Zero-bias Conductance Peak Research Articles

Differential conductance and shot noise of a graphene quantum dot coupled with Majorana bound states

Zigzag and armchair hexagonal graphene quantum dots (GQDs) are employed as tunneling spectrometers to detect the signature of Majorana bound states (MBSs) located at the ends of a hybrid nanowire-superconductor junction. The formulas of tunneling current and shot noise are derived to exhibit the local and non-local Andreev reflections induced by MBSs. When the energy splitting of MBSs in the nanowire (e M ) is zero, the hybridization of zero-bias state which comes from normal tunneling and MBSs appears in the zigzag hexagonal GQD system. For the armchair hexagonal GQD under the condition e M = 0, the zero-bias conductance peak emerges in the energy gap to show the absolute contribution of MBSs. When e M ≠ 0, the zero-bias conductance peak splits into symmetrically distributed multi-peaks. These signify that the connected MBSs open novel channels for electrons to tunnel through the metallic and semiconducting GQDs. Shot noise is enhanced by MBSs to form different appearances depending on concrete GQDs. The zigzag GQD system always displays sub-Poissonian shot noise, while super-Poissonian shot noise appears in the armchair GQD system due to the coupling of MBSs. We can distinguish the contributions of MBSs from that of normal tunneling electrons by shot noise and Fano factor at low energy region.

Distinguishing Majorana zero modes from impurity states through time-resolved transport

We study time-resolved charge transport in a superconducting nanowire using time-dependent Landauer–Büttiker theory. We find that the steady-state Majorana zero-bias conductance peak emerges transiently accompanied by characteristic oscillations after a bias-voltage quench. These oscillations are suppressed for trivial impurity states (IS) that otherwise show a similar steady-state signal as the Majorana zero mode (MZM). In addition, we find that Andreev bound states or quasi-Majorana states (QMS) in the topologically trivial bulk phase can give rise to a zero-bias conductance peak, also retaining the transient properties of the MZM. Our results imply that (1) time-resolved transport may be used as a probe to distinguish between the topological MZM and trivial IS; and (2) the QMS mimic the transient signatures of the topological MZMs.

Transconductance as a probe of nonlocality of Majorana fermions

Each end of a Kitaev chain in topological phase hosts a Majorana fermion. Zero bias conductance peak is an evidence of Majorana fermion when the two Majorana fermions are decoupled. These two Majorana fermions are separated in space and this nonlocal aspect can be probed when the two are coupled. Crossed Andreev reflection is the evidence of the nonlocality of Majorana fermions. Nonlocality of Majorana fermions has been proposed to be probed by noise measurements since simple conductance measurements cannot probe it due to the almost cancellation of currents from electron tunneling and crossed Andreev reflection. Kitaev ladders on the other hand host subgap Andreev states which can be used to control the relative currents due to crossed Andreev reflection and electron tunneling. We propose to employ Kitaev ladder in series with Kitaev chain and show that the transconductance in this setup can be used as a probe of nonlocality of Majorana fermions by enhancing crossed Andreev reflection over electron tunneling.

Topological properties of multilayers and surface steps in the SnTe material class

Surfaces of multilayer semiconductors typically have regions of atomically flat terraces separated by atom-high steps. Here we investigate the properties of the low-energy states appearing at the surface atomic steps in \snte. We identify the important approximate symmetries and use them to construct relevant topological invariants. We calculate the dependence of mirror- and spin-resolved Chern numbers on the number of layers and show that the step states appear when these invariants are different on the two sides of the step. Moreover, we find that a particle-hole symmetry can protect one-dimensional Weyl points at the steps. Since the local density of states is large at the step the system is susceptible to different types of instabilities, and we consider an easy-axis magnetization as one realistic possibility. We show that magnetic domain walls support low-energy bound states because the regions with opposite magnetization are topologically distinct in the presence of non-symmorphic chiral and mirror symmetries, providing a possible explanation for the zero-bias conductance peak observed in the recent experiment [Mazur et al., Phys. Rev. B 100, 041408(R) (2019)]

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.

Half-integer level shift of vortex bound states in an iron-based superconductor

Vortices in topological superconductors may host Majorana zero modes (MZMs), which have been proposed as the building blocks of fault-tolerant topological quantum computers. Recently, a new single-material platform with the potential for realizing MZMs has been discovered in iron-based superconductors, without involving hybrid semiconductor–superconductor structures. Here, we report a detailed scanning tunnelling spectroscopy study of a FeTe0.55Se0.45 single crystal and show that this material hosts two distinct classes of vortex. These differ by a half-integer level shift in the energy spectra of the vortex bound states. This level shift is directly tied to the presence or absence of a zero-bias conductance peak and also alters the ratios of higher energy levels from integer to half-odd-integer. Our model calculations fully reproduce the spectra of these two types of vortex bound state, suggesting the presence of regions with and without topological surface states, which coexist within the same crystal. Our findings provide strong evidence for the presence of MZMs in FeTe0.55Se0.45 and establish it as an excellent platform for further studies. The authors use STM to show that there are two different classes of zero-bias peak in vortex cores of Fe(Te,Se). One class is topological, one not. These are distinguished by a shift in the energy levels of the excited states.

Anomalous zero bias conductance peaks in a graphene-based ferromagnet/insulator/p-wave superconductor hybrid structure

We theoretically study graphene-based ferromagnet/insulator/p-wave superconductor hybrid structure, where an anomalous zero bias conductance peak (ZBCP) is exhibited. With the exchange field h increased, the zero-bias conductance dips (ZBCDs) for both the px- and py-wave situations develop into ZBCPs at h∕EF>1, which are just contrary to the situation at h∕EF<1. Furthermore, with the enhancement of barrier strength χ, the conversion from the ZBCD to ZBCP is displayed in the region of h∕EF>1 for the px-wave, whereas the sharp ZBCP remains all the time at any h for the py-wave. More interestingly, the zero-bias conductance for the px-wave keeps unchanged upon increasing χ, while for the py-wave, exhibits periodical modulation of χ. The singular features can be used to not only identify the p-wave superconductivity and spin polarization in graphene but also pave the way to a new class of tunable superconducting spintronic devices based on large-scale graphene.

Presence versus absence of end-to-end nonlocal conductance correlations in Majorana nanowires: Majorana bound states versus Andreev bound states

By calculating the differential tunneling conductance spectra from the two ends of a Majorana nanowire with a quantum dot embedded at one end, we establish that a careful examination of the nonlocal correlations of the zero-bias conductance peaks, as measured separately from the two ends of the wire, can distinguish between topological Majorana bound states and trivial Andreev bound states. In particular, there will be identical correlated zero-bias peaks from both ends for Majorana bound states, and thus the presence of correlated zero-bias conductance from the two wire ends could imply the presence of topological Majorana zero modes in the system. On the contrary, there will not be identical correlated zero-bias peaks from both ends for Andreev bound states, so the absence of correlated zero-bias conductance from the two wire ends implies the absence of topological Majorana zero modes in the system. We present detailed results for the calculated conductance, energy spectra, and wave functions for different chemical potentials at the same magnetic field values to motivate end-to-end conductance correlation measurements in Majorana nanowires.

Anomalous zero bias conductance peak in a ferromagnetic graphene junction with d-wave anisotropic superconducting pair symmetry

We theoretically present an anomalous zero bias conductance peak (ZBCP) in graphene junctions with proximity-induced ferromagnetism and d-wave anisotropic superconducting pair symmetry (ASPS) herein. It is revealed that in the thin insulator limit, the ZBCP can be periodically recovered by adjusting the sandwiched insulating barrier strength χ regardless of exchange field h and the phase of the periodical behaviours for h larger than its Fermi energy EF (h &amp;gt; EF) is exactly opposite to that for h &amp;lt; EF. Most interestingly, in the context of h &amp;gt; EF, the periodic oscillation of the nonzero bias conductance located in the ZBCP versus χ, is accompanied by an explicit splitting peak. Moreover, under the situation of the insulator with finite width, the conductance exhibits a stronger damping oscillation with bias voltage eV for any h, which is also accompanied by a splitting ZBCP at h &amp;gt; EF. These singular features originate from ferromagnetic-modulated midgap states characteristic by the relativistic nodal fermions, which confirms the spin polarization and ASPS of the graphene, and thus will be of great interest in the designing and fabrication of graphene superconducting spintronic devices.

Coexistence of induced superconductivity and quantum Hall states in InSb nanosheets

Hybrid superconducting devices based on high-mobility two-dimensional electron gases with strong spin-orbit coupling are considered to offer a flexible and scalable platform for topological quantum computation. Here, we report the realization and electrical characterization of hybrid devices based on high-quality InSb nanosheets and superconducting niobium (Nb) electrodes. In these hybrid devices, we observe gate-tunable proximity-induced supercurrent and multiple Andreev reflections, indicating a transparent Nb-InSb nanosheet interface. The high critical magnetic field of Nb combined with high-mobility InSb nanosheets allows us to exploit the transport properties in the exotic regime where the superconducting proximity effect coexists with the quantum Hall effect. Transport spectroscopy measurements in such a regime reveal an enhancement of the conductance at the quantum Hall plateaus, accompanied by a pronounced zero-bias peak in the differential conductance. We discuss that these features originate from the formation of Andreev edge states at the superconductor-InSb nanosheet interface in the quantum Hall regime. In addition to shedding light on the interplay between superconductivity and quantum Hall effect, our work opens a new possibility to develop hybrid superconducting devices based on 2D semiconductor nanosheets with strong spin-orbit coupling.

Spin-dependent zero-bias peak in a hybrid nanowire-quantum dot system: Distinguishing isolated Majorana fermions from Andreev bound states

Hybrid system composed by a semiconducting nanowire with proximity-induced superconductivity and a quantum dot at the end working as spectrometer was recently used to quantify the so-called degree of Majorana nonlocality [Deng et al., Phys.Rev.B, 98, 085125 (2018)]. Here we demonstrate that spin-resolved density of states of the dot responsible for zero-bias conductance peak strongly depends on the separation between the Majorana bound states (MBSs) and their relative couplings with the dot and investigate how the charging energy affects the spectrum of the system in the distinct scenarios of Majorana nonlocality (topological quality). Our findings suggest that spin-resolved spectroscopy of the local density of states of the dot can be used as a powerful tool for discriminating between different scenarios of the emergence of zero-bias conductance peak.

Concomitant opening of a bulk-gap with an emerging possible Majorana zero mode

Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum. Only under certain experimental parameters, a closing of the superconducting bulk-gap that is followed by its reopening, appears simultaneously with a ZBCP at the edge. Such events suggest the occurrence of a topologically non-trivial phase. Yet, we also find that ZBCPs are observed under different tuning parameters without simultaneous reopening of a bulk-gap. This demonstrates the importance of simultaneous probing of bulk and edge in the identification of Majorana edge-states.

Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor (Li0.84Fe0.16)OHFeSe**Supported by the National Natural Science Foundation of China, the National Key R&D Program of China under Grant Nos 2016YFA0300200, 2017YFA0303004 and 2017YFA0303003, and the Key Research of Frontier Sciences of CAS under Grant No QYZDY-SSW-SLH001.

The Majorana zero mode (MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in (Li0.84Fe0.16)OHFeSe. Here using scanning tunneling spectroscopy, we demonstrate that Majorana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state, and consequently, the conductance at zero bias is quantized as 2e2/h. Our results present a hallmark signature of the MZM in the vortex of an intrinsic topological superconductor, together with its intriguing behavior.

Theory of the spin-filtering effect in ferromagnet/ferromagnetic insulator/superconductor junctions

Although it is well known that the ferromagnetic insulator at the interface of the superconducting junctions works as a spin-filter, its detailed mechanism has not yet been clarified. Here we present a simple factor inducing the spin-filtering effect in ferromagnet/ferromagnetic insulator/superconductor junctions by applying the extended Blonder-Thinkham-Klapwijk theory. From the factor, one can see easily how the spin-filtering effect is induced by the ferromagnetic insulator. Furthermore, it is also shown that the spin-filtering effect can be caused only by ferromagnet without ferromagnetic insulator. As an interesting application, we study the spin-filtering effect for a chiral p-wave superconductor. In ferromagnet/insulator/chiral p-wave superconductor junction, we find that the zero-bias conductance peak is shifted in opposite bias-voltage directions for Stoner model and spin bandwidth asymmetry ferromagents. It is also shown that the additional shift by ferromagnetic insulator may be useful for identifying the dominant mechanism of the Stoner and spin bandwidth asymmetry mixed ferromagnet.

Observation of zero-bias conductance peak in topologically-trivial hybrid superconducting interfaces

Proximity effects between s-wave superconducting thin films and high spin–orbit topological materials are widely studied using the differential conductance spectroscopy technique, mainly to investigate the topological property of the induced superconductivity. However, very little is probed about the influence of above proximity effect on the depairing properties of the proximitized superconducting film. Here, we provide a phenomenological simulation tool to characterize the different pair-breaking mechanisms that exist at such interfaces and show how they affect the differential tunneling conductance response in applied magnetic fields. Importantly, we probe the quasiparticle-tunneling conductance at the hybrid interface and observe conductance peak pinning at zero bias in a larger field range with eventual signs of weak peak splitting. Further, the effect of varying the spin–orbit scattering and the Landé g-factor in tuning the conductance peaks show interesting trends, such as observation of zero bias conductance peak even in a topologically-trivial superconducting state.

Tunneling spectroscopy in normal/ferromagnetic d-wave superconductor silicene junctions

The tunneling conductance in normal/ferromagnetic d-wave superconductor (N/FdS) silicene junction is studied based on Blonder-Tinkham-Klapwijk (BTK) theory. It is demonstrated that the amplitude of the normalized conductance strongly depends on the applied electric field (EZ) and the exchange field(h) in FdS, the crystal orientation of the dS (α) and the relative orientation of EZ and h. When α=π/4, a dip appears in the conductance spectrum at eV=h for 0<lEz−λSO<h with λSO the spin obit coupling term. In the case of lEz−λSO≥h, however, double dips appear at eV=h and eV=lEz−λSO, respectively. When α=0, the zero-bias conductance peak splits into two peaks as increasing h for anti-parallel configuration. Thus, the obtained result can serve as a method to identify the pairing symmetry of FdS.

Point-contact Andreev reflection spectroscopy on the misfit phase superconductors (PbSe)1.12(TaSe2) doped with Cl or Br

We report point-contact Andreev reflection spectroscopy studies on possible topological superconductor candidates Cl- (Br-) doped (${\mathrm{PbSe})}_{1.12}({\mathrm{TaSe}}_{2})$ with superconducting transition temperature ${T}_{c}\ensuremath{\sim}$ 1.2 K. A common double-peak feature is observed for the conductance curves at low temperature in the absence of a zero-bias conductance peak. We analyze conductance curves with the Blonder-Tinkham-Klapwijk model and the extracted superconducting gap follows a typical Bardeen-Cooper-Schrieffer temperature- and field-dependent behavior, with $2{\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{B}{T}_{c}\ensuremath{\approx}3.7$ and 3.8 for Cl and Br doping, respectively. Our results strongly suggest that both Cl- and Br-doped $({\mathrm{PbSe})}_{1.12}({\mathrm{TaSe}}_{2})$ are fully gapped superconductors in an intermediate-coupling regime.

Robust and Clean Majorana Zero Mode in the Vortex Core of High-Temperature Superconductor (Li0.84Fe0.16)OHFeSe

The Majorana fermion, which is its own anti-particle and obeys non-abelian statistics, plays a critical role in topological quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topological superconductor, or at the ends of a nanowire when both superconductivity and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor, due to contamination from impurity states or other closely-packed Caroli-de Gennes-Matricon (CdGM) states, which hampers further manipulations of Majorana fermions. Here using scanning tunneling spectroscopy, we show that a ZBCP well separated from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect free regions of (Li0.84Fe0.16)OHFeSe, which has a superconducting transition temperature of 42 K. Moreover, a Dirac-cone-type surface state is observed by angle-resolved photoemission spectroscopy, and its topological nature is confirmed by band calculations. The observed ZBCP can be naturally attributed to a MZM arising from this chiral topological surface states of a bulk superconductor. (Li0.84Fe0.16)OHFeSe thus provides an ideal platform for studying MZMs and topological quantum computing.

Unconventional order parameter induced by helical chiral molecules adsorbed on a metal proximity coupled to a superconductor

Following our previous results, which provide evidence for the emergence of a chiral p-wave triplet-pairing component in superconducting Nb upon the adsorption of chiral molecules, we turned to investigate whether such an effect can take place in a proximal superconductor consisting of metal on superconductor bilayer. Note that in such proximity systems, correlated electron-hole (Andreev) pairs exist in the normal metal rather than genuine Cooper pairs. To that end, we used scanning tunneling spectroscopy (STS) on thin Au films grown in-situ on NbN (a conventional s-wave superconductor) before and after adsorbing helical chiral, alpha-helix polyalanine molecules. The tunneling spectra measured on the pristine Au surface showed conventional (s-wave like) proximity gaps. However, upon molecules adsorption the spectra significantly changed, all exhibiting a zero-bias conductance peak embedded inside a gap, indicating unconventional superconductivity. The peak reduced with magnetic field but did not split, consistent with equal-spin triplet-pairing p-wave symmetry. In contrast, adsorption of non-helical chiral cysteine molecules did not yield any apparent change in the order parameter, and the tunneling spectra exhibited only gaps free of in-gap structure.

Quasiparticle gaps in multiprobe Majorana nanowires

We theoretically study a spin-orbit-coupled nanowire proximitized by a superconductor in the presence of an externally applied Zeeman field ("Majorana nanowire") with zero-energy Majorana bound states localized at the two ends of the wire when the Zeeman spin splitting is large enough for the system to enter the topological phase. The specific physics of interest in the current work is the effect of having several tunnel probes attached to the wire along its length. Such tunnel probes should allow, as a matter of principle, one to observe both the predicted bulk superconducting gap closing and opening associated with the topological quantum phase transition as well as the Majorana bound states at the wire ends showing up as zero-bias conductance peaks, depending on which probes are used for the tunneling spectroscopy measurement. Because of the possible invasive nature of the tunnel probes, producing local potential fluctuations in the nanowire, we find the physical situation to be quite complex. In particular, depending on the details of the tunnel barrier operational at the probes, the Majorana nanowire could manifest additional low-energy Andreev bound states which will manifest their own almost-zero-bias peaks, complicating the interpretation of the tunneling data in multiprobe Majorana nanowires. We use two complementary microscopic models to simulate the probes, finding that the tunneling conductance spectrum depends rather sensitively on the details of the tunnel barriers at the probes. We apply our general analysis to simulate a recent multiprobe nanowire experiment commenting on the nature of the quasiparticle gaps likely controlling the experimental observations.