We investigate superconductor-insulator quantum phase transitions in ultrathin capacitively coupled superconducting nanowires with proliferating quantum phase slips. We derive a set of coupled Berezinskii-Kosterlitz-Thouless-like renormalization group equations demonstrating that interaction between quantum phase slips in one of the wires gets modified due to the effect of plasma modes propagating in another wire. As a result, the superconductor-insulator phase transition in each of the wires is controlled not only by its own parameters but also by those of the neighboring wire as well as by mutual capacitance. We argue that superconducting nanowires with properly chosen parameters may turn insulating once they are brought sufficiently close to each other.
We investigate the circuit quantum electrodynamics of anharmonic superconducting nanowire oscillators. The sample circuit consists of a capacitively shunted nanowire with a width of about 20 nm and a varying length up to 350 nm, capacitively coupled to an on-chip resonator. By applying microwave pulses we observe Rabi oscillations, measure coherence times and the anharmonicity of the circuit. Despite the very compact design, simple top-down fabrication and high degree of disorder in the oxidized (granular) aluminum material used, we observe lifetimes in the microsecond range.
Signatures of Majorana fermion bound states in one-dimensional topological insulator (TI) nanowires with proximity effect induced superconductivity are studied. The phase diagram and energy spectra are calculated for single TI nanowires and it is shown that the nanowires can be in the topological invariant phases of winding numbers $W=0, \pm 1$, and $\pm 2$ corresponding to the cases with zero, one and two pairs of Majorana fermions in the single TI nanowires. It is also shown that the topological winding numbers, i.e., the numbers of pairs of Majorana fermions in the TI nanowires can be extra…
Clean topological insulators exposed to a magnetic field develop Landau levels accompanied by a nonzero Hall conductivity for the infinite slab geometry. In this work we consider the case of disordered topological insulator nanowires and find, in contrast, that a zero Hall plateau emerges within a broad energy window close to the Dirac point. We numerically calculate the conductance and its distribution for a statistical ensemble of disordered nanowires, and use the conductance fluctuations to study the dependence of the insulating phase on system parameters, such as the nanowire length, disor…
We derive and analyze the effective low-energy theory for interacting electrons in a cylindrical nanowire made of a strong topological insulator. Three different approaches provide a consistent picture for the band structure, where surface states forming inside the bulk gap correspond to one-dimensional bands indexed by total angular momentum. When a half-integer magnetic flux pierces the nanowire, we find a strongly correlated helical Luttinger liquid topologically protected against weak disorder. We describe how transport experiments can detect this state.
The last several years have witnessed the rapid developments in the study and understanding of topological insulators. In this review, after a brief summary of the history of topological insulators, we focus on the recent progress made in transport experiments on topological insulator films and nanowires. Some quantum phenomena, including the weak antilocalization, the Aharonov Bohm effect and the Shubnikov de Haas oscillations, observed in these nanostructures are described. In addition, the electronic transport evidence of the superconducting proximity effect as well as an anomalous resistan…
The momentum and spin of charge carriers in the topological insulators are constrained to be perpendicular to each other due to the strong spin-orbit coupling. We have investigated this unique spin-momentum locking property in Sb2Te3 topological insulator nanowires by injecting spin-polarized electrons through magnetic tunnel junction electrodes. Non-local voltage measurements exhibit a symmetry with respect to the magnetic field applied perpendicular to the nanowire channel, which is remarkably different from that of a non-local measurement in a channel that lacks spin-momentum locking. In st…
Zero bias anomalies in topological nanowires have recently captured significant attention, as they are possible signatures of Majorana modes. Yet there are many other possible origins of zero bias peaks in nanowires, for example, weak localization, Andreev bound states, or the Kondo effect. Here, we discuss observations of differential conductance peaks at zero bias voltage in nonsuperconducting electronic transport through a 3D topological insulator nanowire. The zero bias conductance peaks show logarithmic temperature dependence and often linear splitting with magnetic fields, both of which …
In this paper we consider charge current generated by maintaining a temperature difference over a nanowire at zero voltage bias. For topological insulator nanowires in a perpendicular magnetic field the current can change sign as the temperature of one end is increased. Here we study how this thermoelectric current sign reversal depends on magnetic field and how impurities affect the size of the thermoelectric current. We consider both scalar and magnetic impurities and show that their influence on the current are quite similar, although the magnetic impurities seem to be more effective in red…
Circular photogalvanic currents are a promising new approach for spin-optoelectronics. To date, such currents have only been induced in topological insulator flakes or extended films. It is not clear whether they can be generated in nanodevices. In this paper, we demonstrate the generation of circular photogalvanic currents in $\text{Bi}_2\text{Se}_3$ nanowires. Each nanowire shows topological surface states. Here, we generate and distinguish the different photocurrent contributions via the driving light wave. We separate the circular photogalvanic currents from those due to thermal Seebeck ef…
We analyze the confinement of electronic surface states in a model of a topological insulator nanowire. Spin-momentum locking in the surface states reduces unwanted backscattering in the presence of non-magnetic disorder and is known to counteract localization for certain values of magnetic flux threading the wire. We show that intentional backscattering can be induced for a range of conditions in the presence of a nanowire constriction. We propose a geometry for a nanowire that involves two constrictions and show that these regions form effective barriers that allow for the formation of a qua…
Three-dimensional topological insulator (3D TI) nanowires display various interesting magnetotransport properties that can be attributed to their spin-momentum-locked surface states such as quasiballistic transport and Aharonov-Bohm oscillations. Here, we focus on the transport properties of a 3D TI nanowire with a gated section that forms an electronic Fabry-Pérot (FP) interferometer that can be tuned to act as a surface-state filter or energy barrier. By tuning the carrier density and length of the gated section of the wire, the interference pattern can be controlled and the nanowire can bec…
We investigate the quantum transport properties of surface electrons on a topological insulator Bi2Te3 nanowire in a magnetotransport study. Although the nanowires are synthesized by using a relatively coarse method of electrochemical deposition, clear Aharonov-Bohm oscillations of phases 0 and pi are observed, owing to the highly coherent surface electron channel. The oscillation amplitude exhibits exponential temperature dependence, suggesting that the phase coherence length L_phi is inversely proportional to the temperature, as in quasi-ballistic systems. In addition, a weak antilocalizatio…
We study semiconductor nanowires coupled to a bilayer of a disordered superconductor and a magnetic insulator, motivated by recent experiments reporting possible Majorana-zero-mode signatures in related architectures. Specifically, we pursue a quasiclassical Usadel equation approach that treats superconductivity in the bilayer self-consistently in the presence of spin-orbit scattering, magnetic-impurity scattering, and Zeeman splitting induced by both the magnetic insulator and a supplemental applied field. Within this framework we explore prospects for engineering topological superconductivit…
We theoretically investigate the emergence of Jackiw-Rebbi zero modes and their conductance signature in non-uniform topological insulator nano-wires. We modelled the non-uniform nano-wires as junction between two cylindrical nano-wires with different radius. In the limit of wire length being much larger than its radius, the surface state of the nanowire splits into one dimensional Dirac modes propagating along the axis of the cylinder owing to radial confinement. The sign of the mass gap in each of these Dirac mode is decided by angular momentum quantum number corresponding to the rotational …
In three-dimensional topological insulators (3D TI) nanowires, transport occurs via gapless surface states where the spin is fixed perpendicular to the momentum[1-6]. Carriers encircling the surface thus acquire a πBerry phase, which is predicted to open up a gap in the lowest-energy 1D surface subband. Inserting a magnetic flux (Φ) of h/2e through the nanowire should cancel the Berry phase and restore the gapless 1D mode[7-8]. However, this signature has been missing in transport experiments reported to date[9-11]. Here, we report measurements of mechanically-exfoliated 3D TI nanowires which …
The discovery of two-dimensional gapless Dirac fermions in graphene and topological insulators (TI) has sparked extensive ongoing research toward applications of their unique electronic properties. The gapless surface states in three-dimensional insulators indicate a distinct topological phase of matter with a non-trivial Z2 invariant that can be verified by angle-resolved photoemission spectroscopy or magnetoresistance quantum oscillation. In TI nanowires, the gapless surface states exhibit Aharonov-Bohm (AB) oscillations in conductance, with this quantum interference effect accompanying a ch…
Quantum-phase transitions in two layers of ultrasmall Josephson junctions, coupled capacitively with each other, are investigated. As the interlayer capacitance is increased, the system at zero temperature is found to exhibit an insulator-to-superconductor transition. It is shown that, unlike one-dimensional arrays with a similar coupling configuration, the transition cannot be accounted for exclusively by particle-hole pairs.
A direct signature of electron transport at the metallic surface of a topological insulator is the Aharonov-Bohm oscillation observed in a recent study of Bi_2Se_3 nanowires [Peng et al., Nature Mater. 9, 225 (2010)] where conductance was found to oscillate as a function of magnetic flux $ϕ$ through the wire, with a period of one flux quantum $ϕ_0=h/e$ and maximum conductance at zero flux. This seemingly agrees neither with diffusive theory, which would predict a period of half a flux quantum, nor with ballistic theory, which in the simplest form predicts a period of $ϕ_0$ but a minimum at zer…
In this review, we present a summary of some recent experiments on topological insulators (TIs) and superconducting nanowires and films. Electron-electron interaction (EEI), weak anti-localization (WAL) and anisotropic magneto-resistance (AMR) effect found in TI films by transport measurements are reported. Then, transport properties of superconducting films, bridges and nanowires and proximity effect in non-superconducting nanowires are described. Finally, the interplay between TIs and superconductors (SCs) is also discussed.
Topological insulator nanowires with uniform cross section, combined with a magnetic flux, can host both a perfectly transmitted mode and Majorana zero modes. Here we consider nanowires with rippled surfaces---specifically, wires with a circular cross section with a radius varying along its axis---and calculate their transport properties. At zero doping, chiral symmetry places the clean wires (no impurities) in the AIII symmetry class, which results in a $\mathbb{Z}$ topological classification. A magnetic flux threading the wire tunes between the topologically distinct insulating phases, with …
We report on ambipolar gate-defined quantum dots in silicon on insulator (SOI) nanowires fabricated using a customised complementary metal-oxide-semiconductor (CMOS) process. The ambipolarity was achieved by extending a gate over an intrinsic silicon channel to both highly doped n-type and p-type terminals. We utilise the ability to supply ambipolar carrier reservoirs to the silicon channel to demonstrate an ability to reconfigurably define, with the same electrodes, double quantum dots with either holes or electrons. We use gate-based reflectometry to sense the inter-dot charge transition(IDT…
We validate the linear dispersion relation and resolve the Dirac cone on the surface of a single Bi2Te3 nanowire via a combination of field-effect and magnetoresistance measurements by which we unambiguously prove the topological insulator nature of the nanowire surface states. Moreover we show that the experimentally determined carrier concentration, mobility and cyclotron mass of the surface states are in excellent agreement with relativistic models. Our method provides a facile way to identify topological insulators that too small for angle-resolved photo emission spectroscopy.
We present a theoretical study of a nanowire made of a three-dimensional topological insulator. The bulk topological insulator is described by a continuum-model Hamiltonian, and the cylindrical-nanowire geometry is modelled by a hard-wall boundary condition. We provide the secular equation for the eigenergies of the systems (both for bulk and surface states) and the analytical form of the energy eigenfunctions. We describe how the surface states of the cylinder are modified by finite-size effects. In particular, we provide a $1/R$ expansion for the energy of the surface states up to second ord…
Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip processes replacing the tunneling of Cooper pairs. When the quantum phase-slip amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can…
Two chains of ultrasmall Josephson junctions, coupled capacitively with each other in the two different ways, straight and slanted coupling, are considered. As the coupling capacitance increases, regardless of the coupling scheme, the transport of particle-hole pairs in the system is found to drive the quantum-phase transition at zero temperature, which is a insulator-to-superfluid transition of the particle-hole pairs and belongs to the Berezinskii-Kosterlitz-Thouless universal class. The different underlying transport mechanisms for the two coupling schemes are reflected in the difference be…
Recently, a new quantum phase, the topological insulator, has been vividly investigated in a variety of materials. Its unique bandstructure allows for optical generation and control of spin-polarized currents based on the circular photogalvanic effect. In this paper, we generate and distinguish the different photocurrent contributions via the the polarization of the driving light wave. We discuss the helicity-dependent spin-polarized current and the polarization independent thermoelectric current as spatially resolved maps, focusing on the influence of the topological insulator/metallic contac…
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi2Se3 nanomaterials with a variety of morpholog…
In this chapter we review our work on the theory of quantum transport in topological insulator nanowires. We discuss both normal state properties and superconducting proximity effects, including the effects of magnetic fields and disorder. Throughout we assume that the bulk is insulating and inert, and work with a surface-only theory. The essential transport properties are understood in terms of three special modes: in the normal state, half a flux quantum along the length of the wire induces a perfectly transmitted mode protected by an effective time reversal symmetry; a transverse magnetic f…
Developing a gate-tunable, scalable, and topologically-protectable supercurrent qubit and integrating it into a quantum circuit are crucial for applications in the fields of quantum information technology and topological phenomena. Here we propose that the nano-hybrid supercurrent transistors, a superconducting quantum analogue of a transistor, made of topological insulator nanowire would be a promising platform for unprecedented control of both the supercurrent magnitude and the current-phase relation by applying a voltage on a gate electrode. We believe that our experimental design will help…
We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively-shunted single elements behave as transmon qubits with electrically tunable transition frequencies. Two-element circuits also exhibit transmon-like behavior near zero applied flux, but behave as flux qubits at half the flux quantum, where non-sinusoidal current-phase relations in the elements produce a double-well Josephson potential. These hybrid Josephson elements are promising for applications requiring microwave su…
A theory of self-excitation in the metal-insulator-metal structure doped with metal nanowires is developed for the case where the power is provided by an external source of radio waves. Both the transient stage of self-excitation and the steady-state regime of self-oscillation are analyzed in a fully analytical form. The numerical estimates demonstrate that this effect can be used for diverse practical purposes, in particular, for radio frequency power harvesting. These findings extend the approach developed in nano-optics to the field of electrical engineering.
Confining two dimensional Dirac fermions on the surface of topological insulators has remained an outstanding conceptual challenge. Here we show that Dirac fermion confinement is achievable in topological crystalline insulators (TCI), which host multiple surface Dirac cones depending on the surface termination and the symmetries it preserves. This confinement is most dramatically reflected in the flux dependence of these Dirac states in the nanowire geometry, where different facets connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the <100>…
The discovery of three-dimensional (3D) topological insulators opens a gateway to generate unusual phases and particles made of the helical surface electrons, proposing new applications using unusual spin nature. Demonstration of the helical electron transport is a crucial step to both physics and device applications of topological insulators. Topological insulator nanowires, of which spin-textured surface electrons form 1D band manipulated by enclosed magnetic flux, offer a unique nanoscale platform to realize quantum transport of spin-momentum locking nature. Here, we report an observation o…
Chip-scale integrated light sources are a crucial component in a broad range of photonics applications. III-V semiconductor nanowire emitters have gained attention as a fascinating approach due to their superior material properties, extremely compact size, and the capability to grow directly on lattice-mismatched silicon substrates. Although there have been remarkable advances in nanowire-based emitters, their practical applications are still in the early stages due to the difficulties in integrating nanowire emitters with photonic integrated circuits (PICs). Here, we demonstrate for the first…
We show theoretically that hot-electron nanobolometers consisting of a small piece of normal metal, capacitively coupled to a superconducting antenna through a pair of normal metal--insulator--superconductor (NIS) tunnel junctions may be used as far-infrared photon counters. To make the device most effective at high counting rates, we suggest the use of the bolometer in the simplest configuration, when the NIS tunnel junctions are used as both an electron cooler and thermometer. The absorption of the photon in the normal metal produces a pulse in the electron temperature, which is measured by …
We report on the fabrication and electrical transport properties of superconducting junctions made of β-Ag$_{2}$Se topological insulator (TI) nanowires in contact with Al superconducting electrodes. The temperature dependence of the critical current indicates that the superconducting junction belongs to a short and diffusive junction regime. As a characteristic feature of the narrow junction, the critical current decreases monotonously with increasing magnetic field. The stochastic distribution of the switching current exhibits the macroscopic quantum tunneling behavior, which is robust up to …
Proximity induced superconducting energy gap in the surface states of topological insulators has been predicted to host the much wanted Majorana fermions for fault tolerant quantum computation. Recent theoretically proposed architectures for topological quantum computation via Majoranas are based on large networks of Kitaevs one dimensional quantum wires, which pose a huge experimental challenge in terms of scalability of the current single nanowire based devices. Here, we address this problem by realizing robust superconductivity in junctions of fabricated topological insulator Bi2Se3 nanowir…
We present a theoretical investigation of the surface plasmon (SP) at the interface between topologically non-trivial cylindrical core and topological-trivial surrounding material, from the axion electrodynamics and modified constitutive relations. We find that the topological effect always leads to a red-shift of SP energy, while the energy red-shift decreases monotonically as core diameter decreases. A qualitative picture based on classical perturbation theory is given to explain these phenomena, from which we also infer that in order to enhance the shift, the difference between the inverse …
We report the development of nanowire field-effect transistors featuring an ultra-thin parylene film as a polymer gate insulator. The room temperature, gas-phase deposition of parylene is an attractive alternative to oxide insulators prepared at high temperatures using atomic layer deposition. We discuss our custom-built parylene deposition system, which is designed for reliable and controlled deposition of <100 nm thick parylene films on III-V nanowires standing vertically on a growth substrate or horizontally on a device substrate. The former case gives conformally-coated nanowires, which we…
The critical current of a superconductor can depend on the direction of current flow due to magnetochiral anisotropy when both inversion and time-reversal symmetry are broken, an effect known as the superconducting (SC) diode effect. Here, we consider one-dimensional (1D) systems in which superconductivity is induced via the proximity effect. In both topological insulator and Rashba nanowires, the SC diode effect due to a magnetic field applied along the spin-polarization axis and perpendicular to the nanowire provides a measure of inversion symmetry breaking in the presence of a superconducto…
We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore, it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model sys…
We show that isolated Weyl nodes can arise in a system of parallel topological insulator nano-wires arranged in a honeycomb fashion. This introduces another theoretical example of a topological semi-metal phase with more than one pair of Weyl nodes and due to the simple form of its Hamiltonian it can be used to study various interesting phenomena associated with this phase. Our result emphasizes that depending on the separation of the Weyl nodes a topological electromagnetic response might or might not emerge and two pairs might have overall cancelling contributions to the net anomalous Hall c…
A topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, is shown to realize a one-dimensional topological superconductor with unpaired Majorana fermions localized at both ends. This situation occurs under a wide range of conditions and constitutes what is possibly the most easily accessible physical realization of the elusive Majorana particles in a solid-state system.
Results from transport measurements in individual $W_{x}V_{1-x}O_{2}$ nanowires with varying extents of $W$ doping are presented. An abrupt thermally driven metal-insulator transition (MIT) is observed in these wires and the transition temperature decreases with increasing $W$ content at a pronounced rate of - (48-56) K/$at.%W$, suggesting a significant alteration of the phase diagram from the bulk. These nanowires can also be driven through a voltage-driven MIT and the temperature dependence of the insulator to metal and metal to insulator switchings are studied. While driving from an insulat…
We present an effective low-energy theory of electron-phonon coupling effects for clean cylindrical topological insulator nanowires. Acoustic phonons are modelled by isotropic elastic continuum theory with stress-free boundary conditions. We take into account the deformation potential coupling between phonons and helical surface Dirac fermions, and also include electron-electron interactions within the bosonization approach. For half-integer values of the magnetic flux $Φ_B$ along the wire, the low-energy theory admits an exact solution since a topological protection mechanism then rules out p…
We study the electronic and transport properties of a topological insulator nanowire including selective magnetic doping of its surfaces. We use a model which is appropriate to describe materials like Bi$_2$Se$_3$ within a k.p approximation and consider nanowires with a rectangular geometry. Within this model the magnetic doping at the (111) surfaces induces a Zeeman field which opens a gap at the Dirac cones corresponding to the surface states. For obtaining the transport properties in a two terminal configuration we use a recursive Green function method based on a tight-binding model which i…
Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
KTH Royal Institute of Technology（皇家理工学院）；Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院、内埃尔研究所）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）
Stimulated by the recent realization of three dimensional topological insulator nanowire interfer- ometers, a theoretical analysis of quantum interference effects on the low energy spectrum of Bi2Se3 nanowires is presented. The electronic properties are analyzed in nanowires with circular, square and rectangular cross-sections starting from a continuum three dimensional model with particular emphasis on magnetic and geometrical effects. The theoretical study is based on numerically exact diagonalizations of the discretized model for all the geometries. In the case of the cylindrical wire, an a…
Coupled electron spins in semiconductor double quantum dots hold promise as the basis for solid-state qubits. To date, most experiments have used III-V materials, in which coherence is limited by hyperfine interactions. Ge/Si heterostructure nanowires seem ideally suited to overcome this limitation: the predominance of spin-zero nuclei suppresses the hyperfine interaction and chemical synthesis creates a clean and defect-free system with highly controllable properties. Here we present a top gate-defined double quantum dot based on Ge/Si heterostructure nanowires with fully tunable coupling bet…
We present the first study of superconducting nanowires shunted with an external resistor, geared towards understanding and controlling coherence and dissipation in nanowires. The dynamics is probed by measuring the evolution of the V-I characteristics and the distributions of switching and retrapping currents upon varying the shunt resistor and temperature. Theoretical analysis of the experiments indicates that as the value of the shunt resistance is decreased, the dynamics turns more coherent presumably due to stabilization of phase-slip centers in the wire and furthermore the switching curr…
Incorporating relativistic physics into quantum tunneling can lead to exotic behavior such as perfect transmission via Klein tunneling. Here, we probe the tunneling properties of spin-momentum locked relativistic fermions by designing and implementing a tunneling geometry that utilizes nanowires of the topological Kondo insulator candidate, SmB6. The nanowires are attached to the end of scanning tunneling microscope tips, and used to image the bicollinear stripe spin-order in the antiferromagnet Fe1.03Te with a Neel temperature of ~50 K. The antiferromagnetic stripes become invisible above 10 …
