Zero-bias Peak Research Articles

Magnetic Excitations in Ferromagnetically Coupled Spin-1 Nanographenes.

In the pursuit of high-spin building blocks for the formation of covalently bonded 1D or 2D materials with controlled magnetic interactions, -electron magnetism offers an ideal framework to engineer ferromagnetic interactions between nanographenes. As a first step in this direction, we explore the spin properties of ferromagnetically coupled triangulenes-triangular nanographenes with spin . By combining in-solution synthesis of rationally designed molecular precursors with on-surface synthesis, we successfully achieve covalently bonded triangulene dimers and trimers on Au(111). Starting with the triangulene dimer, we meticulously characterize its low-energy magnetic excitations using inelastic electron tunneling spectroscopy (IETS). IETS reveals conductance steps corresponding to a quintet-to-triplet excitation, and a zero-bias peak resulting from higher-order spin-spin scattering of the five-fold degenerate ferromagnetic ground state. The Heisenberg model captures the key parameters of inter-triangulene ferromagnetic exchange, and its successful extension to the larger system validates the model's accuracy. We anticipate that incorporating ferromagnetically coupled building blocks into the repertoire of magnetic nanographenes will unlock new possibilities for designing carbon nanomaterials with complex magnetic ground states.

Observation of Zero-Energy Modes with Possible Time-Reversal Symmetry Breaking on Step Edge of CaKFe4As4

Abstract Topologically nontrivial Fe-based superconductors attract extensive attentions due to their ability of hosting Majorana zero modes (MZMs) which could be used for topological quantum computation. Topological defects such as vortex lines are required to generate MZMs. Here, we observe the robust edge states along the surface steps of CaKFe4As4. Remarkably, the tunneling spectra show a sharp zero-bias peak (ZBP) with multiple integer-quantized states at the step edge under zero magnetic field. We propose that the increasing hole doping around step edges may drive the local superconductivity into a state with possible spontaneous time-reversal symmetry breaking. Consequently, the ZBP can be interpreted as an MZM in an effective vortex in the superconducting topological surface state by proximity to the center of a tri-junction with different superconducting order parameters. Our results provide new insights into the interplay between topology and unconventional superconductivity, and pave a new path to generate MZMs without magnetic field.

Signatures of hybridization of multiple Majorana zero modes in a vortex.

Majorana zero modes (MZMs) are emergent zero-energy topological quasiparticles that are their own antiparticles1,2. Detected MZMs are spatially separated and electrically neutral, so producing hybridization between MZMs is extremely challenging in superconductors3,4. Here, we report the magnetic field response of vortex bound states in superconducting topological crystalline insulator SnTe (001) films. Several MZMs were predicted to coexist in a single vortex due to magnetic mirror symmetry. Using a scanning tunnelling microscope equipped with a three-axis vector magnet, we found that the zero-bias peak (ZBP) in a single vortex exhibits an apparent anisotropic response even though the magnetic field is weak. The ZBP can robustly extend a long distance of up to approximately 100 nm at the (001) surface when the magnetic field is parallel to the ( )-type mirror plane, otherwise it displays an asymmetric splitting. Our systematic simulations demonstrate that the anisotropic response cannot be reproduced with trivial ZBPs. Although the different MZMs cannot be directly distinguished due to the limited energy resolution in our experiments, our comparisons between experimental measurements and theoretical simulations strongly support the existence and hybridization of symmetry-protected multiple MZMs. Our work demonstrates a way to hybridize different MZMs by controlling the orientation of themagnetic field and expands the types of MZM available for tuning topological states.

Machine learning detection of Majorana zero modes from zero-bias peak measurements

Machine learning detection of Majorana zero modes from zero-bias peak measurements

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.

Revisit of the anisotropic vortex states of 2H-NbSe2 towards the zero-field limit

We revisited the vortex states of 2H-NbSe2 towards zero fields by a low-temperature scanning tunneling microscope. Fine structures of the anisotropic vortex states were distinguished, one is a spatially non-splitting zero bias peak, and the other is an in-gap conductance anomaly resembling evolved crossing features around the center of the three nearest vortices. Both of them distribute solely along the next nearest neighboring direction of the vortex lattice and become unresolved in much higher magnetic fields, implying an important role played by the vortex–vortex interactions. To clarify these issues, we have studied the intrinsic vortex states of the isolated trapped vortex in zero fields at 0.45 K. It is concluded that the anisotropic zero bias peak is attributed to the superconducting gap anisotropy, and the spatially evolved crossing features are related to the vortex–vortex interaction. The vortex core size under the zero-field limit is determined. These results provide a paradigm for studying the inherent vortex states of type-II superconductors especially based on an isolated vortex.

Signature of correlated electron–hole pair tunneling in multilayer WSe2 at room temperature

Van der Waals (vdW) heterostructures provide a promising platform for high-temperature exciton condensates due to a strong Coulomb interaction, but the fabrication of very clean interface structures with precisely aligned 2D crystals is challenging. Here, we propose that correlated electron–hole pair tunneling can occur at room temperature in a monolithic multilayer WSe2 device with bottom Au contacts. Electron and hole conducting channels separated by an intrinsic, insulating region in the center of the crystal are defined by doping. The monolithic vertical homojunction formed naturally in the bulk vdW crystal provides a defect-free interface structure which shows clear indications of correlated tunneling at room temperature. We interpret zero-bias peaks in the differential conductance curves as a signature of electron–hole pairing when their densities balance. The conductance peak vanishes when the electron and hole densities are unbalanced, which can be controlled by the external electrical field, magnetic field, or temperature. Our results open an opportunity for realization of room-temperature superfluidity in vdW materials with a simple, clean, and effective approach.

Geiger-Mode Operation 4H-SiC Recessed-Window Avalanche Photodiodes Fabricated by N Ion Implantation

In this work, a 4H-SiC n-i-p avalanche photodiode (APD) with n-layer formed by N ion implantation is demonstrated, in which recessed-window structure is used as termination for reducing electrical field crowding effect around the device edge. The APD with 20 μm diameter active region exhibits low dark current of ~5 pA, high gain of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> , zero-bias peak quantum efficiency of 53.8 % at 265 nm. Two-dimensional avalanche photocurrent mapping indicates that uniform gain is realized across the device central region while edge-located premature breakdown is effectively suppressed. Since there is no shading effect of top contact metal, close to 100% percent of fill factor is achieved in the multiplication region. The APD can operate in Geiger mode by using a passive quenching circuit. A room temperature single photon detection capability is obtained at 280 nm, when the dark count rate is ~ 28.8 Hz/μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Electrostatic control of the proximity effect in the bulk of semiconductor-superconductor hybrids

The proximity effect in semiconductor-superconductor nanowires is expected to generate an induced gap in the semiconductor. The magnitude of this induced gap, together with the semiconductor properties like spin-orbit coupling and g-factor, depends on the coupling between the materials. It is predicted that this coupling can be adjusted through the use of electric fields. We study this phenomenon in InSb/Al/Pt hybrids using nonlocal spectroscopy. We show that these hybrids can be tuned such that the semiconductor and superconductor are strongly coupled. In this case, the induced gap is similar to the superconducting gap in the Al/Pt shell and closes only at high magnetic fields. In contrast, the coupling can be suppressed which leads to a strong reduction of the induced gap and critical magnetic field. At the crossover between the strong-coupling and weak-coupling regimes, we observe the closing and reopening of the induced gap in the bulk of a nanowire. Contrary to expectations, it is not accompanied by the formation of zero-bias peaks in the local conductance spectra. As a result, this cannot be attributed conclusively to the anticipated topological phase transition and we discuss possible alternative explanations.

Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires.

We consider a one-dimensional Rashba nanowire in which multiple Andreev bound states in the bulk of the nanowire form an Andreev band. We show that, under certain circumstances, this trivial Andreev band can produce an apparent closing and reopening signature of the bulk band gap in the nonlocal conductance of the nanowire. Furthermore, we show that the existence of the trivial bulk reopening signature in nonlocal conductance is essentially unaffected by the additional presence of trivial zero-bias peaks in the local conductance at either end of the nanowire. The simultaneous occurrence of a trivial bulk reopening signature and zero-bias peaks mimics the basic features required to pass the so-called "topological gap protocol." Our results therefore provide a topologically trivial minimal model by which the applicability of this protocol can be benchmarked.

Steady-state dc transport through an Anderson impurity coupled to leads with spin-orbit coupling

We study the steady-state dc transport characteristics of a system comprised of an interacting quantum dot, modelled as an Anderson impurity, coupled to two metallic non-interacting leads with Rashba SOC, using an interpolative perturbative approach (IPA). The single-particle spectra, current and differential conductance are obtained in weak and strong coupling regimes over a wide range of SOC and bias values. Extensive benchmarking of the IPA validates the method in the linear as well as non-linear response regime. The universal, zero bias ($V_{sd}=0$) peak with a width proportional to the Kondo scale ($T_K$) and two non-universal finite bias peaks around $V_{sd}=\pm U$ in the zero temperature differential conductance show a clear separation with increasing $U$ or increasing SOC. In the strong coupling regime, increasing temperature induces melting of the zero bias peak leading to a crossover from a three-peak conductance to a two-peak conductance. Recent experiments find the emergence of a two-peak structure by increasing SOC at a fixed temperature. Our results appear to provide a qualitative explanation of these observations as a SOC tuned crossover from weak/intermediate to strong coupling, and a simultaneous crossover from low $T/T_K$ to high $T/T_K$ ratio. We also reproduce the experimentally observed temperature dependence of the zero bias conductance.

The magnetic field driven superconductor–metal transition in disordered hole-overdoped cuprates

By solving the Bogoliubov–de Gennes equations for a d-wave superconductor, we explore how the interplay between disorder and the orbital depairing of an external magnetic field influences the superconductor–metal transition of the hole-overdoped cuprates. For highly disordered systems, we find granular Cooper paring to persist above the critical field where the superfluid stiffness goes to zero. We also show that because the vortices are attracted to regions where the superconducting pairing is already weak, the Caroli–de Gennes–Matricon zero-bias peak in the local density of states at the vortex cores disappears already at moderate disorder.

Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks.

Hybrid semiconductor-superconductor devices hold great promise for realizing topological quantum computing with Majorana zero modes1-5. However, multiple claims of Majorana detection, based on either tunnelling6-10 or Coulomb blockade (CB) spectroscopy11,12, remain disputed. Here we devise an experimental protocol that allows us to perform both types of measurement on the same hybrid island by adjusting its charging energy via tunable junctions to the normal leads. This method reduces ambiguities of Majorana detections by checking the consistency between CB spectroscopy and zero-bias peaks in non-blockaded transport. Specifically, we observe junction-dependent, even-odd modulated, single-electron CB peaks in InAs/Al hybrid nanowires without concomitant low-bias peaks in tunnelling spectroscopy. We provide a theoretical interpretation of the experimental observations in terms of low-energy, longitudinally confined island states rather than overlapping Majorana modes. Our results highlight the importance of combined measurements on the same device for the identification of topological Majorana zero modes.

Large Andreev bound state zero-bias peaks in a weakly dissipative environment

We study Andreev bound states in hybrid InAs-Al nanowire devices. The energy of these states can be tuned to zero by gate voltage or magnetic field, revealing large zero bias peaks (ZBPs) near 2e^2/h in tunneling conductance. Probing these large ZBPs using a weakly dissipative lead reveals non-Fermi liquid temperature (T) dependence due to environmental Coulomb blockade (ECB), an interaction effect from the lead acting on the nanowire junction. By increasing T, these large ZBPs either show a height increase or a transition from split peaks to a ZBP, both deviate significantly from non-dissipative devices where a Fermi-liquid T dependence is revealed. Our result demonstrates the competing effect between ECB and thermal broadening on Andreev bound states.

Plateau Regions for Zero-Bias Peaks within 5% of the Quantized Conductance Value 2e^{2}/h.

Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at 2e^{2}/h at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to 2e^{2}/h, mostly within 5% tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Despite the presence of disorder and quantum dots, our result constitutes a step forward toward establishing Majorana zero modes.

Proximity effect and quasi-particle-lifetime effect in ferromagnet/f-wave superconductor junctions

The proximity effect and finite-quasi-particle-lifetime effect in normal metal/insulator/ferromagnet/f-wave superconductor (NM/I/FM/f-wave SC) structures is theoretically investigated by an extended Blonder-Tinkham-Klapwijk approach. Two types of pairings for f-wave are chosen. It is found that due to the proximity effect whether in the case of f1-wave or f2-wave, the conductance spectra exhibit a transition from the “0 state” to “π state” with increasing the ferromagnetic exchange energy. Due to the essential difference between the two pairing potentials of f-wave, the tunneling conductance has a zero-bias peak in NM/I/FM/f1-wave SC junctions while two energy-gap peaks in NM/I/FM/f2-wave SC junctions. Shortening the lifetime of quasi-particle between collisions can suppress the proximity effect and prevent the formation of the Andreev bound states in the junction. These results can be used to determine the pairing symmetry of f-wave and distinguish f1 and f2-wave.

Large zero bias peaks and dips in a four-terminal thin InAs-Al nanowire device

We report electron transport studies of a thin InAs-Al hybrid semiconductor-superconductor nanowire device using a four-terminal design. Compared to previous works, thinner InAs nanowire (diameter less than 40 nm) is expected to reach fewer sub-band regime. The four-terminal device design excludes electrode contact resistance, an unknown value which has inevitably affected previously reported device conductance. Using tunneling spectroscopy, we find large zero-bias peaks (ZBPs) in differential conductance on the order of $2e^2/h$. Investigating the ZBP evolution by sweeping various gate voltages and magnetic field, we find a transition between a zero-bias peak and a zero-bias dip while the zero-bias conductance sticks close to $2e^2/h$. We discuss a topologically trivial interpretation involving disorder, smooth potential variation and quasi-Majorana zero modes.

Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices

Superconducting devices subject to strong charging energy interactions and Coulomb blockade are one of the key elements for the development of nanoelectronics and constitute common building blocks of quantum computation platforms and topological superconducting setups. The study of their transport properties is nontrivial and some of their nonperturbative aspects are hard to capture with the most ordinary techniques. Here we present a matrix product state approach to simulate the real-time dynamics of these systems. We propose a study of their transport based on the analysis of the currents after quantum quenches connecting such devices with external leads. Our method is based on the combination of a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers. In particular, we employ a quasiparticle energy eigenbasis which greatly reduces their entanglement growth and we introduce an auxiliary degree of freedom to encode the device's total charge. This approach allows us to treat nonperturbatively both their charging energy and coupling with external electrodes. We show that our construction is able to describe the Coulomb diamond structure of a superconducting dot with subgap states, including its sequential tunneling and cotunneling features. We also study the conductance zero-bias peaks caused by Majorana modes in a blockaded Kitaev chain and compare our results with common Breit-Wigner predictions.

Nonequilibrium spintronic transport through Kondo impurities

In this work we analyze the nonequilibrium transport through a quantum impurity (quantum dot or molecule) attached to ferromagnetic leads by using a hybrid numerical renormalization group-time-dependent density matrix renormalization group thermofield quench approach.For this, we study the bias dependence of the differential conductance through the system, which shows a finite zero-bias peak, characteristic of the Kondo resonance and reminiscent of the equilibrium local density of states. In the non-equilibrium settings, the resonance in the differential conductance is also found to decrease with increasing the lead spin polarization. The latter induces an effective exchange field that lifts the spin degeneracy of the dot level. Therefore as we demonstrate, the Kondo resonance can be restored by counteracting the exchange field with a finite external magnetic field applied to the system. Finally, we investigate the influence of temperature on the nonequilibrium conductance, focusing on the split Kondo resonance. Our work thus provides an accurate quantitative description of the spin-resolved transport properties relevant for quantum dots and molecules embedded in magnetic tunnel junctions.

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.