4π-Periodic Supercurrent from Surface States in Cd_{3}As_{2} Nanowire-Based Josephson Junctions

Transport Theory for Topological Josephson Junctions with a Majorana Qubit

We construct a semiclassical theory for the transport of topological Josephson junctions starting from a microscopic Hamiltonian that comprehensively includes the interplay among the Majorana qubit, the Josephson phase, and the dissipation process. With the path integral approach, we derive a set of semiclassical equations of motion that can be used to calculate the time evolution of the Josephson phase and the Majorana qubit. In the equations we reveal rich dynamical phenomena such as the qubit-induced charge pumping, the effective spin-orbit torque, and the Gilbert damping. We demonstrate the influence of these dynamical phenomena on the transport signatures of the junction. We apply the theory to study the Shapiro steps of the junction, and find the suppression of the first Shapiro step due to the dynamical feedback of the Majorana qubit.

Evidence of decoupling of surface and bulk states in Dirac semimetal Cd3As2

Dirac semimetals have attracted a great deal of current interests due to their potential applications in topological quantum computing, low-energy electronic devices, and single photon detection in the microwave frequency range. Herein are results from analyzing the low magnetic (B) field weak-antilocalization behaviors in a Dirac semimetal Cd₃As₂thin flake device. At high temperatures, the phase coherence lengthl_ϕfirst increases with decreasing temperature (T) and follows a power law dependence ofl_ϕ∝T^-0.4. Below ∼3 K,l_ϕtends to saturate to a value of ∼180 nm. Another fitting parameterα, which is associated with independent transport channels, displays a logarithmic temperature dependence forT > 3 K, but also tends to saturate below ∼3 K. The saturation value, ∼1.45, is very close to 1.5, indicating three independent electron transport channels, which we interpret as due to decoupling of both the top and bottom surfaces as well as the bulk. This result, to our knowledge, provides first evidence that the surfaces and bulk states can become decoupled in electronic transport in Dirac semimetal Cd₃As₂.

Electrically controlled spin polarized current in Dirac semimetals

We propose a highly tunable [Formula: see text] spin-polarized current generated in a spintronic device based on a Dirac semimetal (DSM) under a magnetic field, which can be achieved merely by controlling electrical parameters, i.e. the gate voltage, the chemical potential in the lead and the coupling strength between the leads and the DSM. These parameters are all related to the special properties of a semimetal. The spin polarized current generated by gate voltage is guaranteed by its semimetallic feature, because of which the density of state vanishes near Dirac nodes. The barrier controlled current results from the different distance of Weyl nodes generated by the Zeeman field. And the coupling strength controlled spin polarized current originates from the surface Fermi arcs. This DSM-based spintronic device is expected to be realized in [Formula: see text] experimentally.

Emergence of topological superconductivity in doped topological Dirac semimetals under symmetry-lowering lattice distortions

Recently, unconventional superconductivity having a zero-bias conductance peak is reported in doped topological Dirac semimetal (DSM) with lattice distortion. Motivated by the experiments, we theoretically study the possible symmetry-lowering lattice distortions and their effects on the emergence of unconventional superconductivity in doped topological DSM. We find four types of symmetry-lowering lattice distortions that reproduce the crystal symmetries relevant to experiments from the group-theoretical analysis. Considering inter-orbital and intra-orbital electron density-density interactions, we calculate superconducting phase diagrams. We find that the lattice distortions can induce unconventional superconductivity hosting gapless surface Andreev bound states (SABS). Depending on the lattice distortions and superconducting pairing interactions, the unconventional inversion-odd-parity superconductivity can be either topological nodal superconductivity hosting a flat SABS or topological crystalline superconductivity hosting a gapless SABS. Remarkably, the lattice distortions increase the superconducting critical temperature, which is consistent with the experiments. Our work opens a pathway to explore and control pressure-induced topological superconductivity in doped topological semimetals.

Intrinsic coupling between spatially-separated surface Fermi-arcs in Weyl orbit quantum Hall states

Topological semimetals hosting bulk Weyl points and surface Fermi-arc states are expected to realize unconventional Weyl orbits, which interconnect two surface Fermi-arc states on opposite sample surfaces under magnetic fields. While the presence of Weyl orbits has been proposed to play a vital role in recent observations of the quantum Hall effect even in three-dimensional topological semimetals, actual spatial distribution of the quantized surface transport has been experimentally elusive. Here, we demonstrate intrinsic coupling between two spatially-separated surface states in the Weyl orbits by measuring a dual-gate device of a Dirac semimetal film. Independent scans of top- and back-gate voltages reveal concomitant modulation of doubly-degenerate quantum Hall states, which is not possible in conventional surface orbits as in topological insulators. Our results evidencing the unique spatial distribution of Weyl orbits provide new opportunities for controlling the novel quantized transport by various means such as external fields and interface engineering.

The spatial distribution of the quantized transport due to the presence of Weyl orbits in topological semimetals remains elusive. Here, the authors report concomitant modulation of doubly-degenerate quantum Hall states, evidencing intrinsic coupling between two spatially separated surface states in the Weyl orbits of a Dirac semimetal film.

Microwave response in a topological superconducting quantum interference device

Photon detection at microwave frequency is of great interest due to its application in quantum computation information science and technology. Herein are results from studying microwave response in a topological superconducting quantum interference device (SQUID) realized in Dirac semimetal Cd₃As₂. The temperature dependence and microwave power dependence of the SQUID junction resistance are studied, from which we obtain an effective temperature at each microwave power level. It is observed the effective temperature increases with the microwave power. This observation of large microwave response may pave the way for single photon detection at the microwave frequency in topological quantum materials.

Topological Transition of Superconductivity in Dirac Semimetal Nanowire Josephson Junctions

We report the topological transition by gate control in a Cd_{3}As_{2} Dirac semimetal nanowire Josephson junction with diameter of about 64 nm. In the electron branch, the quantum confinement effect enforces the surface band into a series of gapped subbands and thus nontopological states. In the hole branch, however, because the hole mean free path is smaller than the nanowire perimeter, the quantum confinement effect is inoperative and the topological property maintained. The superconductivity is enhanced by gate tuning from electron to hole conduction, manifested by a larger critical supercurrent and a larger critical magnetic field, which is attributed to the topological transition from gapped surface subbands to a gapless surface band. The gate-controlled topological transition of superconductivity should be valuable for manipulation of Majorana zero modes, providing a platform for future compatible and scalable design of topological qubits.

Flux Tunable Superconducting Quantum Circuit Based on Weyl Semimetal MoTe2

Weyl semimetals have drawn considerable attention for their exotic topological properties in many research fields. When in combination with s-wave superconductors, the supercurrent can be carried by their topological surface channels, forming junctions mimicking the behavior of Majorana bound states. Here, we present a transmon-like superconducting quantum intereference device (SQUID) consisting of lateral junctions made of Weyl semimetal Td-MoTe₂ and superconducting leads of niobium nitride (NbN). The SQUID is coupled to a readout cavity made of molybdenum rhenium (MoRe), whose response at high power reveals the existence of the constituting Josephson junctions (JJs). The loop geometry of the circuit allows the resonant frequency of the readout cavity to be tuned by the magnetic flux. We demonstrate a JJ made of MoTe₂ and a flux-tunable transmon-like circuit based on Weyl semimetals. Our study provides a platform to utilize topological materials in SQUID-based quantum circuits for potential applications in quantum information processing.

Leakage of Majorana bound states in an inhomogeneous topological nanowire

We present an exact solution of the continuum Bogolyubov-de-Gennes Hamiltonian for Majorana bound states (MBSs) generated in a superconductor-semiconductor hybrid topological nanowire. The full energy spectra that include the band states and in-gap states could be obtained. We show that for relatively short wire length, the zero energy mode could be induced even in the topological trivial regime, which also indicates oscillatory dependence on the chemical potential. With the increase of the Zeeman field, the MBSs are almost fully spin-polarized and do not localize at the wire ends gradually. We also extend our discussion to the property of Majorana modes in an inhomogeneous nanowire, in which a local gate voltage is applied to one end of the nanowire. It is found that the local potential barrier or well could modulate the Majorana energy splitting periodically. The leakage of MBSs to the potential region is exponentially suppressed for the barrier case. A potential well could induce near-zero-energy bound states and these states merge with MBSs, leading to the delocalization of MBSs. In the potential well region, both the spin-up and spin-down components of the trivial states account for a significant proportion, which can be detected experimentally.

Phase Controlled Growth of Cd3As2 Nanowires and Their Negative Photoconductivity

The bottom-up synthesis process often allows the growth of metastable phase nanowires instead of the thermodynamically stable phase. Herein, we synthesized Cd₃As₂ nanowires with a controlled three-dimensional Dirac semimetal phase using a chemical vapor transport method. Three different phases such as the body centered tetragonal (bct), and two metastable primitive tetragonal (P4₂/nbc and P4₂/nmc) phases were identified. The conversion between three phases (bct → P4₂/nbc → P4₂/nmc) was achieved by increasing the growth temperature. The growth direction is [110] for bct and P4₂/nbc and [100] for P4₂/nmc, corresponding to the same crystallographic axis. Field effect transistors and photodetector devices showed the nearly same electrical and photoelectrical properties for three phases. Differential conductance measurement confirms excellent electron mobility (2 × 10⁴ cm²/(V s) at 10 K). Negative photoconductance was first observed, and the photoresponsivity reached 3 × 10⁴ A/W, which is ascribed to the surface defects acting as trap sites for the photogenerated electrons.

Vortex End Majorana Zero Modes in Superconducting Dirac and Weyl Semimetals

Time-reversal invariant Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with s-wave pairing and the doping is lower than a critical level, straight π-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between time-reversal invariant Dirac and Weyl semimetals and Majorana zero modes in vortices.

Topological Semimetal Nanostructures: From Properties to Topotronics

Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.

Induced Topological Superconductivity in a BiSbTeSe2-Based Josephson Junction

A 4 π -periodic supercurrent through a Josephson junction can be a consequence of the presence of Majorana bound states. A systematic study of the radio frequency response for several temperatures and frequencies yields a concrete protocol for examining the 4 π -periodic contribution to the supercurrent. This work also reports the observation of a 4 π -periodic contribution to the supercurrent in BiSbTeSe 2 -based Josephson junctions. As a response to irradiation by radio frequency waves, the junctions showed an absence of the first Shapiro step. At high irradiation power, a qualitative correspondence to a model including a 4 π -periodic component to the supercurrent is found.

Reducing Electronic Transport Dimension to Topological Hinge States by Increasing Geometry Size of Dirac Semimetal Josephson Junctions

The notion of topological phases has been extended to higher-order and has been generalized to different dimensions. As a paradigm, Cd_{3}As_{2} is predicted to be a higher-order topological semimetal, possessing three-dimensional bulk Dirac fermions, two-dimensional Fermi arcs, and one-dimensional hinge states. These topological states have different characteristic length scales in electronic transport, allowing one to distinguish their properties when changing sample size. Here, we report an anomalous dimensional reduction of supercurrent transport by increasing the size of Dirac semimetal Cd_{3}As_{2}-based Josephson junctions. An evolution of the supercurrent quantum interferences from a standard Fraunhofer pattern to a superconducting quantum interference device (SQUID)-like one is observed when the junction channel length is increased. The SQUID-like interference pattern indicates the supercurrent flowing through the 1D hinges. The identification of 1D hinge states should be valuable for deeper understanding of the higher-order topological phase in a 3D Dirac semimetal.

Superconductivity and Shubnikov - de Haas effect in polycrystalline Cd3As2 thin films

In this study we observed the reproducible superconducting state in Cd₃As₂ thin films without any external stimuli. Comparison with our previous results reveals similar qualitative behavior for films synthesized by different methods, while the difference in the values of the critical parameters clearly shows the possibility to control this state. The X-ray diffraction measurements demonstrate the presence of the tetragonal Cd₃As₂ crystal phase in studied films. Measurements of high-field magnetoresistance reveal pronounced Shubnikov - de Haas oscillations. The analysis of these oscillations suggests that, due to high carrier concentration in studied Cd₃As₂ films, the initial Dirac semimetal phase may be partially suppressed, which, however, does not contradict with possible topological nature of the observed superconductivity.

Fermi-arc supercurrent oscillations in Dirac semimetal Josephson junctions

One prominent hallmark of topological semimetals is the existence of unusual topological surface states known as Fermi arcs. Nevertheless, the Fermi-arc superconductivity remains elusive. Here, we report the critical current oscillations from surface Fermi arcs in Nb-Dirac semimetal Cd₃As₂-Nb Josephson junctions. The supercurrent from bulk states are suppressed under an in-plane magnetic field ~0.1 T, while the supercurrent from the topological surface states survives up to 0.5 T. Contrary to the minimum normal-state conductance, the Fermi-arc carried supercurrent shows a maximum critical value near the Dirac point, which is consistent with the fact that the Fermi arcs have maximum density of state at the Dirac point. Moreover, the critical current exhibits periodic oscillations with a parallel magnetic field, which is well understood by considering the in-plane orbital effect from the surface states. Our results suggest the Dirac semimetal combined with superconductivity should be promising for topological quantum devices.

Multifunctional inorganic nanomaterials for energy applications

Our society has been facing more and more serious challenges towards achieving highly efficient utilization of energy. In the field of energy applications, multifunctional nanomaterials have been attracting increasing attention. Various energy applications, such as energy generation, conversion, storage, saving and transmission, are strongly dependent upon the electrical, thermal, mechanical, optical and catalytic functions of materials. In the nanoscale range, thermoelectric, piezoelectric, triboelectric, photovoltaic, catalytic and electrochromic materials have made major contributions to various energy applications. Inorganic nanomaterials' unique properties, such as excellent electrical and thermal conductivity, large surface area and chemical stability, make them highly competitive in energy applications. In this review, the latest research and development of multifunctional inorganic nanomaterials in energy applications were summarized from the perspective of different energy applications. Furthermore, we also illustrated the unique functions of inorganic nanomaterials to improve their performances and the combination of the functions of nanomaterials into a device. However, challenges may be traced back to the limitations set by scaling the relations between multifunctional inorganic nanomaterials and energy devices.