Finite-length Wire Research Articles

Electronic Wigner-molecule polymeric chains in elongated silicon quantum dots and finite-length quantum wires

Electronic Wigner-molecule polymeric chains in elongated silicon quantum dots and finite-length quantum wires

Fast Analytic–Numerical Algorithms for Calculating Mutual and Self-Inductances of Air Coils

This paper deals with a method of calculating the mutual and self-inductances of various air coils located arbitrarily in space. Known elementary solutions (the Biot–Savart formulas) were used to determine the magnetic field of infinitely thin current loops and infinitely thin wires of finite length magnetically linking other coils. Unlike commonly used algorithms, these elementary solutions were not extensively transformed analytically but were used to perform calculations via direct numerical integration. This enabled the very quick and accurate obtaining of the self-inductance values, as well as determining the dependence of mutual inductances on the positions of both coils. This method allows for the analysis of different coil configurations (misaligned coils, inclined to each other, etc.) that other methods do not cover. It also enables the determination of the forces acting on the coils, as well as the calculation of the magnetic field distribution from any coil configuration. The obtained results were compared with those presented by other authors (both computational and measurement results).

A general forward solver for 3D CSEMs with multitype sources and operating environments

To determine the electromagnetic (EM) fields of different three-dimensional (3D) controlled-source electromagnetic methods (CSEMs) using the same parameters of the forward solution, by explicitly considering the commonalities, we present a general 3D forward modeling solver for CSEMs with multitype sources and operating environments. The commonality of the solver is reflected in two aspects. First, the solver is based on a frequency-domain (FD) vector Helmholtz equation for determining the scattered electric field. The different types of sources are imposed on the right-hand term of the equation, expressed as background Green’s function. Second, sources of any CSEM can be composed of electric dipole (ED) or magnetic dipole (MD) superposition. Thus, the focus of the 3D forward modeling of CSEMs is reduced to determining the EM fields of ED or MD sources for the background medium. The quasi-minimal residual (QMR) method is used to solve the large sparse complex linear system. Once the FD EM fields have been calculated, the time-domain (TD) response can be obtained using the cosine/sine transformation. The numerical results show that the relative error is less than 5% between the 3D numerical and analytical solutions, which verifies the accuracy of the solver. We further study the difference between the real (bent) and theoretical (straight) wires. We suggest that the shape of the source must be considered for TD and FD CSEMs with a wire source during data processing and inversion. The last example investigated the characteristics of FD EM fields from a finite-length wire and TD EM fields from a rectangular fixed loop on the same conductive tilted disk model buried in resistive sediments. According to the numerical results, we recommend FD CSEMs with a wire source for detecting deep anomalies.

The Attenuation calculation method for the underwater low-frequency magnetic field of finite-length straight wire

Usually, when solving the magnetic field distribution of a finite-length straight wire in a conducting medium, numerical calculation is required. However, this method has some disadvantages, such as complex calculations and not being conducive to engineering implementation. To solve this problem, this paper studied the attenuation calculation method for the underwater low-frequency magnetic field of the finite-length straight wire and then obtained the analytical calculation formula of magnetic field spatial distribution. The simulation results show that, within a certain distance, the analytical method is in good agreement with the numerical calculation results. The method presented in this paper is convenient for calculation and has good engineering practicability.

The Relativistic Equations of Motion for a Charged Particle in the Magnetic Field of an Infinite Current-Carrying Wire

We show how to produce the closed form solution for the motion of a charged particle in the magnetic field of an infinitely long, current-carrying wire in the relativistic range, thus extending the results produced recently (Asadi-Zeydabadi, M., & Zaidins, C. S., 2019). We outline the areas where the two solutions are similar aa well as where the two solutions are slightly different. We also extend the work in (Asadi-Zeydabadi, M., & Zaidins, C. S., 2019) to the more realistic case where the current generates both a magnetic and an electric field, as is the case in real life. We plan to extend the approach in the future to more complicated cases as the one of the finite length wire. The solution is of great interest for the design of particle accelerators, hence it is interesting for both theoretical physicists and engineers alike.

Ampere’s Law study with the finite length wire hypothesis

Neste artigo é proposto o estudo da Lei de Ampere, que é ensinado nas disciplinas de Física dos cursos de graduação em engenharias no Brasil, utilizando a hipótese do condutor de comprimento finito ao invés do condutor de comprimento infinito. Para isto é necessária a utilização do Teorema de Stokes que no caso do condutor infinito é dispensado. A factibilidade desta proposta é subsidiada pelo fato de que as técnicas para calcular as integrais de linha e integrais de fluxo, necessárias nesta nossa proposta, são ministradas nas disciplinas de Cálculo. Esta abordagem permite uma distinção clara entre a “corrente encerrada” pela curva fechada da integral de linha amperiana e a corrente que efetivamente passa pelo condutor. Com a hipótese do condutor de comprimento infinito estas duas correntes são indistiguíveis. Um outro ganho desta abordagem é que a corrente de deslocamento pode ser introduzida intuitivamente como a integral de fluxo do rotacional do campo magnético que aparece num dos membros da equação de Stokes.

Rényi entropy and negativity for massless Dirac fermions at conformal interfaces and junctions

We investigate the ground state of a (1+1)-dimensional conformal field theory (CFT) built with M species of massless free Dirac fermions coupled at one boundary point via a conformal junction/interface. Each CFT represents a wire of finite length L. We develop a systematic strategy to compute the Rényi entropies for a generic bipartition between the wires and the entanglement negativity between two non-complementary sets of wires. Both these entanglement measures turn out to grow logarithmically with L with an exactly calculated universal prefactor depending on the details of the junction and of the bipartition. These analytic predictions are tested numerically for junctions of free Fermi gases, finding perfect agreement.

Topological signatures in a weakly dissipative Kitaev chain of finite length

We construct a global Lindblad master equation for a Kitaev quantum wire of finite length, weakly coupled to an arbitrary number of thermal baths, within the Born-Markov and secular approximations. We find that the coupling of an external bath to more than one lattice site generates quantum interference effects, arising from the possibility of fermions to tunnel through multiple paths. In the presence of two baths at different temperatures and/or chemical potentials, the steady-state particle current can be expressed through the Landauer-B\"uttiker formula, as in a ballistic transport setup, with the addition of an anomaly factor associated with the presence of the $p$-wave pairing in the Kitaev Hamiltonian. Such a factor is affected by the ground-state properties of the chain, being related to the finite-size equivalent of its Pfaffian topological invariant.

Transient precessing domain structures in finite-size nanomagnets and inversion of magnetization

Transient (in time) uniformly precessing magnetization structures (TUPS) on finite-length ferromagnetic wires are discussed. These rotating around the wire magnetization solutions of the Landau-Lifshits-Slonczewski equation are generalizations of traveling uniformly precessing domain walls of infinite range described by Goussev et al. [Phys. Rev. Lett. 104, 147202 (2010)] and comprise a single parameter family of magnetization profiles controlled by the precession frequency. The latter slowly varies in time resulting in passage of the magnetization structure through different evolution stages. The modulational stability of the TUPS is also discussed. An autoresonance approach using chirped frequency transverse spin polarized current is applied to initiate TUPS with a desired precession frequency. The process of complete inversion of the magnetization of the wire involving passage from spatially uniform to nonuniform and then back to uniform precessing state with opposite magnetization is analyzed.

Traversable wormhole in coupled Sachdev-Ye-Kitaev models with imbalanced interactions

A pair of identical Sachdev-Ye-Kitaev (SYK) models with bilinear coupling forms a quantum dual of a traversable wormhole, with a ground state close to the so called thermofield double state. We use adiabaticity arguments and numerical simulations to show that the character of the ground state remains unchanged when interaction strengths in the two SYK models become imbalanced. Analysis of thermodynamic and dynamical quantities highlights the key signatures of the wormhole phase in the imbalanced case. Further adiabatic evolution naturally leads to the ``maximally imbalanced'' limit where fermions in a single SYK model are each coupled to a free Majorana zero mode. This limit is interesting because it could be more easily realized using various setups proposed to implement the SYK model in a laboratory. We find, based on numerical studies of the quantum mechanical model, that this limiting case is marginal in that it retains some of the characteristic signatures of the wormhole physics, such as the spectral gap and revival dynamics, but lacks others so that it likely does not represent the full-fledged wormhole dual. We discuss how this scenario could be implemented in the proposed realization of the SYK physics in quantum wires of finite length coupled to a disordered quantum dot.

Evading Anderson localization in a one-dimensional conductor with correlated disorder

We show that a one dimensional disordered conductor with correlated disorder has an extended state and a Landauer resistance that is non-zero in the limit of infinite system size in contrast to the predictions of the scaling theory of Anderson localization. The delocalization transition is not related to any underlying symmetry of the model such as particle-hole symmetry. For a wire of finite length the effect manifests as a sharp transmission resonance that narrows as the length of the wire is increased. Experimental realizations and applications are discussed including the possibility of constructing a narrow band light filter.

Three-terminal nonlocal conductance in Majorana nanowires: Distinguishing topological and trivial in realistic systems with disorder and inhomogeneous potential

We develop a theory for the three-terminal nonlocal conductance in Majorana nanowires as existing in the superconductor-semiconductor hybrid structures in the presence of superconducting proximity, spin-orbit coupling, and Zeeman splitting. The key question addressed is whether such nonlocal conductance can decisively distinguish between trivial and topological Majorana scenarios in the presence of chemical potential inhomogeneity and random impurity disorder. We calculate the local electrical as well as nonlocal electrical and thermal conductance of the pristine nanowire (good zero-bias conductance peaks), the nanowire in the presence of quantum dots and inhomogeneous potential (bad zero-bias conductance peaks), and the nanowire in the presence of large disorder (ugly zero-bias conductance peaks). The local conductance by itself is incapable of distinguishing the trivial states from the topological states since zero-bias conductance peaks are generic in the presence of disorder and inhomogeneous potential. The nonlocal conductance, which in principle is capable of providing the bulk gap closing and reopening information at the topological quantum phase transition, is found to be far too weak in magnitude to be particularly useful in the presence of disorder and inhomogeneous potential. Therefore, we focus on the question of whether the combination of the local, nonlocal electrical, and thermal conductance can separate the good, bad, and ugly zero-bias conductance peaks in finite-length wires. Our paper aims to provide a guide to future experiments, and we conclude that a combination of all three measurements would be necessary for a decisive demonstration of topological Majorana zero modes in nanowires---positive signals corresponding to just one kind of measurements are likely to be false positives arising from disorder and inhomogeneous potential.

Band structure and end states in InAs/GaSb core-shell-shell nanowires

Quantum wells in InAs/GaSb heterostructures can be tuned to a topological regime associated with the quantum spin Hall effect, which arises due to an inverted band gap and hybridized electron and hole states. Here, we investigate electron-hole hybridization and the fate of the quantum spin Hall effect in a quasi one-dimensional geometry, realized in a core-shell-shell nanowire with an insulator core and InAs and GaSb shells. We calculate the band structure for an infinitely long nanowire using $\mathbf{k \cdot p}$ theory within the Kane model and the envelope function approximation, then map the result onto a BHZ model which is used to investigate finite-length wires. Clearly, quantum spin Hall edge states cannot appear in the core-shell-shell nanowires which lack one-dimensional edges, but in the inverted band-gap regime we find that the finite-length wires instead host localized states at the wire ends. These end states are not topologically protected, they are four-fold degenerate and split into two Kramers pairs in the presence of potential disorder along the axial direction. However, there is some remnant of the topological protection of the quantum spin Hall edge states in the sense that the end states are fully robust to (time-reversal preserving) angular disorder, as long as the bulk band gap is not closed.

Majorana oscillations and parity crossings in semiconductor nanowire-based transmon qubits

We show that the microwave (MW) spectra in semiconductor-nanowire-based transmon qubits provide a strong signature of the presence of Majorana bound states in the junction. This occurs as an external magnetic field tunes the wire into the topological regime and the energy splitting of the emergent Majorana modes oscillates around zero energy owing to their wave function spatial overlap in finite-length wires. In particular, we discuss how these Majorana oscillations, and the concomitant fermion parity switches in the ground state of the junction, result in distinct spectroscopic features --in the form of an intermitent visibility of absorption lines-- that strongly deviate from standard transmon behavior. In contrast, non-oscillating zero modes, such as topologically trivial Andreev bound states resulting from sufficiently smooth potentials, exhibit an overall standard transmon response. These differences in the MW response could help determine whether the junction contains topological Majoranas or not.

Quantum conductance staircase of holes in silicon nanosandwiches

The results of studying the quantum conductance staircase of holes in one−dimensional channels obtained by the split−gate method inside silicon nanosandwiches that are the ultra−narrow quantum well confined by the delta barriers heavily doped with boron on the n−type Si (100) surface are reported. Since the silicon quantum wells studied are ultra−narrow (~2 nm) and confined by the delta barriers that consist of the negative−U dipole boron centers, the quantized conductance of one−dimensional channels is observed at relatively high temperatures (T > 77 K). Further, the current−voltage characteristic of the quantum conductance staircase is studied in relation to the kinetic energy of holes and their sheet density in the quantum wells. The results show that the quantum conductance staircase of holes in p−Si quantum wires is caused by independent contributions of the one−dimensional (1D) subbands of the heavy and light holes; these contributions manifest themselves in the study of square−section quantum wires in the doubling of the quantum−step height (G0 = 4e2/h), except for the first step (G0 = 2e2/h) due to the absence of degeneracy of the lower 1D subband. An analysis of the heights of the first and second quantum steps indicates that there is a spontaneous spin polarization of the heavy and light holes, which emphasizes the very important role of exchange interaction in the processes of 1D transport of individual charge carriers. In addition, the field−related inhibition of the quantum conductance staircase is demonstrated in the situation when the energy of the field−induced heating of the carriers become comparable to the energy gap between the 1D subbands. The use of the split−gate method made it possible to detect the effect of a drastic increase in the height of the quantum conductance steps when the kinetic energy of holes is increased; this effect is most profound for quantum wires of finite length, which are not described under conditions of a quantum point contact. In the concluding section of this paper we present the findings for the quantum conductance staircase of holes that is caused by the edge channels in the silicon nanosandwiches prepared within frameworks of the Hall. This longitudinal quantum conductance staircase, Gxx, is revealed by the voltage applied to the Hall contacts, Vxy, to a maximum of 4e2/h. In addition to the standard plateau, 2e2/h, the variations of the Vxy voltage appear to exhibit the fractional forms of the quantum conductance staircase with the plateaus and steps that bring into correlation respectively with the odd and even fractional values.

Radiation field of an ideal thin Gaussian bunch moving in a periodic conducting wire structure

A theoretical approach for describing the electromagnetic radiation produced by prolonged electron bunch propagating in the lattice of metallic wires of finite length is presented. This approach is based on vibrator antenna theory and involves approximate solving of Hallen's integral equation. For a single wire, it is also supposed that a wire is sufficiently thin and charge motion is relativistic. For many-wire structures, the approximation similar to kinematic approach of parametric X-ray radiation (PXR) theory is additionally applied. The validity of the method is verified by numerical simulations with COMSOL Multiphysics. Possible applications of interaction between charged particle bunches and artificial wire structures are discussed.

Application of the Method of Moments for Calculating Electrodynamic Characteristics of a Quasistatic Antenna in an Anisotropic Medium

We develop the numerical method of moments for solving an integral equation that describes the distribution of the charge along a thin finite-length antenna wire in an anisotropic medium in the quasistatic approximation. It is shown that the method of moments can be used to calculate the electrodynamic characteristics of such an antenna under the conditions where the kernel of the integral equation has a singularity related to the resonance cone. The influence of the ratio between the elements of the dielectric permittivity tensor and the method of partitioning of the antenna surface on the calculation accuracy is analyzed. It is shown that the relative error of calculations of the antenna characteristics is a fairly small value of about 1% if the antenna wire is divided into ten segments.

Different approaches in calculating AC inductive interference from power lines on pipelines

When dealing with 50–60 Hz inductive electromagnetic interference from power lines on pipelines, the key parameter is represented by the per unit length mutual impedance between the power line conductor-Earth and pipe-Earth circuits. Different philosophies can be followed concerning the evaluation of this parameter, i.e.: modelling the power line conductors by wires of finite length or by wires of infinite length. What is missing in the literature is a comparison of the interference results (i.e. overvoltage and overcurrent induced on the pipeline) that are obtained by following these different approaches. Thus, this study is devoted to investigate this neglected point relevant to the 50–60 Hz interference issue. To this aim, the authors also present and compare some results of interference calculated in real cases and, on the basis of them, they draw some conclusions concerning which, in their opinion, is the best approach.

Hyperbolic Medium of Finite-Length Wires

An artificial medium in the form of a cubic uniaxial photonic crystal (PC) with periodically arranged conducting wire cylinders in a dielectric matrix and oriented along the PC axis is considered. Permittivity \(\tilde \varepsilon \) of the matrix is assumed to be constant, while the permittivity of the cylinders is described by the Drude–Lorentz model. The homogenization of such a medium, the methods of its description, the role of dissipation and spatial dispersion (SD), as well as the possibility of obtaining a hyperbolic dispersion relation are considered. The ambiguity of the PC description with the help of effective material parameters and the introduction of such parameters are demonstrated, as well as the effect of dissipation and SD on the hyperbolicity property under investigation.

Time domain generalized telegrapher’s equations for the electromagnetic field coupling to finite-length wires buried in a lossy half-space

The paper deals with a derivation of a time domain variant of the generalized telegrapher’s equations for transient electromagnetic field coupling to buried wires. The formulation is based on the thin wire antenna theory in the time domain. The influence of a lossy half-space is taken into account by means of the time dependent reflection coefficient approximation arising from the modified image theory (MIT), while the per-unit-length surface impedance accounts for the conductor losses. The obtained space-time integral expressions are handled analytically. The concept of the scattered voltage is naturally included in the full model formulation. Computational examples are given for the induced currents along the buried wire and compared to the results obtained by using the transmission line (TL) approximation.