graphene, InAs and HgTe 2DEGs.
Ballistic point contact (BPC) with zigzag edges in graphene is a main candidate of a valley filter, in which the polarization of the valley degree of freedom can be selected by using a local gate voltage. Here, we propose to detect the valley filtering effect by Andreev reflection. Because electrons in the lowest conduction band and the highest valence band of the BPC possess opposite chirality, the inter-band Andreev reflection is strongly suppressed, after multiple scattering and interference. We draw this conclusion by both the scattering matrix analysis and the numerical simulation. The An…
In noncentrosymmetric superconductors (NCSs), the conversion of a charge current into spin magnetization - the so called magnetoelectric effect - is the direct indicator of the unconventional, mixed-parity order parameter. This paper proposes a scheme to detect the magnetoelectric effect by anomalous, equal-spin Andreev tunneling in NCS/ferromagnet contacts. The proposal relies on the ability to generate spin-polarized triplet pairing by passing an electric current through an NCS. Such an induced triplet pairing bears a similarity to the paradigmatic nonunitary pairing in triplet superfluids w…
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 …
Tunneling across superconducting junctions proceeds by a rich variety of processes, which transfer single electrons, Cooper pairs, or even larger numbers of electrons by multiple Andreev reflections. Photon-assisted tunneling combined with the venerable Tien-Gordon model has long been a powerful tool to identify tunneling processes between superconductors. Here, we probe superconducting tunnel junctions including an impurity-induced Yu-Shiba-Rusinov (YSR) state by exposing a scanning tunneling microscope with a superconducting tip to microwave radiation. We find that a simple Tien-Gordon descr…
Recent development in fabrication of hybrid nanostructures allows for creation of quantum interferometers that combine semiconductor and superconductor materials. We show that in those nanostructures the joint phenomena of Aharonov-Bohm effect and Andreev reflections can be used to determine the length on which the electron is retro-reflected as a hole. We propose to exploit this feature for probing of the quasiparticle coherence length in semiconductor-superconductor hybrids by a magnetoconductance measurement.
We propose a three-terminal structure to probe robust signatures of Majorana zero modes. This structure consists of a quantum dot coupled to the normal metal, s-wave superconducting and Majorana Y-junction leads. The zero-bias differential conductance at zero temperature of the normal-metal lead peaks at $2e^{2}/h$, which will be deflected after Majorana braiding. This quantized conductance can entirely arise from the Majorana-induced crossed Andreev reflection, protected by the energy gap of the superconducting lead. We find that the effect of thermal broadening is significantly suppressed wh…
We consider a biased Normal-Superconducting junction with various types of superconductivity. Depending on the class of superconductivity, a Majorana bound state may appear at the interface. We show that this has important consequences on the distribution of waiting times of electrons flowing out of such an interface. Therefore, the waiting time distribution is shown to be a clear fingerprint of Majorana bound state physics and may be considered as an experimental signature of its presence.
Andreev bound states (ABSs) are localized quantum states that contain both electron and hole components. They ubiquitously reside in inhomogeneous superconducting systems. Following theoretical analysis, we propose to probe the electron-hole weights of an ABS via a local tunneling measurement that detects the transient current under a steplike pulse bias. With our protocol, the ABS energy level can also be obtained from peaks of the Fourier spectrum of the transient current. Our protocol can be applied to detect robust zero-energy Majorana bound states (MBSs), which have equal electron-hole we…
We consider the proximity effect between a singlet s-wave superconductor and the edge of a Quantum Spin Hall (QSH) topological insulator. We establish that Andreev reflection at a QSH edge state/superconductor interface is perfect while nonlocal Andreev processes through the superconductor are totally suppressed. We compute the corresponding conductance and noise.
Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the loc…
Probing Cooper pair momentum by quasiparticle steering with planar Josephson junctions
QuTech, Delft University of Technology（代尔夫特理工大学 QuTech）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学卡弗里纳米科学研究所）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所量子器件中心）
Bound states in superconductor-nanowire hybrid devices play a central role, carrying informationon the ground states properties (Shiba or Andreev states) or on the topological properties of thesystem (Majorana states). The spectroscopy of such bound states relies on the formation of well-defined tunnel barriers, usually defined by gate electrodes, which results in smooth tunnel barriers.Here we used thin InP segments embedded into InAs nanowire during the growth process to forma sharp built-in tunnel barrier. Gate dependence and thermal activation measurements have beenused to confirm the pres…
Crossed Andreev reflection (CAR) is an intriguing effect that occurs in a normal-superconductor-normal junction. In CAR, an incoming electron from one terminal is coherently scattered as an outgoing hole into the other terminal. Here, we reveal that there exists a transverse spatial shift in CAR, i.e., the plane of CAR for the outgoing hole may have a sizable transverse shift from the plane of incidence for the incoming electron. We explicitly demonstrate the effect in a model system based on Weyl semimetals. We further show that the effect is quite general and exists when the terminals have s…
Recent tunneling spectroscopy experiments in semiconducting nanowires with proximity-induced superconductivity have reported robust zero-bias conductance peaks. Such a feature can be compatible with the existence of topological Majorana bound states (MBSs) and with a trivial Andreev bound state (ABS) near zero energy. Here, we argue that additional information, that can distinguish between the two cases, can be extracted from Coulomb-blockade experiments of Majorana islands. The key is the ratio of peak heights of consecutive conductance peaks give information about the electron and hole compo…
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…
Detection of the fusion rule of Majorana zero-modes is a near-term milestone on the road to topological quantum computation. An obstacle is that the non-deterministic fusion outcome of topological zero-modes can be mimicked by the merging of non-topological Andreev levels. To distinguish these two scenarios, we search for dynamical signatures of the ground-state degeneracy that is the defining property of non-Abelian anyons. By adiabatically traversing parameter space along two different pathways one can identify ground-state degeneracies from the breakdown of adiabaticity. We show that the ap…
