Session N22: Superconductivity:Majoranas

Title: Probing the topological character of superconductors via nonlocal Hanbury Brown and Twiss correlations

Abstract: Superconductors can be classified as topological or not based on whether time-reversal symmetry, chiral symmetry, particle-hole symmetry, and spin rotation symmetry in two-dimensional are preserved or not as per ten-fold classification. Further, topological superconductors can also be classified as gapful (chiral, helical) or nodal. Hanbury Brown and Twiss (HBT) correlations and the nonlocal conductance, can be use to probe metal and two-dimensional unconventional superconductors and metal junctions to understand better the pairing of unconventional superconductors. HBT correlations are asymmetric as a function of bias voltage for nontopological, whereas they are symmetric for topological superconductors irrespective of the barrier strength. Topological superconductors are associated with Majorana fermions which are important for topological quantum computation. By distinguishing topological from nontopological superconductors, our study will help search for Majorana fermions, which will aid in designing a topological quantum computer.

    

Kondo effect in a quantum dot embedded between topological superconductors

In this work, we study the quantum transport through a single-level quantum dot in the Kondo regime, coupled to current leads and embedded between two one-dimensional topological superconductors, each hosting Majorana zero modes at their ends. The Kondo effect in the quantum dot is treated by mean-field finite-U auxiliary bosons approximation and solved by using the non-equilibrium Green's function approach. We calculate the density of states as well as the current and the differential conductance through the quantum dot to characterize the interplay between the Kondo resonance and Majorana zero modes. The results reveal that the presence of Majorana zero modes modifies the Kondo resonance exhibiting an anti-resonance structure in the density of states, leading to spin-resolved behavior of the measurable current and differential conductance. Our findings evidence the presence of non-trivial interference phenomena between the Kondo effect and Majorana zero modes. We believe the latter could be helpful to gain a deeper understanding of the behavior of the Kondo effect in connection with Majorana zero modes.

    

Chip-Integrated Vortex-Braiding

Superconducting vortices, in p-wave superconductors, may host non-Abelian Majorana zero-modes. Braiding manipulations of such vortices are considered as “operations” in fault-tolerant quantum computation protocols. Here we present a vortex-control circuit, based on Nb superconducting loops residing below a superconducting flake. Imaging vortices using SQUID-on-Tip (SOT) microscopy demonstrates that well-placed Nb loops can position vortiecies along designated axes with 40nm precision, and ; they can shuttle vortices reliably within a 3 μm range.. Finally, we demonstrate a braiding operation where the system is initialized with two vortices, manipulated to revolve around each other and return to their original positions.

    

Majorana based parity exchange and measurement via quantum dot coupling in planar topological Josephson junctions

Majorana bound states are nucleated in planar topological Josephson junctions when the junction region is permeated by a uniform magnetic flux. Such junctions offer an advantage over traditional wire geometries in that the bound Majorana can be moved along the junction by means of strategically applied biasing voltage or current pulses. In this work, we consider a crossroad of four such planar junctions hosting Majorana bound states that can be coupled to a centrally placed quantum dot. We formulate a scheme to detect the parity of pairs of Majorana shuttled towards the quantum dot as well as to exchange parity between such pairs. We comment on how such schemes can be extended to obtain braiding of Majorana bound states in planar junctions through a series of projective measurements.   

Unequivocal determination of spin-triplet superconductivity using composite rings

Most superconductors are spin-singlet superconductors, such as Nb and cuprates, with Cooper pairs of spin 0. Spin-triplet superconductors with Cooper pairs of spin 1 are rare but essential for the realization of Majorana fermions and the noise-resilient topological quantum computing. The odd-parity of spin-triplet superconductivity, where the sign of gap function reverses upon the inversion of the momentum, or Δk = −Δ−k, can be distinguished from the even-parity of spin-singlet superconductivity via phase-sensitive experiments. The observation of half-integer quantum flux in a composite ring consisting of a single crystal of epitaxial triplet superconductor of interest connected by a singlet s-wave superconductor can unambiguously identify the otherwise elusive spin-triplet superconductor, but such composite rings are very challenging [1]. We have recently successfully fabricated μm-sized composite rings comprising of an epitaxial β-Bi₂Pd segment and Nb in various structures with Nb connecting to different crystalline facets of β-Bi₂Pd. The signature of half-integer quantum flux in the rings with Nb connecting to the opposite β-Bi₂Pd sides unequivocally determines the spin-triplet superconductivity in β-Bi₂Pd [2]. 

[1] V. B. Geshkenbein, A. I. Larkin, and A. Barone, Phys. Rev. B 36, 235 (1987).

[2] Xiaoying Xu, Yufan Li, C. L. Chien, arXiv:2210.08733 (2022).

    

In-situ shadow-wall deposited tin junctions on selective area grown buffered InAs nanowires

Semiconductor nanowires with superconducting shells have been explored widely for studying one-dimensional electron transport and topological effects at cryogenic temperatures. Scalable fabrication of arbitrary designs of such hybrid nanostructures with clean disorder-free interfaces, can prove useful for building the next generation of fault-tolerant quantum hardware. 

In this talk, we demonstrate a completely customizable platform to grow in-plane indium arsenide (InAs) nanowires and subsequently deposit superconductors at predefined positions on the nanowire, without breaking vacuum. The nanowires were grown using chemical beam epitaxy with a selective-area growth (SAG) technique. High aspect ratio dielectric structures that were prefabricated next to the nanowires were used to subsequently shadow-deposit tin (the superconducting shell) at the preferred locations on the nanowire. This enabled the fabrication of high-quality superconductor-semiconductor-superconductor (SNS) junctions with minimal post-processing steps. Transport measurements from the gated SNS devices at millikelvin temperatures demonstrate gate-tunable supercurrent and a clean superconducting gap with a high critical field. This establishes that the in-vacuo method of shadow-depositing superconductors on SAG nanowires as a technique for scalable fabrication of complex hybrid nanostructures, with clean superconductor-semiconductor interfaces. 

    

Superconducting devices based on shadow wall deposited tin on selective area grown buffered InAs nanowires

Clean, disorder free interfaces are one of the key requirements for the unambiguous detection of Majorana zero modes in hybrid semiconductor superconductor systems. To this end, we have recently produced structures where shadow walls were used to deposit tin on selective area grown (SAG) InAs nanowires. In this talk, we present our fabrication techniques for making devices with these InAs/Sn SAG of different geometries. We also present in detail some low temperature characterization results such as gate tunable supercurrent, induced gap, critical magnetic field and 2e-1e charging effect and discuss future potential applications in this material system.   

Hysteretic Supercurrent and Trivial Zero-bias Peaks at Zero External Magnetic Field Due to Stray Fields from Micromagnets in Sn-InSb and Al-InAs Nanowire Junctions

Superconductor-semiconductor-superconductor and superconductor-semiconductor junctions fabricated from InSb and InAs nanowires attract attention in recent years. InSb and InAs nanowires are though to have strong spin orbit interaction and high mobility; coupled with superconductivity, these wires are believed to be appropriate platforms for Majorana bound states. In experiments, specific parameter combinations of chemical potentials and magnetic fields may create states inside superconductor induced gaps. A zero-bias peak of differential conductance sometimes appear, which is a signature of Majorana bound states. In our experiments, we placed micromagnets close to Sn-InSb-Sn junctions and Al-InAs junctions. Magnetized micromagnets produced local magnetic fields penetrating the devices and we observed hysteretic supercurrents in Sn-InSb-Sn junctions and hysteretic Andreev bound states in Al-InAs junctions. At zero external magnetic field and with finite local magnetic fields, zero-bias peaks due to trivial Andreev bound states were observable. The interpretation of our zero-bias data does not require existence of Majorana bound states.

    

Superconductivity in IV-VI/III-V Heterostructures:Tuning Superconductivity via Band Alignment Induced Charge Transfer

Topological superconductivity has been long sought after since it was hypothesized that this state of matter can host Majorana quasi-particles, which could potentially be used for solid-state, fault tolerant quantum computing. One proposed way of realizing this state is via the proximity effect between a superconductor and a semiconductor with strong spin-orbit splitting. In this work, we achieve superconductivity in the IV-VI material, Sn_xIn_1-xTe (SIT), which is interfaced with the III-V semiconductor, InAs_1-ySb_y (IAS). While the overall T_c of SIT decreases when interfaced with IAS, by varying the amount of Sb in the semiconducting layer, we are able to tune the transfer of charge between the two layers, which impacts the critical temperature, T_c, of this system. The Hall Effect becomes nonlinear at high field in SIT on IAS, which is not seen in the control sample without IAS. This is consistent with our hypothesis that charge transfer occurs between the two layers due to band bending. Within this work, T_c between 0.6K and 1.3K has been achieved, while without IAS T_c can exceed 3K. The realization of proximity induced topological superconductivity in this structure will thus require careful control of the band alignment between SIT and IAS, and our work demonstrates that superconductivity in SIT can be readily tuned by small changes in the charge density.

    

Subgap spectroscopy in hybrid nanowires by nm-thick tunnel barriers

Tunneling spectroscopy is a well known technique to measure subgap states in hybrid semiconductor-superconductor nanowires when searching for signatures of Majorana zero modes (MZMs). Currently, semiconductor at the ends of hybrids combined with local gates is generally used as a tunnel barrier in spectroscopy measurememts. Besides the limitation of detecting only the states close to the hybrid ends, such gate-defined tunnel probes have been shown to cause features in subgap spectra that can mimic the signatures of MZMs and additionally complicate measurement interpretations. In this work, we develop an alternative type of tunnel barriers in order to overcome these limitations. After the growth of superconducting Al on a semiconducting InSb nanowire, a precisely controlled in-situ oxidation of Al is performed to yield a nm-thick AlOx layer. In such thin isolating layer, tunnel junctions can be arbitrarily defined at any point along the hybrid region by shadow-wall angle-deposition of normal metal leads. We utilize this and make multiple tunnel probes along single nanowire hybrids. This allows us to successfully detect the subgap spectra at various distances from the hybrid ends and to identify Andreev bound states (ABSs) of various spatial extension residing inside the hybrids.

    

Exploring signatures of Majorana modes in the current-phase relation of S-TI-S Josephson junctions

Majorana bound states (MBS) have been explored as an approach to realizing topologically-protected quantum computing in condensed matter systems. Exhibited in Superconductor-Topological Insulator-Superconductor (S-TI-S) lateral Josephson junctions, it is predicted that MBS are nucleated at the cores of Josephson vortices where the phase difference across the junction is an odd multiple of π. We study the current-phase relation of these junctions, in which a contribution with a 4π-periodic dependence is added due to the presence of MBS. We present experiments designed to probe the current-phase relation of the S-TI-S junction with direct measurements via phase-sensitive Josephson interferometry using a SQUID circuit, and indirectly by transport measurements of the magnetic field dependence of the critical current in asymmetric SQUIDs and Corbino disk junction geometries.   

Quantum dot Josephson junction in a hybrid superconductor-semiconductor transmon device: a novel route for Andreev qubits.

This talk will focus on the physics of a hybrid superconductor-semiconductor transmon device in which the Josephson effect is controlled by a gate-defined quantum dot in an InAs/Al nanowire. Microwave spectroscopy of the transmon's transition spectrum allows us to probe the ground state parity of the quantum dot as a function of gate voltages, external magnetic flux, and magnetic field applied parallel to the nanowire. The measured parity phase diagram is in very good agreement with that predicted by the superconducting single-impurity Anderson model. Interestingly, the quasiparticle dynamics reveal very long parity lifetimes which, together with spin-orbit induced spin splitting of the doublet manifold, hold promise towards realizing Andreev qubits based on superconducting quantum dots.   

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 modes . However, multiple claims of Majorana detection, based on either tunnelling or Coulomb blockade (CB) spectroscopy, 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.   

Time-dependent driving of topological quantum circuits

Time-dependent control of superconducting quantum circuits is a prerequisite for building scalable quantum hardware. The quantum description of these circuits is complicated due to the electromotive force (emf) induced by time-varying magnetic fields. Here, using a perturbative approach, we examine how the emf modifies the fractional Josephson effect between two weakly coupled topological superconductors. We show that, at low frequencies, a time-varying flux introduces a new term that can be probed via charge and current measurements in open-circuit and closed-loop geometries, respectively. This term depends on both the geometry of the circuit and the time-dependent magnetic field. Finally, we generalize to an intermediate frequency regime with numerical methods and study how the supercurrent depends on the induced emf.   

Majorana zero modes in a magnetic and superconducting hybrid vortex

We propose and investigate a new platform for the realization of Majorana zero modes in a thin-film heterostructure composed of an easy-plane ferromagnet and a superconductor with spin-orbit coupling. The system can support an energetically favorable bound state comprising a magnetic vortex and a superconducting vortex. We show that a hybrid vortex thus created can host a robust zero-energy Majorana bound state at its core over a wide range of parameters, with its partner zero mode located at the boundary of a disk-shaped topological region. We identify a novel mechanism underlying the formation of the topological phase that, remarkably, relies on the orbital effect of the magnetization field and not on the usual Zeeman effect. The in-plane components of magnetization couple to electrons as a gauge potential with non-zero curl, thus creating an emergent magnetic field responsible for the gapped topologically non-trivial region surrounding the vortex core. Our construction allows the mobility of magnetic vortices to be imposed on the Majorana zero mode at the core of the superconducting vortex. In addition, the system shows a rich interplay between magnetism and superconductivity which might aid in developing future devices and technologies.