Topological Nanowires Research Articles

Manipulation of Helicity-Dependent Photocurrent and Stokes Parameter Detection in Topological Insulator Bi2Te3 Nanowires.

Helicity-dependent photocurrent (HDPC) and its modulation in topological insulator Bi2Te3 nanowires have been investigated. It is revealed that when the incident plane of a laser is perpendicular to the nanowire, the HDPC is an odd function of the incident angle, which is mainly contributed by the circular photogalvanic effect originating from the surface states of Bi2Te3 nanowire. When the incident plane of a laser is parallel to the nanowire, the HDPC is approximately an even function of the incident angle, which is due to the circular photon drag effect coming from the surface states. It is found that the HDPC can be effectively tuned by the back gate and the ionic liquid top gate. By analyzing the substrate dependence of the HDPC, we find that the HDPC of the Bi2Te3 nanowire on the Si substrate is an order of magnitude larger than that on SiO2, which may be due to the spin injection from the Si substrate to the Bi2Te3 nanowire. In addition, by applying different biases, the Stokes parameters of a polarized light can be extracted by arithmetic operation of the photocurrents measured in the Bi2Te3 nanowire. This work suggests that topological insulator Bi2Te3 nanowires may provide a good platform for opto-spintronic devices, especially in chirality and polarimtry detection.

Spectral and Transport Properties of Andreev Molecule Coupled to Majorana Wire

AbstractThe quasiparticle spectrum and transport properties of the double quantum dot (DQD) deposited on a superconducting substrate (Andreev molecule) and side‐coupled to a nanowire hosting Majorana zero modes (MZMs) are studied. Placing a DQD on the superconducting substrate induces the trivial Andreev‐bound states (ABSs) in quantum dots. However, coupling of DQD with a nanowire causes the leakage of the MZM from the topological nanowire into quantum dots. The relationship between the Andreev states and the Majorana mode for different values of the coupling parameters is analyzed. Additionally, it is shown that the connection point of a metallic tip, treated as an scanning tunneling microscope (STM) tip, affects the measured results of the differential conductance.

Nonlinear Seebeck and Peltier effects in a Majorana nanowire coupled to leads

Abstract We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states (MBSs) at its two ends, a system named as Majorana nanowire (MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient (thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference.

Density Functional Theory Study of the Spin-Orbit Insulating Phase in SnTe Cubic Nanowires: Implications for Topological Electronics.

We investigate the electronic, structural, and topological properties of the SnTe and PbTe cubic nanowires using ab initio calculations. Using standard and linear-scale density functional theory, we go from the ultrathin limit up to the nanowire thicknesses observed experimentally. Finite-size effects in the ultrathin limit produce an electric quadrupole and associated structural distortions; these distortions increase the band gap, but they get reduced with the size of the nanowires and become less and less relevant. Ultrathin SnTe cubic nanowires are trivial band gap insulators; we demonstrate that by increasing the thickness, there is an electronic transition to a spin-orbit insulating phase due to trivial surface states in the regime of thin nanowires. These trivial surface states with a spin-orbit gap of a few meV appear at the same k-point of the topological surface states. Going to the limit of thick nanowires, we should observe the transition to the topological crystalline insulator phase with the presence of two massive surface Dirac fermions hybridized with the persistent trivial surface states. Therefore, we have the copresence of massive Dirac surface states and trivial surface states close to the Fermi level in the same region of the k-space. According to our estimation, the cubic SnTe nanowires are trivial insulators below the critical thickness tc1 = 10 nm, and they become spin-orbit insulators between tc1 = 10 nm and tc2 = 17 nm, while they transit to the topological phase above the critical thickness of tc2 = 17 nm. These critical thickness values are in the range of typical experimental thicknesses, making the thickness a relevant parameter for the synthesis of topological cubic nanowires. Pb1-xSnxTe nanowires would have both these critical thicknesses tc1 and tc2 at larger values depending on the doping concentration. We discuss the limitations of density functional theory in the context of topological nanowires and the consequences of our results on topological electronics.

Effect of bending deformation on suspended topological insulator nanowires: Towards a topological insulator based NEM switch

Nanodevices consisting of the suspended and supported parts of topological insulator Bi2Se3 nanowires were fabricated and measured at low and room temperatures. Probing of topological surface states, accompanied by the electrostatic field effect used to dynamically manipulate bending deformation, was carried out to monitor the external strain introduced into the suspended and supported parts within the same Bi2Se3 nanowire. Depending on the device geometry, pure elastic and elastoplastic types of concave deformation, as well as convex buckling deformation, were realized in the suspended parts of the nanowires. For various types of observed deformations, different magnitudes of increase in the Source-Drain resistance of the deformed part compared to the relaxed part of the same devices were determined. All suspended devices exhibit external strain-sensitive Shubnikov-de Haas oscillation frequencies representing the carriers of top and bottom surface states and bulk, whereas, in the case of supported devices, the bottom surface states are masked by a trivial 2DEG. The obtained results may be useful for strain engineering of TI materials, as well as for applications in NEMS and other areas related to suspended nanostructures.

Electric modulation of the Fermi arc spin transport via three-terminal configuration in topological semimetal nanowires

Spin–momentum locking is a key feature of the topological surface state, which plays an important role in spintronics. The electrical detection of current-induced spin polarization protected by the spin–momentum locking in nonmagnetic systems provides a new platform for developing spintronics, while previous studies were mostly based on magnetic materials. In this study, the spin transport measurement of Dirac semimetal Cd3As2 was studied by three-terminal geometry, and a hysteresis loop signal with high resistance and low resistance state was observed. The hysteresis was reversed by reversing the current direction, which illustrates the spin–momentum locking feature of Cd3As2. Furthermore, we realized the on–off states of the spin signals through electric modulation of the Fermi arc via the three-terminal configuration, which enables the great potential of Cd3As2 in spin field-effect transistors.

Gate-switchable SQUID based on Dirac semimetal Cd3As2 nanowires

Topological semimetal nanowires in proximity with $s$-wave superconductors are promising for Majorana-based topological quantum computers. To braid the Majorana modes, an interconnected nanowire network coupled to superconductor islands is required. Here, we have fabricated the nanostructures based on two Dirac semimetal ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ nanowires connected in parallel to form a symmetric superconducting quantum interference device (SQUID). A proximity-induced superconducting state is achieved in the SQUID, and its gate voltage and magnetic field dependence are investigated. It is found that the supercurrent can be switched on/off by modulating the gate voltage, behaving as a supercurrent field-effect transistor. Under an out-of-plane magnetic field, the SQUID shows an anomalous magnetic field -enhanced superconductivity behavior near the Dirac point. An in-plane magnetic field experiment shows a typical $\ensuremath{\pi}$ periodicity of a critical current with the rotation angle. Our work realizes the implementation and characterization of nanowire SQUID structures, which is a significant step toward integrating Dirac semimetal nanowires into scalable superconducting networks for braiding non-Abelian quantum states.

Quantized Spin Pumping in Topological Ferromagnetic-Superconducting Nanowires.

Semiconducting nanowires with strong spin-orbit coupling in the presence of induced superconductivity and ferromagnetism can support Majorana zero modes. We study the pumping due to the precession of the magnetization in single-subband nanowires and show that spin pumping is robustly quantized when the hybrid nanowire is in the topologically nontrivial phase, whereas charge pumping is not quantized. Moreover, there exists one-to-one correspondence between the quantized conductance, entropy change and spin pumping in long topologically nontrivial nanowires but these observables are uncorrelated in the case of accidental zero-energy Andreev bound states in the trivial phase. Thus, we conclude that observation of correlated and quantized peaks in the conductance, entropy change and spin pumping would provide strong evidence of Majorana zero modes, and we elaborate how topological Majorana zero modes can be distinguished from quasi-Majorana modes potentially created by a smooth tunnel barrier at the lead-nanowire interface. Finally, we discuss peculiar interference effects affecting the spin pumping in short nanowires at very low energies.

Josephson dc Current through T-Shaped Double-Quantum-Dots Hybridized to Majorana Nanowires

We study quantum interference effects on Josephson current in T-shaped double quantum dots (TDQDs) with one of them (the central dot) is sandwiched between the left and right topological superconductor nanowires hosting Majorana bound states (MBSs). We find that the current’s magnitude is suppressed by the inter-dot coupling that induces the quantum interference effect, with unchanged jump in the current at particular phase difference between the two nanowires from which the Josephson effect arises. The current remains as a sinusoidal function with respective to the phase difference in the presence of quantum interference effect, but with significant reduction. The central broad peak in the curve of the Josephson current versus the QDs’ levels are split in different ways depending on the configurations of the latter. We also find that the impacts of the non-z-axial direction magnetic field, bending angle between the two nanowires and the direct hybridization amplitude between the MBSs on the current all depend on the arrangement of the QDs’ energy levels.

Topological Metal MoP Nanowire for Interconnect.

The increasing resistance of copper (Cu) interconnects for decreasing dimensions is a major challenge in continued downscaling of integrated circuits beyond the 7nm technology nodeas it leads to unacceptable signal delays and power consumption in computing. The resistivity of Cu increases due to electron scattering at surfaces and grain boundaries at the nanoscale. Topological semimetals, owing to their topologically protected surface states and suppressed electron backscattering, are promising candidates to potentially replace current Cu interconnects. Here,we report the unprecedented resistivity scaling of topological metal molybdenum phosphide (MoP) nanowires, and it is shown that the resistivity values are superior to those of nanoscale Cu interconnects <500nm2 cross-section areas. The cohesive energy of MoP suggests better stability against electromigration, enabling a barrier-free design . MoP nanowires are more resistant to surface oxidation than the 20nm thick Cu. The thermal conductivity of MoP is comparable to those of Ru and Co. Most importantly, it is demonstrated that the dimensional scaling of MoP, in terms of line resistance versus total cross-sectional area, is competitive to those of effective Cu with barrier/liner and barrier-less Ru, suggesting MoP is an attractive alternative for the scaling challenge of Cu interconnects.

Electronic properties of topological rough nanowires for thermoelectrical performance

We study the electronic states in topological nanowires of narrow-gap semiconductors, such as PbTe or SnTe, with rough surfaces, using a continuous two-band model. We calculate the subband structure and identify topological conducting states located at the surface of the nanowire. In addition, a novel approach to study a nanowire with rough surface demonstrates that the topological surface states are mostly confined in the widest areas of the nanowire. This effect leads to a flattening of the subbands, thus raising the effective mass of carriers. Finally, we analyze the thermoelectric properties of the topological nanowires. The reduction of the radius causes a noticeable enhancement of the thermoelectric efficiency due surface phonon scattering, as expected. However, we also observe that the appearance of topological surface states can play a detrimental role, reducing the thermoelectric efficiency. We conclude that, in addition to nanostructuring, the modulation of the radius of the nanowires, which partially suppress the conduction of the surface states, may be a potential strategy to improve the thermoelectric response of narrow-gap semiconductor nanowires.

Signatures of current in a four-terminal topological Josephson junction

The Majorana zero modes (MZMs) can appear at two ends of the topological nanowire. Here we study the signatures of supercurrent in a hybrid four-terminal Josephson junction with topological nanowires, in which the junction is connected with two superconducting electrodes and two normal electrodes. We show the effect of the MZMs on the Josephson current at each terminal. In the case of a pair of well-separated MZMs in all nanowires, a 4π-periodic current can be observed through the normal terminal and a 2π-periodic current through the superconducting terminal when the applied voltage is high enough. We further demonstrate that, as the number of topological nanowires decreases, the characteristic intensity of the 4π periodic current in normal terminal become increasingly blurred. Until there is no MZMs in the junction, the current periodicity of each terminal will become 2π.

Surface-enhanced Raman spectroscopic activity study on topological ZnSe nanostructures

Topological nanomaterials generally exhibit different defect structures, high specific surface areas, and varying bandgaps. These special geometries, energy-level structures, and interfacial interaction properties provide possibilities to explore interesting properties in the surface-enhanced Raman scattering (SERS). Such properties offer unexplored possibilities for exploring interesting physics and materials science in the field of SERS physical property research and further enhancing substrate materials’ SERS activity. In this paper, the ZnSe topological nanowire crystallite structure was grown using the chemical vapor deposition method, twin defects were introduced, and a topological branched structure that caused the corresponding changes in SERS activity was systematically investigated. On topological ZnSe nanowires, rhodamine 6G (R6G), methylene blue (MB), and crystalline violet (CV) molecules were detected using Raman spectroscopy. The Raman signal enhancement of MB on topological branched nanowires was about 1.9 times that of the trunk nanowires. Finally, the national standard measurement of malachite green (MG) content in water bodies were realized. The results suggest that semiconductor ZnSe topographical nanowires are an emerging class of SERS substrates, and a thorough investigation into the relationship between material structure and SERS performance in specific topological regions will provide new evidence for the principle of chemical enhancement of SERS, as well as recommendations for developing precisely functionalized SERS substrate nanomaterials.

Andreev reflection mediated by Majorana zero modes in T-shaped double quantum dots

We theoretically study the Andreev reflection processes in T-shaped double quantum dots (TDQDs) in terms of the nonequilibrium Green’s function technique. It is considered that one of the TDQDs is coupled to the Majorana zero modes (MZMs) prepared at the ends of a topological superconductor nanowire and simultaneously to one metallic and one superconductor lead. Our numerical results show that the in-gap state originated from the proximity effect due to the superconductor lead being sensitive to the existence of MZMs. The local density of states (LDOS) of the spin-up electrons, which are directly coupled to the MZMs, has a Fano antiresonance at the in-gap state. Meanwhile, the local density of the spin-down electrons, which are free from hybridization to the MZMs due to the helical property of the latter, has a Lorentzian resonance at the same state. The differential Andreev conductance of both the spin directions exhibits Fano-type resonance but with different tails’ directions. The in-gap state is also significantly influenced by the energy level and coupling strength of the other side-coupled dot, as well as the MZM–MZM interaction.

Quantum dot scanning tunneling microscopy for Majorana bound states in continuum

We propose a device composed of a quantum dot (QD) connected to a normal metal lead to detect Majorana bound states (MBSs), which are formed at the ends of a topological superconductor nanowire (TSNW) and coupled to the lead with spin-dependent hybridization strengths. The information of the MBSs leaked into the lead is inferred from the spectral function of the QD serving as the tip of a scanning tunneling microscope (STM). It is found that lead–MBSs interaction induces a bound state characterized by an infinitely high peak in the dot’s zero-energy spectral function. The overlap between the two modes of the MBSs turns this bound state into a resonant one, and thus the zero-energy peak is split into three with the height of the central one equaling that in the absence of lead–MBSs coupling. We also find that the MBSs have lower impacts on the additional peak in the dot’s spectral function induced by intradot Coulomb interaction.

Vapor phase synthesis of topological semimetal MoP2 nanowires and their resistivity

Topological semimetals (TSMs) possess topologically protected surface states near the Fermi level with high carrier densities and high mobilities, holding distinct potential for low-dissipation on-chip interconnects that may outperform current copper interconnects for continued dimensional scaling of CMOS technologies. To translate the exotic properties of TSMs into practical interconnects, developments of high precision synthesis for these emergent semimetals are essential. Here, we report the synthesis of TSM molybdenum diphosphide (MoP2) nanowires with controlled dimensions and crystallinity. By varying the growth temperature in chemical vapor depositions (CVD), we achieve polycrystalline MoP2 as well as single-crystalline MoP2−x nanostructures, which are confined in highly anisotropic forms on crystalline substrates with a miscut angle of 1°. The measured metallic properties, such as room temperature resistivity and temperature-dependent resistance, of the synthesized MoP2 nanostructures show promising dimensional effects for interconnect applications, suggesting potential enhancement of topological surface states in electron transport at reduced dimensions. The demonstration of CVD-grown MoP2 nanowires provides opportunities for careful investigations of design rules for TSMs-based nanoscale interconnects.

Nanomolding of topological nanowires

For more than a decade since their experimental confirmation, topological materials have elicited interest from a wide variety of fields due to their unique symmetry-protected electronic states. Given a large number of theoretically predicted topological materials, new strategies are needed to fabricate topological nanomaterials in a high throughput manner in order to identify promising topological candidates for use in functional devices. In this Perspective, we discuss the use of nanomolding to fabricate topological nanowires; nanomolding is a scalable fabrication process in which a bulk polycrystalline feedstock is pressed into a nanostructured mold at an elevated temperature to form nanowires. Unlike traditional top-down and bottom-up fabrication methods, nanomolding requires minimal optimization of experimental parameters and can work on a wide variety of topological compounds, thus enabling high throughput fabrication of topological nanowires. The fabricated nanowires are single crystalline and defect-free and can have high aspect ratios greater than 1000. We also discuss how future developments in nanomolding can lead to new heterostructures, such as superconductor/semiconductor hybrid nanowires, and other nanomaterial shapes, such as plates or ribbons.

Thermoelectric transport in two-terminal topological nodal-line semimetals nanowires

Recently discovered topological nodal-line semimetals (TNLSMs) have received considerable research interest due to their rich physical properties and potential applications. TNLSMs have the particular band structure to lead to many novel properties. Here we theoretically study the thermoelectric transport of a two-terminal pristine TNLSM nanowires and TNLSMs p–n–p junctions. The Seebeck coefficients S c and the thermoelectrical figure of merit ZT are calculated based on the Landauer-Büttiker formula combined with the nonequilibrium Green’s function method. In pristine TNLSM nanowires, we discuss the effect of the magnetic fields φ, the disorder D, the on-site energy µ z , and the mass term m on the thermoelectric coefficient and find that the transport gap can lead to a large S c and ZT. When transmission coefficient jumps from one integer plateau to another, S c and ZT show a series of peaks. The peaks of S c and ZT are determined by the jump of the transmission coefficient plateau and are not associated with the plateau itself. For TNLSMs p–n–p junctions, S c and ZT strongly depend on the parameter ξ of potential well. We can get a large ZT by adjusting the parameter ξ and magnetic field φ. In TNLSMs p–n–p junctions, ZT has the large value and is easily regulated. This setup has promising application prospects as a thermoelectric device.

Diagnosing topological phase transitions in 1D superconductors using Berry singularity markers

In this work I demonstrate how to characterize topological phase transitions in BDI symmetry class superconductors (SCs) in 1D, using the recently introduced approach of Berry singularity markers (BSMs). In particular, I apply the BSM method to the celebrated Kitaev chain model, as well as to a variant of it, which contains both nearest and next nearest neighbor equal spin pairings. Depending on the situation, I identify pairs of external fields which can detect the topological charges of the Berry singularities which are responsible for the various topological phase transitions. These pairs of fields consist of either a flux knob which controls the supercurrent flow through the SC, or, strain, combined with a field which can tune the chemical potential of the system. Employing the present BSM approach appears to be within experimental reach for topological nanowire hybrids.

Spin Seebeck Effect in a Hybridized Quantum-Dot/Majorana-Nanowire With Spin Heat Accumulation

Properties of spin Seebeck effect (SSE) in a quantum dot (QD) connected to a topological superconductor or semiconductor nanowire with strong spin-orbit interaction are theoretically studied by the noneqilibrium Green’s function method combined with Dyson equation technique. At low temperatures, Majorana zero modes (MZMs) are prepared at the ends of topological superconductor or semiconductor nanowire, and are hybridized to the QD with spin-dependent strength. We consider that the QD is coupled to two leads in the presence of spin heat accumulation (SHA), i.e., spin-dependent temperature in the leads. We find that the thermopower is spin-polarized when the hybridization strength between the QD and one mode of the MZMs depends on electron spin direction, and its spin-polarization can be effectively adjusted by changing the magnitude of SHA. By proper variation of the spin-polarization of the QD-MZM hybridization strength, magnitude of the SHA, dot level, or the direct coupling between the MZMs, 100% spin-polarized or pure thermopower can be generated. Our results may find real usage in high efficiency spintronic devices or detection of the MZMs, which are under current extensive study. The present model is within the reach of current nano-technologies and may by used in high efficiency spin caloritronics devices.