One-dimensional Quantum Wires Research Articles

The energy due to confinement of one-dimensional cylindrical quantum wire

We have determined the energy due to confinement of one-dimensional cylindrical quantum wire by solving Schrödinger’s equation. By considering some boundaries conditions, the Schrödinger’s equation has been transformed to the second-order linear differential equation. From this transformation, the wave function and the expression of the energy due to confinement are easily described. We obtained the energy due to confinement of 1D-CQW is inversely proportional to the square of the wire’s radius. Smaller wires have stronger energy due to confinement than bigger ones.

Zero-Magnetic Field Fractional Quantum States.

Since the discovery of the fractional quantum Hall effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing magnetic field. Although various situations have been theoretically envisaged, particularly lattice models in which band flattening resembles Landau levels, the predicted fractions have never been observed. In this Letter, we show that odd and even denominator fractions can be observed, and manipulated, in the absence of a quantizing magnetic field, when a low-density electron system in a GaAs based one-dimensional quantum wire is allowed to relax in the second dimension. It is suggested that such a relaxation results in formation of a zigzag array of electrons with ring paths which establish a cyclic current and a resultant lowering of energy. The behavior has been observed for both symmetric and asymmetric confinement but increasing the asymmetry of the confinement potential, to result in a flattening of confinement, enhances the appearance of new fractional states. We find that an in-plane magnetic field induces new even denominator fractions possibly indicative of electron pairing. The new quantum states described here have implications both for the physics of low dimensional electron systems and also for quantum technologies. This work will enable further development of structures which are designed to electrostatically manipulate the electrons for the formation of particular configurations. In turn, this could result in a designer tailoring of fractional states to amplify particular properties of importance in future quantum computation.

Designing Nanomagnet Arrays for Topological Nanowires in Silicon

Recent interest in topological quantum computing has driven research into topological nanowires, one-dimensional quantum wires that support topological modes including Majorana fermions. Most topological nanowire designs rely on materials with strong spin-orbit coupling, such as InAs or InSb, used in combination with superconductors. It would be advantageous to fabricate topological nanowires using Si owing to its mature technology. However, the intrinsic spin-orbit coupling in Si is weak. One approach that could circumvent this material deficiency is to rotate the electron spins using nanomagnets. Here, we perform detailed simulations of realistic Si/SiGe systems with an artificial spin-orbit gap induced by a nanomagnet array. Most of our results are also generalizable to other nanomagnet-based topological nanowire designs. By studying several concrete examples, we gain insight into the effects of nanomagnet arrays, leading to design rules and guidelines. Finally, we present an experimentally realizable design using magnets with a single polarization.

Proximity-induced supercurrent through topological insulator based nanowires for quantum computation studies

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 Kitaev’s 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) nanowires proximity-coupled to conventional s-wave superconducting (W) electrodes. Milling technique possesses great potential in fabrication of any desired shapes and structures at nanoscale level, and therefore can be effectively utilized to scale-up the existing single nanowire based design into nanowire based network architectures. We demonstrate the dominant role of ballistic topological surface states in propagating the long-range proximity induced superconducting order with high IcRN product in long Bi2Se3 junctions. Large upper critical magnetic fields exceeding the Chandrasekhar-Clogston limit suggests the existence of robust superconducting order with spin-triplet cooper pairing. An unconventional inverse dependence of IcRN product on the width of the nanowire junction was also observed.

Ballistic One-Dimensional Holes with Strong g-Factor Anisotropy in Germanium.

We report experimental evidence of ballistic hole transport in one-dimensional quantum wires gate-defined in a strained SiGe/Ge/SiGe quantum well. At zero magnetic field, we observe conductance plateaus at integer multiples of 2 e2/ h. At finite magnetic field, the splitting of these plateaus by Zeeman effect reveals largely anisotropic g-factors with absolute values below 1 in the quantum-well plane, and exceeding 10 out-of-plane. This g-factor anisotropy is consistent with a heavy-hole character of the propagating valence-band states, which is in line with a predominant confinement in the growth direction. Remarkably, we observe quantized ballistic conductance in device channels up to 600 nm long. These findings mark an important step toward the realization of novel devices for applications in quantum spintronics.

Instability of the sliding Luttinger liquid

We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or ‘Coulomb-blockade’ type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.

Band and Correlated Insulators of Cold Fermions in a Mesoscopic Lattice

We investigate the transport properties of neutral, fermionic atoms passing through a one-dimensional quantum wire containing a mesoscopic lattice. The lattice is realized by projecting individually controlled, thin optical barriers on top of a ballistic conductor. Building an increasingly longer lattice, one site after another, we observe and characterize the emergence of a band insulating phase, demonstrating control over quantum-coherent transport. We explore the influence of atom-atom interactions and show that the insulating state persists as contact interactions are tuned from moderately to strongly attractive. Using bosonization and classical Monte-Carlo simulations we analyze such a model of interacting fermions and find good qualitative agreement with the data. The robustness of the insulating state supports the existence of a Luther-Emery liquid in the one-dimensional wire. Our work realizes a tunable, site-controlled lattice Fermi gas strongly coupled to reservoirs, which is an ideal test bed for non-equilibrium many-body physics.

Electronic and Optical Properties of Pristine and Vertical and Lateral Heterostructures of Janus MoSSe and WSSe.

On the basis of electron-electron self-energy corrections, quasiparticle band structures of Janus MoSSe and WSSe are identified, and the excitonic effects are demonstrated to play a dominate role in the optical response. Combining together MoSSe and WSSe monolayers to form vertical heterostructures (VHTs) and lateral heterostructures (LHTs) rarely leads to a simple arithmetic sum of their properties, giving rise to novel and unexpected behaviors. In particular, Rashba polarization can be enhanced in VHTs due to improved out-of-plane electric polarity. In the case of LHTs, photoresponse and absorption coefficients show optical activity in a wide visible light range. It is of interest that both VHTs and LHTs reveal type-II band alignment, enabling the separation of excitons. Besides, grain boundaries (GBs) of large angle (60°) in Janus MoSSe due to chalcogen effects behave as one-dimensional (1D) metallic quantum wires, suggesting the possible formation of 1D electron or hole gas in such electronic heterostructures.

Dependence of Strain Distribution on In Content in InGaN/GaN Quantum Wires and Spherical Quantum Dots

The distribution of strain, developed in zero-dimensional quantum spherical dots and one-dimensional cylindrical quantum wires of an InGaN/GaN system is calculated as functions of radius of the structure and indium mole fraction. The strain shows strong dependence on indium mole fraction at small distances from the center. The strain associated with both the structures is found to decrease exponentially with the increase in dot or cylinder radius and increases linearly with indium content.

Localization length versus level repulsion in one-dimensional driven disordered quantum wires

We study the level repulsion and its relationship with the localization length in a disordered one-dimensional quantum wire excited with monochromatic linearly polarized light and described by the Anderson-Floquet model. In the high frequency regime, the linear scaling between the localization length divided by the length of the system and the spectral repulsion is the same as in the one-dimensional Anderson model without driving, although both quantities depend on the parameters of the external field. In the low frequency regime the level repulsion depends mainly on the value of the amplitude of the field and the proportionality between level repulsion and localization length is lost.

Dynamic Transport in a Quantum Wire Driven by Spin-Orbit Interaction

We consider a gated one-dimensional (1D) quantum wire disturbed in a contactless manner by an alternating electric field produced by a tip of a scanning probe microscope. In this schematic 1D electrons are driven not by a pulling electric field but rather by a non-stationary spin-orbit interaction (SOI) created by the tip. We show that a charge current appears in the wire in the presence of the Rashba SOI produced by the gate net charge and image charges of 1D electrons induced on the gate (iSOI). The iSOI contributes to the charge susceptibility by breaking the spin-charge separation between the charge- and spin collective excitations, generated by the probe. The velocity of the excitations is strongly renormalized by SOI, which opens a way to fine-tune the charge and spin response of 1D electrons by changing the gate potential. One of the modes softens upon increasing the gate potential to enhance the current response as well as the power dissipated in the system.

Photon-assisted transport through a 1D-dot-graphene similar to STM model device

By using the nonequilibrium Green function method, the photon-assisted electron transport through a graphene-based device similar to STM model is studied theoretically and numerically. The device is composed of a single central site (quantum dot) modulated by an oscillating electric field, a one-dimensional quantum wire and a two-dimensional graphene sheet. Some interesting results on transmission probability and current–voltage ([Formula: see text]–[Formula: see text]) characteristics of the device are given in this paper. In the presence of an oscillating electric field, we find that besides the central two transmission peaks caused by graphene part, there appear photon-assisted peaks which are distributed on both sides of the Fermi level. The positions of the photon-assisted peaks are linear to the frequency of the oscillating electric field, and the widths of the photon-assisted peaks are relevant to the amplitude of the oscillating electric field. It is found that the current–voltage graphs exhibit step growth due to the existence of photon-assisted tunneling. We hope these results may have guidance meaning for the fabrication of optoelectronic devices.

Correlated atomic wires on substrates. II. Application to Hubbard wires

In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [arXiv:1704.07350]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely paramagnetic Mott insulators, Luttinger liquids, and spin-$1/2$ Heisenberg chains. The validity of the effective ladder models is assessed by studying the convergence with the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate.

Correlated atomic wires on substrates. I. Mapping to quasi-one-dimensional models

We present a theoretical study of correlated atomic wires deposited on substrates in two parts. In this first part, we propose lattice models for a one-dimensional quantum wire on a three-dimensional substrate and map them onto effective two-dimensional lattices using the Lanczos algorithm. We then discuss the approximation of these two-dimensional lattices by narrow ladder models that can be investigated with well-established methods for one-dimensional correlated quantum systems, such as the density-matrix renormalization group or bosonization. The validity of this approach is studied first for noninteracting electrons and then for a correlated wire with a Hubbard electron-electron repulsion using quantum Monte Carlo simulations. While narrow ladders cannot be used to represent wires on metallic substrates, they capture the physics of wires on insulating substrates if at least three legs are used. In the second part [arXiv:1704.07359], we use this approach for a detailed numerical investigation of a wire with a Hubbard-type interaction on an insulating substrate.

Perfect valley polarization in MoS2

We study perfect valley polarization in a molybdenum disulfide MoS2 nanoribbon monolayer using two bands Hamiltonian model and non-equilibrium Green's function method. The device consists of a one-dimensional quantum wire of MoS2 monolayer sandwiched between two zigzag MoS2 nanoribbons such that the sites A and B of the honeycomb lattice are constructed by the molecular orbital of Mo atoms, only. Spin-valley coupling is seen in energy dispersion curve due to the inversion asymmetry and time-reversal symmetry. Although, the time reversal symmetry is broken by applying an external magnetic field, the valley polarization is very small. A valley polarization equal to 46% can be achieved using an exchange field of 0.13 eV. It is shown that a particular spin-valley combination with perfect valley polarization can be selected based on a given set of exchange field and gate voltage as input parameters. Therefore, the valley polarization can be detected by detecting the spin degree of freedom.

A free-electron model for the Dirac bands in graphene

We present a new method for describing the electronic structure of graphene, by treating the honeycomb lattice as an arrangement of crisscrossing one-dimensional quantum wires. The electrons travel as free particles along the wires and interfere at the three-way junctions formed by the carbon atoms. The approach produces the linearly dispersive Dirac band structure as well as the chiral pseudo-spin-wave functions. When vacancies are incorporated, the model reproduces the well known zero mode states.

Helical gaps in interacting Rashba wires at low electron densities

Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap ("helical gap") in the energy spectrum of noninteracting or weakly interacting one-dimensional quantum wires. By comparing kinetic energy and Coulomb energy we show that this gap opening typically occurs at low electron densities where the Coulomb energy dominates. To address this strongly correlated limit, we investigate Rashba wires using Wigner crystal theory. We find that the helical gap exists even in the limit of strong interactions but its dependence on electron density differs significantly from the weakly interacting case. In particular, we find that the critical magnetic field for opening the gap becomes an oscillatory function of electron density. This changes strongly the expected signature of the helical gap in conductance measurements.

Fermionic approach to junctions of multiple quantum wires attached to Tomonaga-Luttinger liquid leads

Junctions of multiple one-dimensional quantum wires of interacting electrons have received considerable theoretical attention as a basic constituent of quantum circuits. While results have been obtained on these models using bosonization and Density Matrix Renormalization Group (DMRG) methods, another powerful technique is based on direct perturbation theory in the bulk interactions, combined with the Renormalization Group (RG) and summed in the Random Phase Approximation (RPA). This technique has so far only been applied to the case where finite length interacting wires are attached to non-interacting Fermi liquid leads. We reformulate it in terms of the single-particle S-matrix, formally unifying treatments of junctions of different numbers of leads, and extend this method to cover the case of infinite length interacting leads obtaining results on 2-lead and 3-lead junctions in good agreement with previous bosonization and DMRG results.

Topological phase in one-dimensional Rashba wire**Project supported by the National Natural Science Foundation of China (Grant Nos. 115074045 and 11204187) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20131284).

We study the possible topological phase in a one-dimensional (1D) quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps forming in the bulk energy band and fractional boundary states residing in the gap when the system has an inversion symmetry. These states are topologically nontrivial and can be characterized by a quantized Berry phase ±π or nonzero Chern number through dimensional extension. When the Rashba spin–orbital coupling varies slowly with time, the system can pump out 2 charges in a pumping cycle because of the spin flip effect. This quantized pumping is protected by topology and is robust against moderate disorders as long as the disorder strength does not exceed the opened energy gap.

Non-Abelian topological spin liquids from arrays of quantum wires or spin chains

We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in $(1+1)$-dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges $c<1$. These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but non-zero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, non-chiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the ten-fold way classification of two-dimensional non-interacting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.