States In Nanowires Research Articles

Confined vs. extended Dirac surface states in topological crystalline insulator nanowires

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 \langle 100 \rangle‹100› type display novel Aharonov-Bohm oscillations, while nanowires with the four facets of the \langle 110 \rangle‹110› type such oscillations are absent due to strong confinement of the Dirac states to each facet separately. Our results place TCI nanowires as a versatile platform for confining and manipulating Dirac surface states.

Aprotic Solvent Effect in Preparation of Organo Lead Iodide Perovskite Nanowires by Two-Step Spin-Coating Procedure

Lead-iodide perovskite (CH3NH3PbI3 ≡ MAPbI3) nanowires (NWs) were prepared by a two-step spin-coating technique by modifying one of the perovskite precursors with a small amount of aprotic solvent. In the two-step spin-coating technique, the perovskite precursors are MAI and PbI2. The first MAI powder is dissolved in isopropanol (IPA) to produce an isopropanol-MAI solution, while the second PbI2 is used in N, N-dimethylformamide (DMF) as an aprotic solvent. Here, a small amount of DMF was used with an IPA solution of MAI to grow 1D NWs based on MAPbI3 perovskite. Then, the film was formed directly from the MAPbI3 perovskite nanowires (PNWs) by coating the PbI2 layer with an IPA solution of MAI modified by DMF. The amount of DMF in the MAI/IPA solution was adjusted in the range between 0 and 50 μl. One-dimensional (1D) PNWs (∼100 nm diameter) and three-dimensional (3D) perovskite nanocrystals are compared. The structural and optical properties of the PNWs films are systematically investigated using X-ray diffraction patterns (XRD), scanning electron microscopy images (SEM), UV–vis absorption, and photoluminescence (PL). The result is that the presence of an additional solvent and its optimized amount in the MAI/IPA solution can increase the length and efficiency of charge transfer by facilitating perovskite transformation, as evidenced by the intensity of PL and the formation of a high-quality perovskite film. Compact, hole-free films with low trap states (crystal defects) were obtained. Further investigation of the lead iodide perovskite showed that reducing the dimensionality from 3D to 1D resulted in shorter wavelengths of the absorption edge and the PL peak in both the absorption and PL spectra. The shorter wavelengths indicate more localized exciton states in NWs. Finally, the amplified spontaneous emission (ASE) properties were obtained under picosecond laser excitation and a low ASE threshold was found at 10 and 53 μJ/cm2 for 1D and 3D, respectively, at about 300 nm film thickness.

Spectroscopy of the local density of states in nanowires using integrated quantum dots

In quantum dot (QD) electron transport experiments additional features can appear in the differential conductance $dI/dV$ that do not originate from discrete states in the QD, but rather from a modulation of the density-of-states (DOS) in the leads. These features are particularly pronounced when the leads are strongly confined low dimensional systems, such as in a nanowire (NW) where transport is one-dimensional and quasi-zero dimensional lead-states can emerge. In this paper we study such lead-states in InAs NWs. We use a QD integrated directly into the NW during the epitaxial growth as an energetically and spatially well-defined tunnel probe to perform $dI/dV$ spectroscopy of discrete bound states in the `left' and `right' NW lead segments. By tuning a sidegate in close proximity of one lead segment, we can distinguish transport features related to the modulation in the lead DOS and to excited states in the QD. We implement a non-interacting capacitance model and derive expressions for the slopes of QD and lead resonances that appear in two-dimensional plots of $dI/dV$ as a function of source-drain bias and gate voltage in terms of the different lever arms determined by the capacitive couplings. We discuss how the interplay between the lever arms affect the slopes. We verify our model by numerically calculating the $dI/dV$ using a resonant tunneling model with three non-interacting quantum dots in series. Finally, we used the model to describe the measured $dI/dV$ spectra and extract quantitatively the tunnel couplings of the lead segments. Our results constitute an important step towards a quantitative understanding of normal and superconducting subgap states in hybrid NW devices.

Magnetic field dependence of partially-separated Andreev bound states in semiconductor-superconductor nanowires with finite coherence length

We study numerically and analytically magnetic field dependence of partially separated Andreev bound states (ps-ABSs), which are localized on both sides of hybrid semiconductor-superconductor nanowire, considering the spatial inversion symmetry of proximity-induced pairing potential with finite coherence length and tunnel one. Finite coherence length results in the occurrence of topologically nontrivial regions near the ends of the nanowire, where near-zero energy ps-ABSs are energetically degenerate due to the spatial inversion symmetry. With increasing the applied magnetic field, the degeneracy is lifted by the overlap between the ps-ABSs near the opposite ends of the nanowire, leading to the appearance of a robust near-zero energy Majorana bound state (MBS) localized at both ends and a nanowire bulk-like state. Our findings provide a mechanism for coexisting of near-zero energy ps-ABS and bulk-like state in the nanowire.

Electronic States in Nanowires with Hexagonal Cross-Section

The electron spectrum in a uniform nanowire with a hexagonal cross-section is calculated by means of a numerical diagonalization of the effective-mass Hamiltonian. Two basis sets are utilized. The wave-functions of low-lying states are calculated and visualized. The approach has an advantage over mesh methods based on finite-differences (or finite-elements) schemes: non-physical solutions do not arise. Our scheme can be easily generalized to the case of multi-band (Luttinger or Kane) ${\bf k}\cdot{\bf p}$ Hamiltonians. The external fields (electrical, magnetic or strain) can be consistently introduced into the problem as well.

Complex band-structure analysis and topological physics of Majorana nanowires

We review applications of complex band structure theory to describe Majorana states in nanowires and nanowire junctions. The dimensionality of the considered wires is gradually increased, from strictly 1D to quasi-1D with one and two transverse dimensions. The complex wave number analysis is applied to two main types of Majorana modes: end states in hybrid semiconductor wires and chiral edge states in hybrid wires of quantum-anomalous Hall insulators. In topological NS and NSN junctions with Majorana modes conductance oscillations and spatial distributions of density and current are described. Finally, the optical absorption in finite systems with both types of Majorana modes is considered.

Improving Photovoltaic Performance of ZnO Nanowires Based Colloidal Quantum Dot Solar Cells via SnO2 Passivation Strategy

Colloidal quantum dot solar cells (CQDSCs) based on one-dimensional metal oxide nanowires (NWs) as electron transport layer (ETL) have attracted much attention due to its larger ETL/colloidal quantum dots (CQDs) contact area and longer electron transport length than other structure CQDSCs, such as planar CQDSCs. However, it is known that defect states in NWs would increase the recombination rate because of the high surface area of NWs. Here, the defect species on the ZnO NWs surface which resulted in the surface recombination and SnO2 passivation effects were investigated. Comparing with the solar cells using pristine ZnO NWs, the CQDSCs which based on SnO2 passivated ZnO NWs electrode exhibited a beneficial band alignment to charge separation, and the interfacial recombination at ZnO/CQDs interface was reduced, eventually resulted in a 40% improvement of power conversion efficiency (PCE). Overall, these findings indicate that surface passivation and the reduction of deep level defect in ETLs could contribute to improve the PCE of CQDSCs.

Selective-Area Superconductor Epitaxy to Ballistic Semiconductor Nanowires.

Semiconductor nanowires such as InAs and InSb are promising materials for studying Majorana zero modes and demonstrating non-Abelian particle exchange relevant for topological quantum computing. While evidence for Majorana bound states in nanowires has been shown, the majority of these experiments are marked by significant disorder. In particular, the interfacial inhomogeneity between the superconductor and nanowire is strongly believed to be the main culprit for disorder and the resulting "soft superconducting gap" ubiquitous in tunneling studies of hybrid semiconductor-superconductor systems. Additionally, a lack of ballistic transport in nanowire systems can create bound states that mimic Majorana signatures. We resolve these problems through the development of selective-area epitaxy of Al to InSb nanowires, a technique applicable to other nanowires and superconductors. Epitaxial InSb-Al devices generically possess a hard superconducting gap and demonstrate ballistic 1D superconductivity and near-perfect transmission of supercurrents in the single mode regime, requisites for engineering and controlling 1D topological superconductivity. Additionally, we demonstrate that epitaxial InSb-Al superconducting island devices, the building blocks for Majorana-based quantum computing applications, prepared using selective-area epitaxy can achieve micron-scale ballistic 1D transport. Our results pave the way for the development of networks of ballistic superconducting electronics for quantum device applications.

Controlled Growth of Heterostructured Ga/GaAs Nanowires with Sharp Schottky Barrier

Because of the inevitable Fermi level pinning on surface/interface states of nanowires, achieving high-performance nanowire devices with controllable nanoscale contacts is always challenging but important. Herein, single-crystalline heterostructured Ga/GaAs nanowires with sharp hetero-Schottky interfaces have been successfully synthesized on amorphous substrates by utilizing Au nanoparticles as catalytic seeds via chemical vapor deposition. These nanowires are found to grow with the hemispherical Au7Ga2 catalytic tips following the vapor–liquid–solid mechanism. During the growth, simply by manipulating the source and growth temperatures, the Ga precipitation rate from Au–Ga alloy tips as well as the reaction rate of Ga precipitates with As can be reliably controlled in order to tailor the length (0–170 nm) of Ga nanowire segments obtained in the heterostructure. When configured into field-effect transistors, these Ga/GaAs NWs exhibit the p-type conductivity with a sharp hetero-Schottky barrier of ∼1.0 eV at the atomically connected Ga segment/GaAs NW body interface, in which this barrier height is close to the theoretical difference between the GaAs Fermi level (5.1–5.3 eV) and the Ga work function (∼4.3 eV), suggesting the effective formation of nanoscale contact by minimizing the Fermi level pinning, being advantageous for advanced nanoelectronics.

Distinguishing topological Majorana bound states from trivial Andreev bound states: Proposed tests through differential tunneling conductance spectroscopy

Trivial Andreev bound states arising from chemical potential variations could lead to zero-bias tunneling conductance peaks at finite magnetic fields in class $D$ nanowires, precisely mimicking the predicted zero-bias conductance peaks arising from the topological Majorana bound states. This finding raises a serious question on the efficacy of using zero-bias tunneling conductance peaks, by themselves, as evidence supporting the existence of topological Majorana bound states in nanowires. In the current work, we provide specific experimental protocols for tunneling spectroscopy measure- ments to distinguish between Andreev and Majorana bound states without invoking more demand- ing nonlocal measurements which have not yet been successfully performed in nanowire systems. In particular, we discuss three distinct experimental schemes involving response of the zero-bias peak to local perturbations of the tunnel barrier, overlap of bound states from the wire ends, and most compellingly, introducing a sharp localized potential in the wire itself to perturb the zero-bias tun- neling peaks. We provide extensive numerical simulations clarifying and supporting our theoretical predictions.

Aharonov–Bohm oscillations caused by non-topological surface states in Dirac nanowires

One intriguing fingerprint of surface states in topological insulators is the Aharonov-Bohm effect in magnetoconductivity of nanowires. We show that surface states in nanowires of Dirac materials (bismuth, bismuth antimony, and lead tin chalcogenides) being in non-topological phase, exhibit the same effect as amendment to magnetoconductivity of the bulk states. We consider a simple model of a cylindrical nanowire, which is described by the 3D Dirac equation with a general $T$-invariant boundary condition. The boundary condition is determined by a single phenomenological parameter whose sign defines topological-like and non-topological surface states. The non-topological surface states emerge outside the gap. In longitudinal magnetic field $B$ they lead to Aharonov-Bohm amendment for the density of states and correspondingly for conductivity of the nanowire. The phase of these magnetooscillations increases with $B$ from $\pi$ to $2\pi$.

Quantum Transport and Nano Angle-resolved Photoemission Spectroscopy on the Topological Surface States of Single Sb2Te3 Nanowires.

We report on low-temperature transport and electronic band structure of p-type Sb2Te3 nanowires, grown by chemical vapor deposition. Magnetoresistance measurements unravel quantum interference phenomena, which depend on the cross-sectional dimensions of the nanowires. The observation of periodic Aharonov-Bohm-type oscillations is attributed to transport in topologically protected surface states in the Sb2Te3 nanowires. The study of universal conductance fluctuations demonstrates coherent transport along the Aharonov-Bohm paths encircling the rectangular cross-section of the nanowires. We use nanoscale angle-resolved photoemission spectroscopy on single nanowires (nano-ARPES) to provide direct experimental evidence on the nontrivial topological character of those surface states. The compiled study of the bandstructure and the magnetotransport response unambiguosly points out the presence of topologically protected surface states in the nanowires and their substantial contribution to the quantum transport effects, as well as the hole doping and Fermi velocity among other key issues. The results are consistent with the theoretical description of quantum transport in intrinsically doped quasi-one-dimensional topological insulator nanowires.

Quantum chemical simulations of doped ZnO nanowires for photocatalytic hydrogen generation

Zinc oxide (ZnO) is considered in general as a promising material for solar water splitting. Its wurtzite‐structured bulk samples, however, can be considered as active for photocatalytic applications only under UV irradiation, where they possess ∼1% efficiency of sunlight energy conversion due to their wide band gap (3.4 eV). Although pristine ZnO nanowires (NWs) possess noticeably narrower band gaps than the bulk, the tendency of band gap reduction with increasing NW diameter is insufficient, and further modification is required. We have contributed to filling this gap by performing a series of ab initio calculations on ZnO NWs of different diameters (dNW), which are mono‐doped by metal (Ag) and non‐metal atoms (C, N) or contain oxygen vacancies with varied concentration (∼3 vs. ∼6%). To reproduce qualitatively the energies of one‐electron states of nanowires in our calculations, the hybrid DFT + HF Hamiltonian has been used, based on the PBE0 exchange‐correlation functional. We have analyzed changes in the electronic structure induced in a few defect composition scenarios, showing that, for specific concentrations and locations of the dopants, the optical absorption peak of doped ZnO can be shifted to the visible light range with promising efficiency. In agreement with experimental observation, the most significant results have been achieved for carbon‐doped ZnO nanowires. They possess the highest photocatalytic suitability, since the band gap is reduced in this case down to 2.1–2.2 eV (for nanowire diameters of 2.9–3.5 nm), which corresponds to optimal 15–17% efficiency of solar energy conversion.

Probing variations of the Rashba spin–orbit coupling at the nanometre scale

The Rashba effect as an electrically tunable spin-orbit interaction is the base for a multitude of possible applications such as spin filters, spin transistors, and quantum computing using Majorana states in nanowires. Moreover, this interaction can determine the spin dephasing and antilocalization phenomena in two dimensions. However, the real space pattern of the Rashba parameter has never been probed, albeit it critically influences, e.g., the more robust spin transistors using the spin helix state and the otherwise forbidden electron backscattering in topologically protected channels. Here, we map this pattern down to nanometer length scales by measuring the spin splitting of the lowest Landau level using scanning tunnelling spectroscopy. We reveal strong fluctuations correlated with the local electrostatic potential for an InSb inversion layer with a large Rashba coefficient (~1 eV{\AA}). The novel type of Rashba field mapping enables a more comprehensive understanding of the critical fluctuations, which might be decisive towards robust semiconductor-based spintronic devices.

Nanowire perovskite solar cell.

Organolead iodide perovskite, CH3NH3PbI3, was prepared in the form of nanowire by means of a small quantity of aprotic solvent in two-step spin-coating procedure. One-dimensional nanowire perovskite with the mean diameter of 100 nm showed faster carrier separation in the presence of hole transporting layer and higher lateral conductivity than the three-dimensional nanocuboid crystal. Reduction in dimensionality resulted in the hypsochromic shift of both absorption and fluorescence spectra, indicative of more localized exciton states in nanowires. The best performing device employing nanowire CH3NH3PbI3 delivered photocurrent density of 19.12 mA/cm(2), voltage of 1.052 V, and fill factor of 0.721, leading to a power conversion efficiency (PCE) of 14.71% at standard AM 1.5G solar illumination. A small I-V hysteresis was observed, where a PCE at forward scan was measured to be 85% of the PCE at reverse scan.

Thermoelectrical detection of Majorana states

We discuss the thermoelectrical properties of nanowires hosting Majorana edge states. For a Majorana nanowire directly coupled to two normal reservoirs the thermopower always vanishes regardeless of the value of the Majorana hybridization. This situation changes drastically if we insert a quantum dot. Then, the dot Majorana side coupled system exhibits a different behavior for the thermopower depending on the Majorana hybridization parameter. Thermopower reverses its sign when the half fermionic state is fully developed. As long as the hybridization becomes finite the Seebeck coefficient behaves similarly to a resonant level system. The sign change of the thermopower when Majorana physics takes place and the fact that both, the electrical and thermal conductances reach, their half fermionic value could serve as a proof of the existence of Majorana edge states in nanowires. Finally, we perform some predictions about the gate dependence of the Seebeck coefficient when Kondo correlations are present in the dot.

Analysis of surface states in ZnO nanowire field effect transistors

Nanowires (NWs) have attracted considerable interests for scaled electronic and optoelectronic device applications. However, NW based semiconductor devices normally suffer from surface states due to the existence of dangling bonds or surface reconstruction. Because of their large surface-to-volume ratio, surface states in NWs can easily affect the metallic contacts to NWs and electron transport in NW. Here, we present ZnO NW surface analysis by performing current–voltage characterization on ZnO NW Schottky barrier field effect transistors with different metal contacts (Ti, Al, Au) at both room temperature and cryogenic temperature. Our results show that three metal contacts are all Schottky contacts to ZnO NWs due to surface states. Our further study reveals: (a) the surface states related Schottky barrier height (SBH) can be extracted from a back to back Schottky diodes model and the SBH values are in the range of 0.34–0.37eV for three metal contacts; (b) the trap activation energy determined from the Arrhenius plots of different Schottky metal contacts is in the range of 0.23–0.29eV, which is oxygen vacancies related; and (c) based on the space-charge-limited model, the surface state density of ZnO NW is in the range of 1.04×1010–1.24×1010/cm2.

Two types of topological transitions in finite Majorana wires

Motivated by the recent advances in studying Majorana states in nanowires under conditions of superconducting proximity effect, we address the correspondence between the common topological transition in infinite system and the topological transition of other type that manifests itself in the positions of the poles of the scattering matrices. We establish a universal dependence of the pole positions in the vicinity of the common transition on the parameter controlling the transition, and discuss the manifestations of the pole transitions in the differential conductance.

Influence of scattering processes on electron quantum states in nanowires

In the framework of quantum perturbation theory the self-consistent method of calculation of electron scattering rates in nanowires with the one-dimensional electron gas in the quantum limit is worked out. The developed method allows both the collisional broadening and the quantum correlations between scattering events to be taken into account. It is an alternativeper seto the Fock approximation for the self-energy approach based on Green’s function formalism. However this approach is free of mathematical difficulties typical to the Fock approximation. Moreover, the developed method is simpler than the Fock approximation from the computational point of view. Using the approximation of stable one-particle quantum states it is proved that the electron scattering processes determine the dependence of electron energy versus its wave vector.

Surface states of wurtzite semiconductor nanowires with identical lateral facets: A transfer-matrix approach

The focus of this paper is to investigate systematically surface states of semiconductor nanowires of wurtzite crystals with identical lateral surfaces. We first calculate the surface spectrum of a semi-infinite crystal. Then, using cyclic boundary conditions, we calculate the quantized spectrum of the surface states in nanowires. We find that the spectrum of the nanowire surfaces consists of a number of quantized levels inside the band gap. We further study absorption coefficients due to dipole transitions between the surface states in such nanowires. We demonstrate that such transitions lead to absorption above the fundamental band edge transition. Our calculations also show that the absorption coefficient induced by the transitions between the surface states depends weakly on the light polarization.