Zero-bias Conductance Peak Research Articles

Critical Lengths of Kitaev Chains for Majorana Zero Modes with a Microsecond Coherence Time and a Quantized Conductance Signature

The problems of disorder and insufficient system length are generally regarded as central problems in the realization of Majorana zero modes (MZM), which are a promising platform for realizing fault-tolerant topological quantum computing (TQC). In this work, we analyze eigenenergy spectra and transport properties of finite Kitaev chains using quantum transport simulations in a wide design space of hopping amplitude (t), superconductor pairing (Δ), and electrochemical potential. Our goal is to determine critical or minimum acceptable chain lengths to obtain oscillation-free MZMs with suitable microsecond coherence times, and observable zero-bias conductance peaks (ZBCP) quantized almost at ~2e2/h. Due to qualitative equivalence of the Kitaev and Oreg–Lutchyn models, we approximately determine the foreseeable critical length of topological superconducting nanowires (TS NWs) as well. We find that the ZBCP length requirement is looser in comparison to the limit imposed by the coherence time. For a large t/Δ mismatch of ~40 corresponding to the experimental TS NWs, the first condition sets the minimum length to 344 sites (≈5.5 μm), while the second condition requires 605 sites (≈9.7 μm). The calculated lengths are far from the reported experimental hybrid device dimensions, explaining difficulties in observing MZMs in TS NWs fabricated so far. Nonetheless, a decreasing t/Δ mismatch allows for shorter systems, which argues in favor of the proximitized quantum dot path for MZMs in a solid-state system.

Perspective on Majorana bound-states in hybrid superconductor-semiconductor nanowires

A personal perspective is given on a decade of research on Majorana bound states (MBS) in hybrid devices of semiconducting nanowires covered with a superconductor. Predicted experimental signatures like zero-bias anomalies turned out to be false positive evidence for topological MBS. Zero-bias conductance peaks have found alternative explanations in terms of material disorder and smooth boundary potentials. A recount is given on various predictions, observations and re-interpretations, as well as the lessons learned in retrospect and an outlook on the future.

Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems

The emergence of Majorana bound states in finite length superconductor-semiconductor hybrid systems has been predicted to occur in the form of oscillatory energy levels with parity crossings around zero energy. Each zero-energy crossing is expected to produce a quantized zero-bias conductance peak but several studies have reported conductance peaks pinned at zero energy over a range of Zeeman fields, whose origin, however, is not clear. In this work, we consider superconducting systems with spin-orbit coupling under a Zeeman field and demonstrate that non-Hermitian effects, due to coupling to ferromagnet leads, induce zero-energy pinning of Majorana and trivial Andreev bound states. We find that this zero-energy pinning effect occurs due to the formation of non-Hermitian spectral degeneracies known as exceptional points, whose emergence can be controlled by the interplay of non-Hermiticity, the applied Zeeman field, and chemical potentials. Moreover, depending on the non-Hermitian spatial profile, we find that non-Hermiticity changes the single point Hermitian topological phase transition into a flattened zero energy line bounded by exceptional points from multiple low energy levels. This seemingly innocent change notably enables a gap closing well below the Hermitian topological phase transition, which can be in principle simpler to achieve. Furthermore, we reveal that the energy gaps separating Majorana and trivial Andreev bound states from the quasicontinuum remain robust for the values that give rise to the zero-energy pinning effect. While reasonable values of non-Hermiticity can be indeed beneficial, very strong non-Hermitian effects can be detrimental as it might destroy superconductivity. Our findings can be therefore useful for understanding the zero-energy pinning of trivial and topological states in Majorana devices. Published by the American Physical Society 2024

A two-site Kitaev chain in a two-dimensional electron gas.

Artificial Kitaev chains can be used to engineer Majorana bound states (MBSs) in superconductor-semiconductor hybrids1-4. In this work, we realize a two-site Kitaev chain in a two-dimensional electron gas by coupling two quantum dots through a region proximitized by a superconductor. We demonstrate systematic control over inter-dot couplings through in-plane rotations of the magnetic field and via electrostatic gating of the proximitized region. This allows us to tune the system to sweet spots in parameter space, where robust correlated zero-bias conductance peaks are observed in tunnelling spectroscopy. To study the extent of hybridization between localized MBSs, we probe the evolution of the energy spectrum with magnetic field and estimate the Majorana polarization, an important metric for Majorana-based qubits5,6. The implementation of a Kitaev chain on a scalable and flexible two-dimensional platform provides a realistic path towards more advanced experiments that require manipulation and readout of multiple MBSs.

Interplay between magnetic gap and quasi-particle lifetime in topological insulator ferromagnet/f-wave superconductor junctions

Using the modified Blonder–Tinkham–Klapwijk (BTK) theory, the interplay between the lifetime of quasi particles and the magnetic gap in a topological insulator-based ferromagnet/f-wave superconductor (TI-based FM/f–wave SC) tunnel structure is theoretically studied. Two symmetries of f 1 and f 2 waves are considered for superconducting pairing states. The results indicate that reducing the finite quasi-particle lifetime will induce a transformation of energy-gap peaks into a zero-bias peak in tunneling conductance spectrum, as well as a transformation of energy-gap dips into a zero-bias dip in shot noise spectrum, ultimately resulting in the smoothing of the zero-bias conductance peak and the zero-bias shot noise dip. An increase in magnetic gap will suppress the tunnel conductance and shot noise when the conventional Andreev retro-reflection dominates, but will enhance them when the specular Andreev reflection is dominant. Both specular Andreev reflection and conventional Andreev retro-reflection will be enhanced as the quasi-particle lifetime increases. When Fermi energy equals the magnetic gap, shot noise and tunneling conductance vanish across all energy ranges. These findings not only contribute to a better understanding of specular Andreev reflection in the FM/f–wave SC junction based on TIs but also provide insights for experimentally determining the f-wave pairing symmetry.

Andreev reflection in graphene nanoribbons induced by d-wave superconductors

Honeycomb and square lattices are combined as a tight-binding model to examine the Andreev reflection in graphene nanoribbons induced by a superconductor. The superconducting symmetry is assumed to be the d-wave. The zero-bias tunneling conductance peak, which is generally produced by the d-wave superconductor, is absent for the nanoribbons under conditions similar to those when a quantum wire is the normal conductor. For the anisotropic superconductivity, propagating modes appear in the superconductor even for biases below the top of the superconducting energy gap. Features appear in the conductance at the subgap population thresholds of these propagating modes as a finite-size effect of the lattice system. The surface Andreev bound states responsible for the zero-bias anomaly also cause transport resonances in the vicinity of the zero bias despite the aforementioned destruction of the anomaly. The conductance spectra revealing these excitation behaviors are fairly unchanged regardless of the presence of a hopping barrier at the interface with the superconductor. The insensitivity to the interface scattering highlights the fact that barrier-less situation cannot be realized for the model due to the heterogeneous lattice. Concerning specular Andreev reflection, the wavefunction parity gives rise to its blocking for single-mode zigzag-edged nanoribbons. The blocking is suppressed when the anisotropic superconductivity is asymmetric for the nanoribbons.

Intrinsic surface p-wave superconductivity in layered AuSn4

The search for topological superconductivity (TSC) is currently an exciting pursuit, since non-trivial topological superconducting phases could host exotic Majorana modes. However, the difficulty in fabricating proximity-induced TSC heterostructures, the sensitivity to disorder and stringent topological restrictions of intrinsic TSC place serious limitations and formidable challenges on the materials and related applications. Here, we report a new type of intrinsic TSC, namely intrinsic surface topological superconductivity (IS-TSC) and demonstrate it in layered AuSn4 with Tc of 2.4 K. Different in-plane and out-of-plane upper critical fields reflect a two-dimensional (2D) character of superconductivity. The two-fold symmetric angular dependences of both magneto-transport and the zero-bias conductance peak (ZBCP) in point-contact spectroscopy (PCS) in the superconducting regime indicate an unconventional pairing symmetry of AuSn4. The superconducting gap and surface multi-bands with Rashba splitting at the Fermi level (EF), in conjunction with first-principle calculations, strongly suggest that 2D unconventional SC in AuSn4 originates from the mixture of p-wave surface and s-wave bulk contributions, which leads to a two-fold symmetric superconductivity. Our results provide an exciting paradigm to realize TSC via Rashba effect on surface superconducting bands in layered materials.

Honing in on a topological zero-bias conductance peak

A popular signature of Majorana bound states in topological superconductors is the quantized zero-energy conductance peak. However, a similar zero energy conductance peak can also arise due to non-topological reasons. Here we show that these trivial and topological zero energy conductance peaks can be distinguished via the zero energy local density of states (LDOSs) and local magnetization density of states (LMDOSs). We find that the zero-energy LDOSs and the LMDOSs exhibit periodic oscillations for a trivial zero-bias conductance peak (ZBCP). In contrast, these oscillations disappear for the topological ZBCP because of perfect Andreev reflection at zero energy in topological superconductor junctions. Our results suggest that the zero-energy LDOSs and the LMDOSs can be used as an experimental probe to distinguish a trivial zero-energy conductance peak from a topological zero-energy conductance peak.

Proximity-induced superconductivity in type-II Weyl semimetal NbIrTe4

Heterostructures between conventional superconductors and materials with different electronic ground states have emerged as a powerful method for exploring the exotic superconducting properties induced by the proximity effect. Here, we investigate Andreev transport through the interface between an s-wave superconductor Nb and a type-II Wely semimetal NbIrTe4. The differential conductance measurement reveals an anomalous zero-bias conductance peak and prominent subgap structures at low temperatures. Furthermore, we found that these subgap structures are not only related to the interface coupling strength but also influenced by the thickness of the NbIrTe4 flake. For thin devices (≤100 nm), the differential conductance spectra only exhibit a single-gap structure. While in thicker devices (∼150 nm), we observed the distinct double-gap structure, which is likely to originate from the proximity-induced superconductivity gap on the bulk and surface of the NbIrTe4 flakes. These results can provide a good reference for understanding the superconducting phase in type-II Weyl semimetals and take a step toward its future application in the field of superconducting electronics.

Weakly coupled Majorana wire arrays under tilted magnetic fields

An array of Rashba-coupled semiconducting nanowires lying in proximity to an s-wave superconducting substrate, with weak inter-wire coupling, in the presence of an external magnetic field shows even–odd effect in the differential conductance over a chosen parameter space. Such an effect is a direct consequence of end Majoranas in each nanowire hybridizing into bonding and anti-bonding states. In the present work, we study in detail the impact of tilting of external magnetic field on the differential conductance of an array of both uncoupled and weakly coupled wires. The phase diagram evolution with various control parameters including the tilt angle of the magnetic field has also been presented. From detailed analysis of the field-angle dependence of the odd–even effect, and the evolution of the same over a large parameter space we summarize that the results can be used to exploit magnetic-field angle in an array of Rashba-coupled semiconducting nanowires on a superconducting substrate as an important tuning parameter to investigate zero-bias conductance peak arising from Majorana edge modes vis-a-vis that arising from a non-topological origin.

Nanoscale Manipulation of Wrinkle-Pinned Vortices in Iron-Based Superconductors

The controlled manipulation of Abrikosov vortices is essential for both fundamental science and logical applications. However, achieving nanoscale manipulation of vortices while simultaneously measuring the local density of states within them remains challenging. Here, we demonstrate the manipulation of Abrikosov vortices by moving the pinning center, namely one-dimensional wrinkles, on the terminal layers of Fe(Te,Se) and LiFeAs, by utilizing low-temperature scanning tunneling microscopy/spectroscopy (STM/S). The wrinkles trap the Abrikosov vortices induced by the external magnetic field. In some of the wrinkle-pinned vortices, robust zero-bias conductance peaks are observed. We tailor the wrinkle into short pieces and manipulate the wrinkles by using an STM tip. Strikingly, we demonstrate that the pinned vortices move together with these wrinkles even at high magnetic field up to 6 T. Our results provide a universal and effective routine for manipulating wrinkle-pinned vortices and simultaneously measuring the local density of states on the iron-based superconductor surfaces.

Theoretical proposal to obtain strong Majorana evidence from scanning tunneling spectroscopy of a vortex with a dissipative environment

It is predicted that a vortex in a topological superconductor contains a Majorana zero mode (MZM). The confirmative Majorana signature, i.e., the $2{e}^{2}/h$ quantized conductance, however, is easily sabotaged by unavoidable interruptions, e.g., instrument broadening, non-Majorana signal, and extra particle channels. To avoid these interruptions, we propose to obtain strong Majorana evidence following our novel Majorana hunting protocol that relies on dissipation introduced by disorders at, e.g., the sample-substrate interface. Within this protocol, we highlight three features, each of which alone can provide a strong evidence to identify MZM. First, dissipation suppresses a finite-energy Caroli-de Gennes-Matricon (CdGM) conductance peak into a valley, while it does not split MZM zero-bias conductance peak (ZBCP). Second, we predict a dissipation-dependent scaling feature of the ZBCP. Third, the introduced dissipation manifests the MZM signal by suppressing nontopological CdGM modes. Importantly, the observation of these features does not require a quantized conductance value $2{e}^{2}/h$.

Widely Varying Kondo and Magnetic Interactions in Molecule Gold Nanostructured Materials by Changing the Gold Nanoarchitecture

Delocalized-localized electron interactions are central to strongly correlated electron phenomena. Here, we study the Kondo effect, a prototypical strongly correlated phenomena, in a tunable fashion using gold nanostructures (nanoparticle, NP, and nanoshell, NS) + molecule cross-linkers (butanedithiol, BDT). NP films exhibit hallmark signatures of the Kondo effect, including (1) a log temperature resistance upturn as temperature decreases in a metallic regime, and (2) zero-bias conductance peaks (ZBCPs) that are well fit by a Frota function near a percolation insulator transition, previously used to model Kondo peaks observed using tunnel junctions. Remarkably, NP + NS films exhibit ZBCPs that persist to >220 K, i.e., >10-fold higher than that in NP films. Magnetic measurements reveal that moments in NP powders align, and in NS powders, they antialign at low temperatures. Based on these observations, we propose a mechanism in which varying such material nanobuilding blocks can modify electron-electron interactions to such a large degree.

Kondo effect in defect-bound quantum dots coupled to NbSe2

We report the fabrication of a van der Waals tunneling device hosting a defect-bound quantum dot coupled to NbSe$_2$. We find that upon application of magnetic field, the device exhibits a zero-bias conductance peak. The peak, which splits at higher fields, is associated with a Kondo effect. At the same time, the junction retains conventional quasiparticle tunneling features at finite bias. Such coexistence of a superconducting gap and a Kondo effect are unusual, and are explained by noting the two-gap nature of the superconducting state of NbSe$_2$, where a magnetic field suppresses the low energy gap associated with the Se band. Our data shows that van der Waals architectures, and defect-bound dots in them, can serve as a novel and effective platform for investigating the interplay of Kondo screening and superconducting pairing in unconventional superconductors.

Gatemon Qubit Based on a Thin InAs-Al Hybrid Nanowire

We study a gate-tunable superconducting qubit (gatemon) based on a thin InAs-Al hybrid nanowire. Using a gate voltage to control its Josephson energy, the gatemon can reach the strong coupling regime to a microwave cavity. In the dispersive regime, we extract the energy relaxation time T 1 ∼ 0.56 μs and the dephasing time μs. Since thin InAs-Al nanowires can have fewer or single sub-band occupation and recent transport experiment shows the existence of nearly quantized zero-bias conductance peaks, our result holds relevancy for detecting Majorana zero modes in thin InAs-Al nanowires using circuit quantum electrodynamics.

Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions.

We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs-Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2×2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A model of the device, with disorder treated phenomenologically, shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs.

Scanning tunneling spectroscopy of Majorana zero modes in a Kitaev spin liquid

The experimental detection of Majorana zero modes represents a major open problem. In topological superconductors, scanning tunneling spectroscopy provides evidence through zero-bias conductance peaks, which can however be confused with disorder-induced Andreev states. The theory here suggests that the Majorana zero modes bound to vortices in Kitaev spin liquids offer a more favorable testing ground: the Majorana-induced conductance features found are quite distinct from those of an alternative scenario based on magnons.

Robust and Fragile Majorana Bound States in Proximitized Topological Insulator Nanoribbons.

Topological insulator (TI) nanoribbons with proximity-induced superconductivity are a promising platform for Majorana bound states (MBSs). In this work, we consider a detailed modeling approach for a TI nanoribbon in contact with a superconductor via its top surface, which induces a superconducting gap in its surface-state spectrum. The system displays a rich phase diagram with different numbers of end-localized MBSs as a function of chemical potential and magnetic flux piercing the cross section of the ribbon. These MBSs can be robust or fragile upon consideration of electrostatic disorder. We simulate a tunneling spectroscopy setup to probe the different topological phases of top-proximitized TI nanoribbons. Our simulation results indicate that a top-proximitized TI nanoribbon is ideally suited for realizing fully gapped topological superconductivity, in particular when the Fermi level is pinned near the Dirac point. In this regime, the setup yields a single pair of MBSs, well separated at opposite ends of the proximitized ribbon, which gives rise to a robust quantized zero-bias conductance peak.

Emergence of Interlayer Coherence in Twist-Controlled Graphene Double Layers

We report enhanced interlayer tunneling with reduced linewidth at zero interlayer bias in a twist-controlled double monolayer graphene heterostructure in the quantum Hall regime, when the top (ν_{T}) and bottom (ν_{B}) layer filling factors are near ν_{T}=±1/2,±3/2 and ν_{B}=±1/2,±3/2, and the total filling factor ν=±1 or ±3. The zero-bias interlayer conductance peaks are stable against variations of layer filling factor, and signal the emergence of interlayer phase coherence. Our results highlight twist control as a key attribute in revealing interlayer coherence using tunneling.

Random matrix theory for the robustness, quantization, and end-to-end correlation of zero-bias conductance peaks in a class D ensemble

We develop a general theory to study strong random quenched disorder effects in systems of experimental relevance in the search for Majorana zero modes in topological superconductors. Using the random matrix theory in a class D ensemble, we simulate the transport properties of random quantum dots by attaching leads, and calculating the differential conductance in the $S$-matrix formalism. To add the concept of the length to the random system so that disordered Majorana nanowires can be simulated by the random matrix theory, we generalize the model of a single quantum dot to a chain of quantum dots by analogy with the superconductor-semiconductor nanowire Majorana platform. We first define a new concept, the robustness of zero-bias conductance peaks, in terms of an effective random Hamiltonian considering the self-energy of leads. We then study the joint distribution for the robustness and zero-bias conductance peaks, and find a strong correlation that the zero-bias conductance peak with stronger robustness is also prone to carry a larger conductance peak near $2{e}^{2}/h$. This trend is more prominent in shorter chains than in longer chains. This is consistent with experimentally observed zero-bias conductance associated with disorder-induced trivial Andreev bound states (the so-called ugly zero-bias peaks). Finally, we study the end-to-end correlation of the disorder-induced zero-bias conductances from two leads by calculating the normalized mutual information, which estimates the degrees of the correlation arising from the trivial zero-bias conductance peaks. Our work provides an estimate of several important metrics used in superconductor-semiconductor experiments to determine the nature of zero-bias conductance peaks, including the robustness, the quantization, and the end-to-end correlation of the trivial zero-bias peaks. Therefore, in order to claim any evidence for the Majorana zero modes, one must establish the observed zero-bias conductance peaks to have considerable statistical significance well beyond what we find in this work to exist for the trivial peaks.