Zero-bias Peak Research Articles

Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states.

A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks-features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.

A Majorana look-alike

Mesoscopic Physics Most experimental claims of Majorana bound states, unusual quasiparticles that may become the cornerstone of topological quantum computing, rest on the observation of a persistent zero bias peak (ZBP) in tunneling spectra. In semiconductor–superconductor heterostructures, this feature may also be caused by the topologically trivial Andreev bound states. Valentini et al. provide comprehensive evidence that the ZBPs observed in their experiments with semiconductor nanowires fully coated with a superconducting shell are indeed of this topologically trivial origin, in contrast to the interpretation of similar earlier experiments. The researchers identify the length of the tunnel junction in their devices as a crucial experimental parameter. Science , abf1513, this issue p. [82][1] [1]: /lookup/doi/10.1126/science.abf1513

Closing of the induced gap in a hybrid superconductor-semiconductor nanowire

Hybrid superconductor-semiconductor nanowires are predicted to undergo a field-induced phase transition from a trivial to a topological superconductor, marked by the closure and re-opening of the excitation gap, followed by the emergence of Majorana bound states at the nanowire ends. Many local density-of-states measurements have reported signatures of the topological phase, however this interpretation has been challenged by alternative explanations. Here, by measuring nonlocal conductance, we identify the closure of the excitation gap in the bulk of the semiconductor before the emergence of zero-bias peaks. This observation is inconsistent with scenarios where zero-bias peaks occur due to end-states with a trivially gapped bulk, which have been extensively considered in the theoretical and experimental literature. We observe that after the gap closes, nonlocal signals fluctuate strongly and persist irrespective of the presence of local-conductance zero-bias peaks. Thus, our observations are also incompatible with a simple picture of clean topological superconductivity. This work presents a new experimental approach for probing the spatial extent of states in Majorana wires, and reveals the presence of a regime with a continuum of spatially extended states and uncorrelated zero-bias peaks.

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.

Tunneling conductance of the ( d+ip )-wave superconductor

We theoretically investigate the tunneling conductance of the $d+ip$-wave superconductor which is recently proposed to be realised at the (110) surface of a high-$T_c$ cuprate superconductor. Utilizing the quasiclassical Eilenberger theory, we obtain the self-consistent pair potentials and the differential conductance of the normal-metal/$d+ip$-wave superconductor junction. We demonstrate that the zero-bias peak of a $d$-wave superconductor is robust against the spin-triplet $p$-wave surface subdominant order even though it is fragile against the spin-singlet $s$-wave one. Comparing our numerical results and the experimental results, we conclude the spin-triplet $p$-wave surface subdominant order is feasible.

Competing Energy Scales in Topological Superconducting Heterostructures.

Artificially engineered topological superconductivity has emerged as a viable route to create Majorana modes. In this context, proximity-induced superconductivity in materials with a sizable spin–orbit coupling has been intensively investigated in recent years. Although there is convincing evidence that superconductivity may indeed be induced, it has been difficult to elucidate its topological nature. Here, we engineer an artificial topological superconductor by progressively introducing superconductivity (Nb), strong spin–orbital coupling (Pt), and topological states (Bi2Te3). Through spectroscopic imaging of superconducting vortices within the bare s-wave superconducting Nb and within proximitized Pt and Bi2Te3 layers, we detect the emergence of a zero-bias peak that is directly linked to the presence of topological surface states. Our results are rationalized in terms of competing energy trends which are found to impose an upper limit to the size of the minigap separating Majorana and trivial modes, its size being ultimately linked to fundamental materials properties.

Charge and spin transport through a normal lead coupled to an s -wave superconductor and a Majorana zero mode

Zero-bias charge conductance peak (ZBCCP) is a significant symbol of Majorana zero modes (MZMs). The proximity effect of $s$-wave superconductor is usually demanded in the fabrication of MZMs. So in transport experiments, the system is inevitably coupled to the $s$-wave superconductor. Here we study how the ZBCCP is affected by coupling of the $s$-wave superconductor. The results show that the ZBCCP could be changed into a zero-bias valley due to the coupling of $s$-wave superconductor, although the conductance at the zero bias still keeps a quantized value $2{e}^{2}/h$. So it does not mean no MZM exists when no ZBCCP is experimentally observed. In addition, the spin transport is investigated. Four reflection processes (the normal reflection, spin-flip reflection, normal Andreev reflection, and equal-spin Andreev reflection) usually occur. The reflection coefficients are strongly dependent on the spin direction of the incident electron, and they may be symmetrical or Fano resonance shapes. But the spin conductance always shows a zero-bias peak with the height $e/2\ensuremath{\pi}$ regardless of the direction of the spin bias and the coupling strength of the $s$-wave superconductor. So measuring spin transport properties could be a more reliable method to judge the existence of MZMs.

Induced superconductivity in linear carbon chains and engineering of zero-bias peaks with geometric angles: a new approach

We investigated the effect of slip angle, a geometric parameter named as α in superconducting quasi-one-dimensional carbon structures, by engendering resonant peak of linear carbon chains. We studied also the density of states and the effect of different slip angles on this structure. We found the interesting role of the slip angle, similar to the mixed superconducting state, creating a mass-like gap in the electron-hole excitation spectrum of the superconducting quasi-one-dimensional carbon structure. In the framework of the Dirac-Bogoliubov–de Gennes formalism, we investigated the transport properties in the superconducting linear carbon chain. The superconductor gap is taken to be a spin-singlet and spin-triplet superconducting state.

Effects of Rashba-spin–orbit coupling on superconducting boron-doped nanocrystalline diamond films: evidence of interfacial triplet superconductivity

Among the many remarkable properties of diamond, the ability to superconduct when heavily doped with boron has attracted much interest in the carbon community. When considering the nanocrystalline boron doped system, the reduced dimensionality and confinement effects have led to several intriguing observations most notably, signatures of a mixed superconducting phase. Here we present ultra-high-resolution transmission electron microscopy imaging of the grain boundary and demonstrate how the complex microstructure leads to enhanced carrier correlations. We observe hallmark features of spin–orbit coupling (SOC) manifested as the weak anti-localization effect. The enhanced SOC is believed to result from a combination of inversion symmetry breaking at the grain boundary interfaces along with antisymmetric confinement potential between grains, inducing a Rashba-type SOC. From a pronounced zero bias peak in the differential conductance, we demonstrate signatures of a triplet component believed to result from spin mixing caused by tunneling of singlet Cooper pairs through such Rashba-SOC grain boundary junctions.

High-Tc Cooper-pair injection in a semiconductor–superconductor structure

We observe Andreev reflection in a YBCO–GaN junction through differential conductance spectroscopy. A strong characteristic zero-bias peak was observed and persisted up to the critical temperature of the superconductor with a smaller superconducting order parameter Δ ∼ 1 meV. The presence of Andreev reflection with the small Δ in comparison to its value for high-Tc superconductors forms an important milestone toward demonstration of superconducting proximity in high-Tc/semiconductor junctions. Experimental results were then compared to the theoretical model with good agreement. Efficient injection of Cooper pairs into direct bandgap semiconducting structures, together with high transition temperature of YBCO, can pave the way to novel optoelectronics and quantum optical studies of high-Tc materials.

Zero-bias conductance peak in Dirac semimetal-superconductor devices

Majorana zero modes (MZMs), fundamental building blocks for realizing topological quantum computers, can appear at the interface between a superconductor and a topological material. One of the experimental signatures that has been widely pursued to confirm the existence of MZMs is the observation of a large, quantized zero-bias conductance peak (ZBCP) in the differential conductance measurements. In this Letter, we report observation of such a large ZBCP in junction structures of normal metal (titanium/gold Ti/Au) + Dirac semimetal (cadmium arsenide Cd3As2) + conventional superconductor (aluminum Al), with a value close to four times that of the normal state conductance. Our detailed analyses suggest that this large ZBCP is most likely not caused by MZMs. We attribute the ZBCP, instead, to the existence of a supercurrent between two far-separated superconducting Al electrodes, which shows up as a zero-bias peak because of the circuitry and thermal fluctuations of the supercurrent phase, a mechanism conceived by Ivanchenko and Zil'berman more than 50 years ago [JETP 28, 1272 (1969)]. Our results thus call for extreme caution when assigning the origin of a large ZBCP to MZMs in a multiterminal semiconductor or topological insulator/semimetal setup. We thus provide criteria for identifying when the ZBCP is definitely not caused by an MZM. Furthermore, we present several remarkable experimental results of a supercurrent effect occurring over unusually long distances and clean perfect Andreev reflection features.

Physical mechanisms for zero-bias conductance peaks in Majorana nanowires

Motivated by the need to understand and simulate the ubiquitous experimentally-observed zero-bias conductance peaks in superconductor-semiconductor hybrid structures, we theoretically investigate the tunneling conductance spectra in one-dimensional nanowires in proximity to superconductors in a systematic manner taking into account several different physical mechanisms producing zero-bias conductance peaks. The mechanisms we consider are the presence of quantum dots, inhomogeneous potential, random disorder in the chemical potential, random fluctuations in the superconducting gap, and in the effective $g$ factor with the self-energy renormalization induced by the parent superconductor in both short ($L\sim1~\mu$m) and long nanowires ($L\sim3~\mu$m). We classify all foregoing theoretical results for zero-bias conductance peaks into three types: the good, the bad, and the ugly, according to the physical mechanisms producing the zero-bias peaks and their topological properties. We find that, although the topological Majorana zero modes are immune to weak disorder, strong disorder (ugly) completely suppresses topological superconductivity and generically leads to trivial zero bias peaks. Compared qualitatively with the extensive existing experimental results in the superconductor-semiconductor nanowire structures, we conclude that most current experiments are likely exploring trivial zero-bias peaks in the ugly situation dominated by strong disorder. We also study the nonlocal end-to-end correlation measurement in both the short and long wires, and point out the limitation of the nonlocal correlation in ascertaining topological properties particularly when applied to short wires. The goal of the work is to establish with a very high confidence level the real physical possibility that essentially all experimentally observed zero bias peaks in Majorana nanowires are most likely ugly.

Effect of Zeeman coupling on the Majorana vortex modes in iron-based topological superconductors

In the superconducting regime of FeTe$_{(1-x)}$Se$_x$, there exist two types of vortices which are distinct by the presence or absence of zero energy states in their core. To understand their origin, we examine the interplay of Zeeman coupling and superconducting pairings in three-dimensional metals with band inversion. Weak Zeeman fields are found to suppress the intra-orbital spin-singlet pairing, known to localize the states at the ends of the vortices on the surface. On the other hand, an orbital-triplet pairing is shown to be stable against Zeeman interactions, but leads to delocalized zero-energy Majorana modes which extend through the vortex. In contrast, the finite-energy vortex modes remain localized at the vortex ends even when the pairing is of orbital-triplet form. Phenomenologically, this manifests as an observed disappearance of zero-bias peaks within the cores of topological vortices upon increase of the applied magnetic field. The presence of magnetic impurities in FeTe$_{(1-x)}$Se$_x$, which are attracted to the vortices, would lead to such Zeeman-induced delocalization of Majorana modes in a fraction of vortices that capture a large enough number of magnetic impurities. Our results provide an explanation to the dichotomy between topological and non-topological vortices recently observed in FeTe$_{(1-x)}$Se$_x$.

Reaching a conductance plateau

Topological Matter The surface of the iron-based superconductor FeTe0.55Se0.45 satisfies the necessary conditions to support topological superconductivity. Under the application of a magnetic field, vortices with zero-bias peaks that are consistent with Majorana bound states have been observed. Using scanning tunneling spectroscopy, Zhu et al. studied the conductance of these states as the tip-sample distance was reduced (see the Perspective by Sau). The researchers found that the value of the conductance increased and eventually saturated. For one of the vortices they studied, the conductance reached a quantized value that is characteristic of the Majorana bound states. Science , this issue p. [189][1]; see also p. [145][2] [1]: /lookup/doi/10.1126/science.aax0274 [2]: /lookup/doi/10.1126/science.aaz9589

Unraveling a concealed resonance by multiple Kondo transitions in a quantum dot

Kondo correlations are responsible for the emergence of a zero-bias peak in the low temperature differential conductance of Coulomb blockaded quantum dots. In the presence of a global SU(2)$\otimes$SU(2) symmetry, which can be realized in carbon nanotubes, they also inhibit inelastic transitions which preserve the Kramers pseudospins associated to the symmetry. We report on magnetotransport experiments on a Kondo correlated carbon nanotube where resonant features at the bias corresponding to the pseudospin-preserving transitions are observed. We attribute this effect to a simultaneous enhancement of pseudospin-non-preserving transitions occurring at that bias. This process is boosted by asymmetric tunneling couplings of the two Kramers doublets to the leads and by asymmetries in the potential drops at the leads. Hence, the present work discloses a fundamental microscopic mechanisms ruling transport in Kondo systems far from equilibrium.

Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor.

Majorana zero modes (MZMs) are spatially localized, zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold promise for topological quantum computing. Owing to the particle-antiparticle equivalence, MZMs exhibit quantized conductance at low temperature. By using variable-tunnel-coupled scanning tunneling spectroscopy, we studied tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e 2/h quantum conductance (where e is the electron charge and h is Planck's constant). By contrast, no plateaus were observed on either finite energy vortex bound states or in the continuum of electronic states outside the superconducting gap. This behavior of the zero-mode conductance supports the existence of MZMs in FeTe0.55Se0.45.

Reproducing topological properties with quasi-Majorana states

Andreev bound states in hybrid superconductor-semiconductor devices can have near-zero energy in the topologically trivial regime as long as the confinement potential is sufficiently smooth. These quasi-Majorana states show zero-bias conductance features in a topologically trivial phase, mimicking spatially separated topological Majorana states. We show that in addition to the suppressed coupling between the quasi-Majorana states, also the coupling of these states across a tunnel barrier to the outside is exponentially different for increasing magnetic field. As a consequence, quasi-Majorana states mimic most of the proposed Majorana signatures: quantized zero-bias peaks, the 4\pi4π Josephson effect, and the tunneling spectrum in presence of a normal quantum dot. We identify a quantized conductance dip instead of a peak in the open regime as a distinguishing feature of true Majorana states in addition to having a bulk topological transition. Because braiding schemes rely only on the ability to couple to individual Majorana states, the exponential control over coupling strengths allows to also use quasi-Majorana states for braiding. Therefore, while the appearance of quasi-Majorana states complicates the observation of topological Majorana states, it opens an alternative route towards braiding of non-Abelian anyons and protected quantum computation.

Atomic structures and nanoscale electronic states on the surface of MgB2 superconductor observed by scanning tunneling microscopy and spectroscopy

The systematic study of the nanoscale local electronic states on the MgB2 surface was performed using the low-temperature scanning tunnel microscopy/spectroscopy (STM/STS). The STM topography shows the atomic image of the hexagonal lattice with the constant parameter a’ = 0.31 nm, which is identified as mainly the Mg site occupancy. The temperature-dependent STS measurements were analyzed assuming the existence of two energy gaps. As a result, the fitting gap amplitudes Δfit ≃ 10.2 meV and 4.8 meV were found at T = 4.9 K. The scanned conductance (dI/dV) maps in the area of 4 × 2 nm2 show homogenous distributions of the gaps associated with the π-band. In addition, the conductance peaks at zero-bias voltage were observed through defined lines with lengths about ∼0.8 nm, which is much smaller than the superconducting coherence length ξab∼40nm of MgB2. The form of the zero-bias peaks looks like that in the case of the Andreev-Saint-James reflection at the tip-sample contact.

Zero-energy pinning of topologically trivial bound states in multiband semiconductor-superconductor nanowires

Recent tunneling conductance measurements on semiconductor-superconductor nanowires find zero-bias peaks to be ubiquitous across wide ranges of chemical potential and Zeeman energy. Motivated by this, we demonstrate that topologically-trivial Andreev abound states (ABSs) pinned near zero energy are produced rather generically in inhomogeneous systems with multi-band occupancy in the presence of inter-band coupling. We first investigate the inter-band coupling mechanism responsible for the pinning within a multi-band 1D toy model, then we confirm the findings using a 3D Schr\"{o}dinger-Poisson approach that incorporates the geometric and electrostatic details of the actual device. Our analysis shows that level-repulsion generated by inter-band coupling can lead to a rather spectacular pinning of the lowest-energy mode near zero energy in systems (or regions) characterized by very-short length scales ($\sim100~$nm).We show that level repulsion between the lowest energy levels can mimic the gap opening feature (simultaneous with the emergence of a near-zero energy mode) predicted to occur in Majorana hybrid systems. We also demonstrate that nearly-zero bias differential conductance features exhibiting particle-hole asymmetry are due to the presence of (topologically-trivial) ABSs pinned near zero-energy by level repulsion, not to Majorana zero modes, quasi-Majoranas, or any other low-energy mode that involves (partially) separated Majorana bound states. Our findings demonstrate the importance of understanding in detail multi-band physics and electrostatic effects in the context of the ongoing search for Majorana modes in semiconductor-superconductor heterostructures.

Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices.

We perform tunneling measurements on indium antimonide nanowire-superconductor hybrid devices fabricated for the studies of Majorana bound states. At finite magnetic field, resonances that strongly resemble Majorana bound states, including zero-bias pinning, become common to the point of ubiquity. Since Majorana bound states are predicted in only a limited parameter range in nanowire devices, we seek an alternative explanation for the observed zero-bias peaks. With the help of a self-consistent Poission-Schrödinger multiband model developed in parallel, we identify several families of trivial subgap states that overlap and interact, giving rise to a crowded spectrum near zero energy and zero-bias conductance peaks in experiments. These findings advance the search for Majorana bound states through improved understanding of broader phenomena found in superconductor-semiconductor systems.