Finite-length Nanowire Research Articles

Editorial: innovative quantum materials

Quantum Materials are materials where the manifestation of the quantum mechanical nature of matter constituents, which comes into evidence at the macroscopic scale, is used to obtain new functionalities. The study of quantum materials is relevant both on the fundamental and on the applied side. Indeed, this class of materials provides a common thread between physics, materials science and engineering. The focus is on emergent excitations, such as Dirac and Majorana fermions. In particular, it analyzes their sensitivity to external perturbations, such as electric and magnetic fields, and boundary conditions that can be controlled by surface/edge terminations, defect states and nanostructuring. The topical issue provides a broad description of innovative quantum materials discussing a variety of different phenomena: (1) interference phenomena in quantum devices made up of a topological insulator, (2) bound states in finite length nanowires with an inhomogeneous spin–orbit coupling profile relevant for Majorana physics, (3) sensitivity of graphene transport properties to defect states and edge functionalization, (4) role of Moiré phonons on the energy properties of twisted bilayer graphene at the magic angle important for van der Waals materials, (5) emergent spin excitations and anisotropic magnetotransport properties in iridates, (6) magnetoelectric couplings and improper magnetoelectric behavior in manganites significant for the realization of novel spintronic devices.

Effects of the electrostatic environment on superlattice Majorana nanowires

Finding ways of creating, measuring and manipulating Majorana bound states (MBSs) in superconducting-semiconducting nanowires is a highly pursued goal in condensed matter physics. It was recently proposed that a periodic covering of the semiconducting nanowire with superconductor fingers would allow both gating and tuning the system into a topological phase while leaving room for a local detection of the MBS wavefunction. We perform a detailed, self-consistent numerical study of a three-dimensional (3D) model for a finite-length nanowire with a superconductor superlattice including the effect of the surrounding electrostatic environment, and taking into account the surface charge created at the semiconductor surface. We consider different experimental scenarios where the superlattice is on top or at the bottom of the nanowire with respect to a back gate. The analysis of the 3D electrostatic profile, the charge density, the low energy spectrum and the formation of MBSs reveals a rich phenomenology that depends on the nanowire parameters as well as on the superlattice dimensions and the external back gate potential. The 3D environment turns out to be essential to correctly capture and understand the phase diagram of the system and the parameter regions where topological superconductivity is established.

Nonequilibrium Green's function study of magnetoconductance features and oscillations in clean and disordered nanowires

We explore various aspects of magneto-conductance oscillations in semiconductor nanowires, developing quantum transport models based on the non-equilibrium Green's function formalism. In the clean case, Aharonov-Bohm (AB - h/e) oscillations are found to be dominant, contingent upon the surface confinement of electrons in the nanowire. We also numerically study disordered nanowires of finite length, bridging a gap in the existing literature. By varying the nanowire length and disorder strength, we identify the transition where Al'tshuler-Aronov-Spivak (AAS - h/2e) oscillations start dominating, noting the effects of considering an open system. Moreover, we demonstrate how the relative magnitudes of the scattering length and the device dimensions govern the relative dominance of these harmonics with energy, revealing that the AAS oscillations emerge and start dominating from the center of the band, much higher in energy than the conduction band-edge. We also show the ways of suppressing the oscillatory components (AB and AAS) to observe the non-oscillatory weak localization corrections, noting the interplay of scattering, incoherence/dephasing, the geometry of electronic distribution, and orientation of magnetic field. This is followed by a study of surface roughness which shows contrasting effects depending on its strength and type, ranging from magnetic depopulation to strong AAS oscillations. Subsequently, we show that dephasing causes a progressive degradation of the higher harmonics, explaining the re-emergence of the AB component even in long and disordered nanowires. Lastly, we show that our model qualitatively reproduces the experimental magneto-conductance spectrum in [Holloway et al, PRB 91, 045422 (2015)] reasonably well while demonstrating the necessity of spatial-correlations in the disorder potential, and dephasing.

On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires

AbstractWe investigate the stability features of steady-states of a two-dimensional system of ferromagnetic nanowires. We constitute a system with the finite number of nanowires arranged on the(e→1,e→2){(\vec{e}_{1},\vec{e}_{2})}plane, where(e→1,e→2,e→3){(\vec{e}_{1},\vec{e}_{2},\vec{e}_{3})}is the canonical basis ofℝ3{\mathbb{R}^{3}}. We consider two cases: in the first case, each nanowire is considered to be of infinite length, whereas in the second case, we deal with finite length nanowires to design the system. In both cases, we establish a sufficient condition under which these steady-states are shown to be exponentially stable.

Integral equation technique for scatterers with mesoscopic insertions: Application to a carbon nanotube

We present the electromagnetic scattering theory for a finite-length nanowire with an embedded mesoscopic object. The theory is based on a synthesis of the integral equation technique of classical electrodynamics and the quantum transport formalism. We formulate Hall\'en-type integral equations, where the canonical integral operators from wire antenna theory are combined with special terms responsible for the mesoscopic structure. The theory is applied to calculate the polarizability of a finite-length single-walled carbon nanotube (CNT) with a short low-conductive section (LCS) in the microwave and subterahertz ranges. The LCS is modeled as a multichannel two-electrode mesoscopic system. The effective resistive sheet impedance boundary conditions for the scattered field are applied on the CNT surface. It is shown that the imaginary part of the polarizability spectrum has three peaks. Two of them are in the terahertz range, while the third is in the gigahertz range. The polarizability spectrum of the CNT with many LCSs has only one gigahertz peak, which shifts to low frequencies as the number of LCSs increases. The physical nature of these peaks is explained, and potential applications of nanoantennas are proposed.

Transmission of Plasmons through a Nanowire

Exact quantitative understanding of plasmon propagation along nanowires is mandatory for designing and creating functional devices. Here we investigate plasmon transmission through top-down fabricated monocrystalline gold nanowires on a glass substrate. We show that the transmission through finite-length nanowires can be described by Fabry-P\'{e}rot oscillations that beat with free-space propagating light launched at the incoupling end. Using an extended Fabry-P\'{e}rot model, experimental and simulated length dependent transmission signals agree quantitatively with a fully analytical model.

Transport through a quantum dot coupled to two Majorana bound states

We investigate electron transport inside a ring system composed of a quantum dot (QD) coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows $2\pi$ periodicity when the two Majorana bound states are nonoverlapping (as in an infinitely long nanowire) but displays $4\pi$ periodicity when the overlapping becomes nonzero (as in a finite length nanowire). We map the model system into a QD--Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.

Stability of Eshelby dislocations in FCC crystalline nanowires

The thermally activated escape of Eshelby dislocations in face-centered-crystal (FCC) nanowires of finite length with surface steps at the ends is investigated by combining atomistic and continuum models. The energy barriers for the dislocation escape from face-centered-cubic 〈110〉 nanowires are predicted from atomistic models as a function of nanowire radius, escape location, and surface step orientation. The dissociation of a dislocation into partials has a significant effect on the energy barrier. The dislocation prefers to escape from the end of nanowire with an extended node, where the dissociation width is greater than the equilibrium width in the bulk. The energy barrier is further lowered if the surface step aligns with the dislocation's slip plane. A continuum line tension model that accounts for partial dislocations is constructed and benchmarked against atomistic predictions for FCC nanowires. The continuum model is then used to make predictions on the stability of Eshelby dislocations over a wide range of nanowire radii.

Ballistic-diffusive heat conduction in multiply-constrained nanostructures

Ballistic-diffusive heat conduction in multiply-constrained nanostructures is theoretically studied based on the phonon Boltzmann transport equation. The results show that different constraints influence the thermal transport in different ways. In the direction parallel to the heat flow, the phonon ballistic transport can cause temperature jumps at the boundaries in contact with the phonon baths. In contrast, for lateral constraint, the heat flux is reduced near the boundaries due to phonon-boundary scattering. A thermal conductivity model for multiply-constrained nanostructures is then derived from the phonon Boltzmann transport equation. The influences of different constraints are combined on the basis of Matthiessen's rule. The model accurately characterizes the thermal conductivities of various typical nanostructures, including nanofilms (in-plane and cross-plane) and finite length nanowires of various cross-sectional shapes (e.g. circular and rectangular). The model predictions also agree well with Monte Carlo simulations and experimental data for silicon nanofilms and nanowires.

Antenna resonances in low aspect ratio semiconductor nanowires.

We present numerical simulations of low aspect ratio gallium phosphide nanowires under plane wave illumination, which reveal the interplay between transverse and longitudinal antenna-like resonances. A comparison to the limiting case of the semiconducting sphere shows a gradual, continuous transition of resonant electric and magnetic spherical Mie modes into Fabry-Pérot cavity modes with mixed electric and magnetic characteristics. As the length of the nanowires further increases, these finite-wire modes converge towards the leaky-mode resonances of an infinite cylindrical wire. Furthermore, we report a large and selective enhancement or suppression of electric and magnetic field in structures comprising two semiconducting nanowires. For an interparticle separation of 20 nm, we observe up to 300-fold enhancement in the electric field intensity and an almost complete quenching of the magnetic field in specific mode configurations. Angle-dependent extinction spectra highlight the importance of symmetry and phase matching in the excitation of cavity modes and show the limited validity of the infinite wire approximation for describing the response of finite length nanowires toward glancing angles.

Robust interface between flying and topological qubits.

Hybrid architectures, consisting of conventional and topological qubits, have recently attracted much attention due to their capability in consolidating robustness of topological qubits and universality of conventional qubits. However, these two kinds of qubits are normally constructed in significantly different energy scales, and thus the energy mismatch is a major obstacle for their coupling, which can support the exchange of quantum information between them. Here we propose a microwave photonic quantum bus for a strong direct coupling between the topological and conventional qubits, where the energy mismatch is compensated by an external driving field. In the framework of tight-binding simulation and perturbation approach, we show that the energy splitting of Majorana fermions in a finite length nanowire, which we use to define topological qubits, is still robust against local perturbations due to the topology of the system. Therefore, the present scheme realizes a rather robust interface between the flying and topological qubits. Finally, we demonstrate that this quantum bus can also be used to generate multipartitie entangled states with the topological qubits.

Standing wave plasmon modes interact in an antenna-coupled nanowire.

In a standing wave optical cavity, the coupling of cavity modes, for example, through a nonlinear medium, results in a rich variety of nonlinear dynamical phenomena, such as frequency pushing and pulling, mode-locking and pulsing, modal instabilities, even complex chaotic behavior. Metallic nanowires of finite length support a hierarchy of longitudinal surface plasmon modes with standing wave properties: the plasmonic analog of a Fabry-Pérot cavity. Here we show that positioning the nanowire within the gap of a plasmonic nanoantenna introduces a passive, hybridization-based coupling of the standing-wave nanowire plasmon modes with the antenna structure, mediating an interaction between the nanowire plasmon modes themselves. Frequency pushing and pulling, and the enhancement and suppression of specific plasmon modes, can be controlled and manipulated by nanoantenna position and shape.

Purcell effect for finite-length metal-coated and metal nanowires

We investigate the modification (enhancement and suppression) of the spontaneous emission rate of a dipole emitter in two configurations: inside a finite-length semiconductor nanowire surrounded by bulk metal and in the vicinity of a finite metal nanowire. Our analysis is based on a first-principle approach, which is reduced to a seminumeric one in the limit of large nanowire aspect ratios. The numerical calculations are carried out for an emitter in a GaAs nanowire embedded in Ag or Au and for that nearby an Ag or Au nanowire in vacuum or dielectric. We consider in detail the Purcell and β factors as functions of the cylinder radius, the emitter position, and the transition frequency for both configurations. We contrast the results for finite-length nanowires with those obtained in the infinite-length approximation and find considerable differences in the Purcell factor magnitude.

Ac Josephson Effect in Finite-Length Nanowire Junctions with Majorana Modes

It has been predicted that superconducting junctions made with topological nanowires hosting Majorana bound states (MBS) exhibit an anomalous 4π-periodic Josephson effect. Finding an experimental setup with these unconventional properties poses, however, a serious challenge: for finite-length wires, the equilibrium supercurrents are always 2π periodic as anticrossings of states with the same fermionic parity are possible. We show, however, that the anomaly survives in the transient regime of the ac Josephson effect. Transients are, moreover, protected against decay by quasiparticle poisoning as a consequence of the quantum Zeno effect, which fixes the parity of Majorana qubits. The resulting long-lived ac Josephson transients may be effectively used to detect MBS.

Energy spectrum and broken spin-surface locking in topological insulator quantum dots

We consider the energy spectrum and the spin-parity structure of the eigenstates for a quantum dot made of a strong topological insulator. Using the effective low-energy theory in a finite-length cylinder geometry, numerical calculations show that even at the lowest energy scales, the spin direction in a topologically protected surface mode is not locked to the surface. We find "zero-momentum" modes, and subgap states localized near the "caps" of the dot. Both the energy spectrum and the spin texture of the eigenstates are basically reproduced from an analytical surface Dirac fermion description. Our results are compared to microscopic calculations using a tight-binding model for a strong topological insulator in a finite-length nanowire geometry.

Repulsive force vs. source number: Competing mechanisms in the yield of twinned gold nanowires of finite length

Nanoscale twin boundaries play a significant role in the yield behavior of nanowires. They serve as both a source of dislocation nucleation and a generator of the repulsive force which acts against the nucleation of dislocations. In the present paper molecular dynamics (MD) simulations are performed to investigate the tensile deformation of twinned gold nanowires (NWs) of finite length. Emphasis is placed on competing mechanisms in the initial yield of nanowires: dislocation source number vs. repulsive force, both of which are controlled by the twin boundary spacing. The simulation results reveal that with decreasing twin boundary spacing there is a transition from softening to strengthening due to a change in the dominant mechanism of plastic deformation. An analytical model based on kinetic rate theory is also established to provide an insight into the competing mechanisms indicated by the simulation results.

Stabilization of walls for nano-wires of finite length

In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Interplay between structural and electronic properties of bundledMo6S9 − xIx nanowires

Using first principles density functional theory, we investigate thestructural, electronic and magnetic properties of isolated and bundledMo6S9 − xIx nanowireswith x = 3, 4.5, and 6. The unit cell of each system contains twoMo6 octahedra decorated with S and I atoms and twoS3 linkages. Due to the bistability of each sulfur linkage, finite-length nanowires or nanowirebundles exhibit many stable structural minima. We explore the structural stability,elastic behavior and electronic structure at all these minima for each compositionx. We find that the axial strain and inter-wire interaction in bundles significantly modifythe electronic structure. The most intriguing changes occur in nanowires withx = 4.5 and 6, which change from metal to semiconductor or undergo a magnetic transition uponaxially stretching or compressing the nanowires or upon changing the inter-wire separation.

Superconductor to normal-metal transition in finite-length nanowires: Phenomenological model

In this paper we discuss the interplay of quantum fluctuations and dissipation in uniform superconducting nanowires. We consider a phenomenological model with superconducting and normal components and a finite equilibration rate between these two fluids. We find that phase-slip dipoles proliferate in the wire and decouple the two fluids within its bulk. This implies that the normal fluid only couples to the superconductor fluid through the leads at the edges of the wire, and the local dissipation is unimportant. Therefore, while long wires have a superconductor-metal transition tuned by local properties of the superconducting fluid, short wires have a transition when the total resistance is ${R}_{\text{tot}}={R}_{Q}=h/4{e}^{2}$.

Scalar relativistic effect on lattice dimerization in metastable gold nanowire of finite length

Recent observation by Xiao et al. [L. Xiao, B. Tollberg, X. Hu, L. Wang, J. Chem. Phys. 124 (2006) 114309.] suggested substantial lattice distortion in linear gold nanowires of finite chain length up to 2 nm and remarkably they have predicted the disappearance of Peierls distortion in the infinite limit. In the present study we adopt the method of constrained relaxation search to find out the existence of true dimerization in these systems. The role of scalar relativistic effect on lattice dimerization in these nanowires has been investigated using first-principle density functional calculations at zero-order regular approximation level. It is well known that real lattice dimerization in gold nanowires are perceptible just immediately before the breakage of the wires. While exploring the role of scalar relativity, it has been observed that scalar relativity decreases the dimerization amplitude of each of the linear metastable gold nanowires compared to its non-relativistic counterpart. Another interesting observation is the greater stabilization of Au 5 and Au 7 in constrained relaxation search compared to that of the unconstrained relaxation scheme in relativistic method. The dramatic even–odd oscillations are observed in the values of the dimerization amplitudes, HOMO–LUMO energy gap, and second differences of wire energies. The results are very stable and consistent up to Au 9.