Zero-bias Conductance Research Articles

Observation of triplet superconductivity in CoSi2/TiSi2 heterostructures.

Unconventional superconductivity and, in particular, triplet superconductivity have been front and center of topological materials and quantum technology research. Here, we report our observation of triplet pairing in nonmagnetic CoSi2/TiSi2 heterostructures on silicon. CoSi2 undergoes a sharp superconducting transition at a critical temperature T c ≃ 1.5 K, while TiSi2 is a normal metal. We investigate conductance spectra of both two-terminal CoSi2/TiSi2 contact junctions and three-terminal T-shaped CoSi2/TiSi2 superconducting proximity structures. Below T c, we observe (i) a narrow zero-bias conductance peak on top of a broad hump, accompanied by two symmetric side dips in the contact junctions, (ii) a narrow zero-bias conductance peak in T-shaped structures, and (iii) hysteresis in the junction magnetoresistance. These three independent and complementary observations point to chiral p-wave pairing in CoSi2/TiSi2 heterostructures. The excellent fabrication compatibility of CoSi2 and TiSi2 with present-day silicon-based integrated-circuit technology suggests their potential use in scalable quantum-computing devices.

Quantized and unquantized zero-bias tunneling conductance peaks in Majorana nanowires: Conductance below and above 2e2/h

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 and low-energy Andreev bound states arising from smooth potential variations, and disorder-induced subgap bound states. Our focus is on the conductance peak value (i.e., equal to, greater than, or less than $2e^2/h$), as well as the robustness (plateau- or spike-like) against the tuning parameters (e.g., the magnetic field and tunneling gate voltage) for zero-bias peaks arising from the different mechanisms. We find that for Majoranas and quasi-Majoranas, the zero-bias peak values are no more than $2e^2/h$, and a quantized conductance plateau forms generically as a function of parameters. By contrast, for conductance peaks due to low-energy Andreev bound states or disorder-induced bound states, the peak values may exceed $2e^2/h$, and a conductance plateau is rarely observed unless through careful postselection and fine-tuning. Our findings should shed light on the interpretation of experimental measurements on the tunneling spectroscopy of normal-superconductor junctions of hybrid Majorana nanowires.

Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections

Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.

Effect of chiral anomaly on Andreev reflection in a tilted Weyl semimetal hybrid junction

We study the influence of the chiral anomaly of a time-reversal broken Weyl semimetal on Andreev reflection in a superconductor junction. It is found that the chiral chemical potential can lead to the switching between the retro Andreev reflection (RAR) and specular Andreev reflection (SAR), which appears in both intraband and interband electron-hole conversion, violating the common rule that the intraband conversion is the RAR while the interband one is the SAR. This switching effect is dependent on the tilt of the Weyl cones and the direction of the line connecting the two Weyl points. In addition, a perfect Andreev reflection is found at the incident angle, not perpendicular to the junction interface. We also discuss the zero-bias differential conductance which provides an observable signature of the switching effect, especially for the switching between RAR and SAR caused by band transition. These findings are useful in better understanding the Andreev reflection types and detecting the chiral anomaly.

Universality and thermoelectric transport properties of quantum dot systems

We discuss the temperature-dependent thermoelectric transport properties of semiconductor nanostructures comprising a quantum dot coupled to quantum wires: the thermal dependence of the electrical conductance, thermal conductance, and thermopower. We explore the universality of the thermoelectric properties in the temperature range associated with the Kondo crossover. In this thermal range, general arguments indicate that any equilibrium property's temperature dependence should be a universal function of the ratio ${T}^{*}=T/{T}_{K}$, where ${T}_{K}$ is the Kondo temperature. Considering the particle-hole symmetric, spin-degenerate Anderson model, the zero-bias electrical conductance has already been shown to map linearly onto a universal conductance through a quantum dot embedded or side-coupled to a quantum wire. Employing rigorous renormalization-group arguments, we calculate universal thermoelectric transport coefficients that allow us to extend this result to the thermopower and the thermal conductance. We present numerical renormalization-group results to illustrate the physics in our findings. Applying the universal thermoelectric coefficients to recent experimental results of the electrical conductance and thermovoltages versus ${V}_{\mathrm{gate}}$, at different temperatures in the Kondo regime, we calculate all the thermoelectric properties and obtain simple analytical fitting functions that can be used to predict the experimental results of these properties. However, we cannot check all of them, due to the lack of available experimental results over a broad temperature range.

Zero-Bias Conductance Peaks Effectively Tuned by Gating-Controlled Rashba Spin-Orbit Coupling.

Zero-bias conductance peaks (ZBCPs) can manifest a number of notable physical phenomena and thus provide critical characteristics to the underlying electronic systems. Here, we report observations of pronounced ZBCPs in hybrid junctions composed of an oxide heterostructure LaAlO_{3}/SrTiO_{3} and an elemental superconductor Nb, where the two-dimensional electron system (2DES) at the LaAlO_{3}/SrTiO_{3} interface is known to accommodate gate-tunable Rashba spin-orbit coupling (SOC). Remarkably, the ZBCPs exhibit a domelike dependence on the gate voltage, which correlates strongly with the nonmonotonic gate dependence of the Rashba SOC in the 2DES. The origin of the observed ZBCPs can be attributed to the reflectionless tunneling effect of electrons that undergo phase-coherent multiple Andreev reflection, and their gate dependence can be explained by the enhanced quantum coherence time of electrons in the 2DES with increased momentum separation due to SOC. We further demonstrate theoretically that, in the presence of a substantial proximity effect, the Rashba SOC can directly enhance the overall Andreev conductance in the 2DES-barrier-superconductor junctions. These findings not only highlight nontrivial interplay between electron spin and superconductivity revealed by ZBCPs, but also set forward the study of superconducting hybrid structures by means of controllable SOC, which has significant implications in various research fronts from superconducting spintronics to topological superconductivity.

Tunable spin-valley polarized transport channel in silicene-based superconducting hybrid structures

We investigate the influence of spin-valley polarized transport channel (SVPTC) mismatch modulated by the perpendicular electric field and the exchange field in a silicene-based ferromagnet/ferromagnet/superconductor junction and the barrier strength in a ferromagnet/insulator/ferromagnet/superconductor junction. In the former junction, due to the mismatch of SVPTC caused by the different electric fields applied in the two ferromagnet (F) layers, the zero-bias Andreev reflection and zero-bias conductance peak (ZBCP) are suppressed. Moreover, by shifting the band, the exchange field can lead to the different mismatch of SVPTC between the two F layers with opposite magnetization orientations, and thus, the conversion from ZBCP to a zero-bias conductance valley can be observed. For the latter junction, due to the electrically tunable SVPTC, the phase shift of conductance oscillation with barrier strength is created by changing the electric field but not by altering the exchange field. Particularly, for the variation from the parallel to the antiparallel magnetic configuration, there is a phase shift π/2 of conductance vs the barrier strength.

Three-terminal nonlocal conductance in Majorana nanowires: Distinguishing topological and trivial in realistic systems with disorder and inhomogeneous potential

We develop a theory for the three-terminal nonlocal conductance in Majorana nanowires as existing in the superconductor-semiconductor hybrid structures in the presence of superconducting proximity, spin-orbit coupling, and Zeeman splitting. The key question addressed is whether such nonlocal conductance can decisively distinguish between trivial and topological Majorana scenarios in the presence of chemical potential inhomogeneity and random impurity disorder. We calculate the local electrical as well as nonlocal electrical and thermal conductance of the pristine nanowire (good zero-bias conductance peaks), the nanowire in the presence of quantum dots and inhomogeneous potential (bad zero-bias conductance peaks), and the nanowire in the presence of large disorder (ugly zero-bias conductance peaks). The local conductance by itself is incapable of distinguishing the trivial states from the topological states since zero-bias conductance peaks are generic in the presence of disorder and inhomogeneous potential. The nonlocal conductance, which in principle is capable of providing the bulk gap closing and reopening information at the topological quantum phase transition, is found to be far too weak in magnitude to be particularly useful in the presence of disorder and inhomogeneous potential. Therefore, we focus on the question of whether the combination of the local, nonlocal electrical, and thermal conductance can separate the good, bad, and ugly zero-bias conductance peaks in finite-length wires. Our paper aims to provide a guide to future experiments, and we conclude that a combination of all three measurements would be necessary for a decisive demonstration of topological Majorana zero modes in nanowires---positive signals corresponding to just one kind of measurements are likely to be false positives arising from disorder and inhomogeneous potential.

Quadrupole spin polarization as signature of second-order topological superconductors

We study theoretically second-order topological superconductors characterized by the presence of pairs of zero-energy Majorana corner states. We uncover a quadrupole spin polarization at the system edges that provides a striking signature to identify topological phases, thereby complementing standard approaches based on zero-bias conductance peaks due to Majorana corner states. We consider two different classes of second-order topological superconductors with broken time-reversal symmetry and show that both classes are characterized by a quadrupolar structure of the spin polarization that disappears as the system passes through the topological phase transition. This feature can be accessed experimentally using spin-polarized scanning tunneling microscopes. We study different models hosting second-order topological phases, both analytically and numerically, and using Keldysh techniques we provide numerical simulations of the spin-polarized currents probed by scanning tips.

Transport characterization of topological superconductivity in a planar Josephson junction

Inspired by two recent experiments in Nature [Fornieri et al., Nature (London) 569, 89 (2019); Ren et al., Nature (London) 569, 93 (2019)], we numerically studied the transport properties of topological superconductivity in a planar Josephson junction. Our numerical calculations suggest that the origin of a zero-bias conductance peak is not unique. In addition to the single pair of Majorana zero modes, multiple pairs of Majorana zero modes can also exist at the ends of the junction. Although the bulk energy spectra in these two regions are distinguished, the signal measured through conductance cannot reveal the true information of the bulk energy spectrum. Thus the zero-bias conductance peaks measured in both two regions are quite similar and are hard to distinguish. In order to reveal the right information regarding the topological region, more methods in addition to the local conductance measurements are needed. Moreover, these multiple Majorana zero modes are not stable and fragile for topological quantum computation. To realize a topological Josephson junction with stable Majorana zero modes, the junction width should be smaller than half of the superconducting coherence length, and the superconducting bulk width should be larger than the coherence length.

Kondo Breakdown in a Spin-1/2 Chain of Adatoms on a Dirac Semimetal.

We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the decoupled fixed point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum MonteCarlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.

Phonon-assisted Andreev reflection driven by a Majorana zero mode

We investigate the Andreev reflection in the heterostructure formed by the indirect coupling between the metallic lead and Majorana zero mode (MZM) via one quantum dot which suffers from the electron-phonon interaction. Our calculation results show that at the zero-temperature limit, the MZM-governed zero-bias conductance value is independent of the electron-phonon interaction. However at finite temperature, the electron-phonon interaction exacerbates the suppression of the magnitude of zero-bias conductance. We believe that the results in this work can help to further differentiate the signature of the MZM in the Andreev reflection process.

Anomalous proximity effect of planar topological Josephson junctions

The anomalous proximity effect in dirty superconducting junctions is one of most striking phenomena highlighting the profound nature of Majorana bound states and odd-frequency Cooper pairs in topological superconductors. Motivated by the recent experimental realization of planar topological Josephson junctions, we describe the anomalous proximity effect in a superconductor/semiconductor hybrid, where an additional dirty normal-metal segment is extended from a topological Josephson junction. The topological phase transition in the topological Josephson junction is accompanied by a drastic change in the low-energy transport properties of the attached dirty normal-metal. The quantization of the zero-bias differential conductance, which appears only in the topologically nontrivial phase, is caused by the penetration of the Majorana bound states and odd-frequency Cooper pairs into a dirty normal-metal segment. As a consequence, we propose a practical experiment for observing the anomalous proximity effect.

Effects of an indirectly-coupled quantum dot on the Andreev reflection induced by Majorana modes

The Majorana-induced Andreev reflection is theoretically investigated, by considering an additional quantum dot coupled to the normal metallic lead. We find that the quantum dot takes variable effect on the zero-bias conductance induced by the Majorana zero mode. The non-superconducting dot with zero-energy level can suppress the Andreev reflection. Otherwise, the quantum dot only changes the width of the Andreev reflection peak around the zero-bias point with its magnitude equal to 2e2h. Alternatively for the Majorana nonzero mode, the effect of quantum dot becomes dominant, including the zero-bias result. Our findings provide new insights for understanding the Andreev reflection driven by the Majorana modes in experiment.

Stability of Majorana bound states in the presence of spin-flip scattering

A popular evidence of the existence of Majorana bound states(MBS) is a quantized zero-bias conductance peak(ZBCP) which is robust to scattering by impurities, a consequence of its topological protection. In this work we examine the stability of this MBS induced ZBCP in a metal-superconductor junction in the vicinity of a spin flipper. We analytically calculate the differential charge conductance for metal-spin flipper-superconductor junction with two distinct superconductors: (a) spin less $p$-wave superconductor(pSc) and (b) spin-orbit-coupled s-wave superconducting wire in presence of a Zeeman field(SOCSW). We see that the quantized ZBCP remains stable in presence of spin-flip(SF) scattering for metal-pSc junction, while it loses its stability when pSc is replaced by SOCSW. Further, the scattering matrix(S-Matrix) of the metal-pSc junction satisfies BDI symmetry class regardless of SF scattering. For BDI symmetry class, both Hamiltonian as well as S-Matrix satisfy particle-hole(PH), time reversal(TR) and chiral symmetries. However, in case of metal-SOCSW junction the Hamiltonian as well as S-Matrix belongs to symmetry class D in absence of SF scattering. In symmetry class D both Hamiltonian and S-Matrix satisfy PH symmetry, but do not satisfy TR and chiral symmetry relations. In presence of SF scattering, the S-Matrix for metal-SOCSW junction belongs to symmetry class A for which S-Matrix does not satisfy either PH or TR or chiral symmetry relations. The reason for ZBCP at a metal-pSc junction is perfect Andreev reflection regardless of SF scattering, while for metal-SOCSW junction it is the exact cancellation between normal and Andreev reflection probabilities at zero bias and not perfect Andreev reflection, in absence of SF scattering. However, in presence of SF scattering, there is no exact cancellation at zero bias which leads to loss of quantized ZBCP for a metal-SOCSW junction.

Multiple-Band Andreev Transport in Optimally Doped Superconducting Oxypnictides

Using multiple Andreev reflections (MAR) effect spectroscopy of SnS junctions, we directly determine temperature dependences of the superconducting order parameters, excess Andreev current, and zero-bias conductance (ZBC) in polycrystalline samples of superconducting oxypnictides Sm0.7Th0.3OFeAs and NdO0.6H0.36FeA with almost optimal critical temperatures. It is shown that the results obtained are self-consistent and could be described in the framework of a two-band model. We estimate a dominating contribution 70–85% of the bands with the large gap to the total conductance.

Quantum Dot Parity Effects in Trivial and Topological Josephson Junctions.

An odd-occupied quantum dot in a Josephson junction can flip transmission phase, creating a π junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a full-shell hybrid interferometer, using gate voltage to control dot-junction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zero-bias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zero-energy modes in the leads.

Zero-bias peaks at zero magnetic field in ferromagnetic hybrid nanowires

We report transport measurements and tunneling spectroscopy in hybrid nanowires with epitaxial layers of superconducting Al and the ferromagnetic insulator EuS, grown on semiconducting InAs nanowires. In devices where the Al and EuS covered facets overlap, we infer a remanent effective Zeeman field of order 1 T, and observe stable zero-bias conductance peaks in tunneling spectroscopy into the end of the nanowire, consistent with topological superconductivity at zero applied field. Hysteretic features in critical current and tunneling spectra as a function of applied magnetic field support this picture. Nanowires with non-overlapping Al and EuS covered facets do not show comparable features. Topological superconductivity in zero applied field allows new device geometries and types of control.

Transport properties of Majorana drumhead surface states in topological nodal-ring superconductors

We propose a topological nodal-ring superconductor (TNRSC) by inducing superconductivity on a topological nodal-ring semimetal (NRSM). Such a TNRSC can map to a one-dimensional BDI class topological superconductor and host both ${N}_{\mathrm{BDI}}=1$ and 2 topological phases in the Brillouin zone. These two topological phases support one and two Majorana drumhead surface states, respectively. By virtue of these novel Majorana modes, we find (i) the presence of drumhead surface states can be identified inside the nodal ring, and the radius of the nodal ring can be accurately determined by the zero-bias conductance of a normal-metal (NM)/TNRSC junction; and (ii) the spin-polarized and correlated currents can be generated in the leads of a NM/TNRSC/NM junction. The conclusions are robust even for NRSMs with dispersive drumhead surface states, and they can also apply to the topological NRSM ${\mathrm{HgCr}}_{2}{\mathrm{Se}}_{4}$.

Possible unconventional two-band superconductivity in MoTe2

The coexistence of the type-II Weyl semimetal phase and superconductivity in the layered transition-metal dichalcogenide $\mathrm{Mo}{\mathrm{Te}}_{2}$ is of great interest as it is considered a promising candidate for an intrinsic topological superconductor. However, the ultralow superconducting critical temperature (${T}_{c}$) of \ensuremath{\sim}0.1 K limits the exploration of the intrinsic superconducting properties. Here the superconductivity in $\mathrm{Mo}{\mathrm{Te}}_{2}$ is investigated by systematic ultralow temperature transport measurements with standard four-electrode configuration, together with the hard point-contact (PC) technique which can enhance the ${T}_{c}$ and detect the in situ spectroscopic information of the pairing symmetry. The temperature dependence of the superconducting critical field from transport measurements and the two-step double conductance peaks from the PC spectra measurements both suggest the two-band superconductivity in $\mathrm{Mo}{\mathrm{Te}}_{2}$. Together with the occasional observation of zero-bias conductance peaks in the spectra, our results suggest the unconventional two-band superconductivity with potential ${s}_{+\ensuremath{-}}$ pairing in $\mathrm{Mo}{\mathrm{Te}}_{2}$.