Superconductor/Semiconductor Devices for Majorana Zero Modes

Majorana zero modes (MZMs) at the boundary of topological superconductors (TSC) have garnered significant attention for their application in quantum computation. In this study, we demonstrate that in heterostructures composed of the one-dimensional (1D) chiral nanowire and a superconductor, structural chirality could induce the spin-triplet-polarized MZMs. Interestingly, the opposite spin-polarized MZMs are robustly localized at the end of nanowire, whose direction depends on the chirality. Furthermore, this spin-triplet polarization gives rise to chirality-dependent spin-polarized local Andreev reflection (LAR) processes at the TSC/normal metal interface, providing a mechanism for detecting MZMs in TSC-based devices. Finally, we also demonstrate that the chirality-dependent spin-polarized MZMs and LAR processes could be realized in the experimentally accessible 1D helical ${\mathrm{NbSe}}_{\text{3}}$ nanowire. Thus, our findings offer insights into the realization and manipulation of MZMs in 1D chiral systems, with implications for spintronic applications in TSC-based devices.

Majorana zero modes in iron-based superconductors

A topological superconducting state can be induced in the surface state of a topological insulator (TI) by way of proximity coupling to a conventional $s$-wave superconductor ($s\ensuremath{-}\mathrm{SC}$). Planar $s\ensuremath{-}\mathrm{SC}/\mathrm{TI}$ junction structures were proposed as a scalable platform for controlled generation and manipulation of Majorana zero mode (MZM), which holds intriguing promise for fault-tolerant quantum computing. Despite intensive research efforts, the presence of MZM has not been definitively demonstrated in $s\ensuremath{-}\mathrm{SC}/\mathrm{TI}/s\ensuremath{-}\mathrm{SC}$ lateral junctions. A key factor is a lack of direct measurement and quantitative understanding of the proximity coupling between the $s\ensuremath{-}\mathrm{SC}$ and TI. Here we report evidence for strong superconducting proximity effect between a three-dimensional strong TI and Al, a conventional $s\ensuremath{-}\mathrm{SC}$ with minimal intrinsic spin-orbit coupling, in the form of pronounced enhancement of the in-plane critical field (${H}_{c||}$) of the thin Al. Specifically, the ${H}_{c||}$ of a 6-nm-thick Al film deposited on a TI is found to be 2.7 times its Pauli limit and about three times that of a simultaneously deposited reference film on $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_{2}$. The analysis of the ${H}_{c||}$ enhancement within the Maki theory indicates significant induced spin-orbit interaction in the Al due to electronic coupling to the TI. Our results revealed a pathway for producing SC/TI devices of high interfacial electrical transparency conducive for MZM generation and manipulation.

Recent experimental progress introduced devices that can combine topological superconductivity with Coulomb-blockade effects. Experiments with these devices have already provided additional evidence for Majorana zero modes in proximity-coupled semiconductor wires. They also stimulated numerous ideas for how to exploit interactions between Majorana zero modes generated by Coulomb charging effects in networks of Majorana wires. Coulomb effects promise to become a powerful tool in the quest for a topological quantum computer as well as for driving topological superconductors into topologically ordered insulating states. Here, we present a focused review of these recent developments, including discussions of recent experiments, designs of topological qubits, Majorana-based implementations of universal quantum computation, and topological quantum error correction. Motivated by the analogy between a qubit and a spin-1/2 degree of freedom, we also review how coupling between Cooper-pair boxes leads to emergent topologically ordered insulating phases.

We propose a systematic magnetic-flux-free approach to detect, manipulate, and braid Majorana fermions in a semiconductor-nanowire-based topological Josephson junction by utilizing the Majorana spin degree of freedom. We find an intrinsic $\ensuremath{\pi}$-phase difference between spin-triplet pairings enforced by the Majorana zero modes (MZMs) at the two ends of a one-dimensional spinful topological superconductor. This $\ensuremath{\pi}$ phase is identified to be a spin-dependent superconducting phase, referred to as the spin phase, which we show to be tunable by controlling spin-orbit coupling strength via electric gates. This electric controllable spin phase not only affects the coupling energy between MZMs but also leads to a fractional Josephson effect in the absence of any applied magnetic flux, which enables the efficient topological qubit readout. We thus propose an all-electrically controlled superconductor-semiconductor hybrid circuit to manipulate MZMs and to detect their non-Abelian braiding statistics properties. Our work on spin properties of topological Josephson effects potentially opens up a new thrust for spintronic applications with Majorana-based semiconductor quantum circuits.

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely, charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.

The ability to detect single photons has become increasingly essential due to the rise of photon-based quantum computing. In this theoretical work, we propose a system consisting of a quantum dot (QD) side-coupled to a superconducting nanowire. The coupling opens a gap in both the QD mode and the Majorana zero mode (MZM) at the nanowire edge, enabling photon absorption in the system. We show that the absorbed photoelectron decays via rapid (subnanosecond to nanosecond) nonradiative heat transfer to the nanowire phonon modes rather than by spontaneous emission. Furthermore, we calculate the temperature increase and associated resistance increase induced by the absorption of a photon for a given appropriate set of material and environmental parameters, yielding a temperature increase in the millikelvin range and a resistance increase in the kiloohm range, vastly exceeding the photon-absorption-induced temperature and resistance increases for competing 2D-3D hybrid systems by 5 and 9 orders of magnitude, respectively. Last, we determine the detector efficiency and discuss the system density required for deterministic photon number measurement, demonstrating that a photon absorption probability of over 99.9 percent can be achieved for an integrated system consisting of an array of nanowire-QD complexes on-chip inside a cavity. Our results thus provide a basis for a deterministic microwave photon number detector with an unprecedented photon-number-detection resolution.

A Majorana Fermion (MF), defined as a particle that is its own anti-particle, can be engineered in the form of quasi-particles appearing in condensed matter systems. Majorana zero modes (MZMs), topologically protected zero-energy states, can exist at the topological phase boundary of one- or two-dimensional systems. These MZMs follow non-Abelian statistics and can be used as a building block for fault-tolerant quantum computers. Here, we introduce the conceptual development of MZMs based on Kitaev’s chain model and give a brief history of the experimental realization of MZMs.

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.

In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Mapping Pauli's spin operators of transverse Ising chain to spinless fermionic creation and annihilation operators by Inverse Jordan-Wigner transformation leads to a Hamiltonian form closely related to Kitaev Chain, which exhibits topological phase transition where phases are characterized by different topological invariant that changes discontinuously at the transition point. Kitaev Chain supports two Majorana zero modes (MZMs) in the non-trivial topological phase, while none is in the trivial phase. The doubly degenerate ground state of the transverse Ising in ferromagnetic phase corresponds to non-local free fermion degree made from MZMs. The quasi-particle excitations of Ising chain, viz., domain wall formation in the ferromagnetic phase and spin-flip in paramagnetic phase maps to Bogoliubon excitations. The mapping suggests that a non-local order parameter can be defined for Kitaev Chain to work with the usual paradigm of Landau's theory.

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.

Single-crystal indium antimony (InSb) nanowire was fabricated into middle-infrared photodetectors based on a metal–semiconductor-metal (M-S-M) structure. The InSb nanowires were synthesized using an electrochemical method at room temperature. The characteristics of the FET reveal an electron concentration of 3.6 × 1017 cm−3 and an electron mobility of 215.25 cm2 V−1 s−1. The photodetectors exhibit good photoconductive performance, excellent stability, reproducibility, superior responsivity (8.4 × 104 A W−1), and quantum efficiency (1.96 × 106%). These superior properties are attributed to the high surface-to-volume ratio and single-crystal 1D nanostructure of photodetectors that significantly reduce the scattering, trapping, and the transit time between the electrodes during the transport process. Furthermore, the M-S-M structure can effectively enhance space charge effect by the formation of the Schottky contacts, which significantly assists with the electron injection and photocurrent gain.

Majorana zero-modes-a type of localized quasiparticle-hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance. The height of the Majorana zero-bias peak is predicted to be quantized at the universal conductance value of 2e2/h at zero temperature (where e is the charge of an electron and h is the Planck constant), as a direct consequence of the famous Majorana symmetry in which a particle is its own antiparticle. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. Previous experiments, however, have mostly shown zero-bias peaks much smaller than 2e2/h, with a recent observation of a peak height close to 2e2/h. Here we report a quantized conductance plateau at 2e2/h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing.

ABSTRACTThere have been reports of improvements in the thermoelectric figure of merit through the use of nanostructured materials to suppress the lattice thermal conductivity. Here, we report on a fundamental study of the combined effects of defect planes and surface scattering on phonon transport and thermoelectric properties of defect-engineered InAs nanowires. A microfabricated device is employed to measure the thermal conductivity and thermopower of individual suspended indium arsenide nanowires grown by metal organic vapor phase epitaxy. The four-probe measurement device consists of platinum resistance thermometers and electrodes patterned on two adjacent SiNx membranes. A nanowire was suspended between the two membranes, and electrical contact between the nanowire and the platinum electrodes was made with the evaporation of a Ni/Pd film through a shadow mask. The exposed back side of the device substrate allows for characterization of the crystal structure of the suspended nanowire with transmission electron microscopy (TEM) following measurement. The 100-200 nm diameter zincblende (ZB) InAs nanowire samples were grown with randomly spaced twin defects, stacking faults, or phases boundaries perpendicular to the nanowire growth direction, as revealed by transmission electron microscopy (TEM) analysis. Compared to single-crystal ZB InAs nanowires with a similar lateral dimension, the thermal conductivity of the defect-engineered nanowires is reduced by fifty percent at room temperature.

Owing to the unique properties of nitride material system (binary and ternary alloys of In, Al, and Ga with N) like bandgap spanning the whole solar spectrum (InN = 0.7 eV, AlN = 6.2 eV), high saturation velocity, and high breakdown electric field, nanostructures and nanodevices made from Gallium Nitride and related materials have great potential to be the used for realizing next generation of efficient nanoscale UV/visible light emitters, detectors, and high temperature electronic devices. Developing integrated devices and systems from these nanowires would yield more efficient sensors, light emitters, detectors, and ultrahigh density data storage systems. Nanostructures are also a great vehicle for studying fundamental transport properties in mesoscopic material systems. Although, few results of individual GaN nanowire devices has been reported so far (1)-(2), but most of these often involve fabrication processes unsuitable for large scale nanosystems development. True potentials of these nanostructures will be realized only through large scale self assembling technique which will eliminate the need for individual nanowire manipulation. In this work we have demonstrated nanoscale GaN device structures made from GaN nanowires utilizing both conventional optical lithography and electric field assisted aligning to achieve large scale functional nanowire networks. The GaN nanowires were grown by direct reaction of Ga and NH3 and had diameters ranging from 100 nm to 250 nm and lengths up to 200 µm. A conventional furnace results in a growth matrix which is collected from the growth chamber. This matrix contains single crystal GaN nanowires and platelets as shown in Fig. 1. After the growth, the growth matrix is sonicated in Isopropanol. The solution is then dispersed on to a prepatterned SiO2 coated Si substrates with Ti/Al/Ti pads already fabricated on them. Square waves of varying peak to peak voltage and frequency was applied during the dispersion. After the solvent dries out it was observed that these nanowires align themselves in response to the electric field following the field lines between the two metal pads. It was also noted that the degree of alignment is dependent on the frequency and peak to peak voltage of the ac signal applied. It was observed that the nanowires align best at 1 KHz as shown in Fig. 2 (a)-(b). After alignment, the sample is annealed at 750 °C for 30 sec in UHP argon. This ensures the contact pads react with the nanowires forming mechanically stable ohmic contacts. I-V characteristics of the aligned nanowires are measured using the prepatterned pads and shown in Fig. 3. This eliminates the need for further processing and results in a functional network which can be used for applications like sensors and light emitting arrays. We have also assembled nanowires of different material system like GaN and InN on the same substrate to give rise to hybrid integration.