Quantum Wire Model Research Articles

Analytical and numerical calculation of the effect of edge states of the Kane-Mele model on the RKKY interaction

In this paper, we investigate the Kane-Mele model and endeavor to demonstrate, through analytical calculations, how the presence of topological edge states influences the RKKY interaction. We illustrate that the effect diminishes as one moves away from the edges. To facilitate our analytical approach, we initially utilize a one-dimensional wire exhibiting linear dispersion for each spin as an approximation to the Kane-Mele model. We examine its impact on the RKKY interaction. Subsequently, we establish a correspondence between the edge states of the Kane-Mele model and a one-dimensional quantum wire model, wherein the coupling strength diminishes with increasing distance from the edges. Finally, we compare the analytical results with numerical findings obtained using the Landauer-Buttiker formulation.

Квантовая проводимость в одиночных и связанных квантово-размерных частицах узкозонных полупроводников

An organo-modified ordered layered structure with three-dimensional close packing based on colloidal quantum-sized particles (QP) of InSb, PbS, CdSe semiconductors and Langmuir-Blodgett films has been fabricated and studied. According to the current-voltage characteristics (CVC) of single-electron transport in the model of a nanocell with a linear chain QP across the layers, the processes limiting conductivity were established: emission-injection tunneling from a probe into a nanoparticle, motion in a nanoparticle determined by the establishment of an electronic wave process in it, and tunneling through a nanogap between nanoparticles. Quasi-periodic oscillations of the current and resonant peaks of quantum conductivity are observed on the I–V characteristics, which were estimated in the quantum wire model. For an even number of layers (QP, 2, or 4), the I–V characteristics were used to determine the attenuation of size quantization and the decrease in current due to the weak interaction of nanoparticles. With an odd number (3 or 5), the nanochain acts as a single quantum thread with manifestations on the CVC similar to the cases of one QP. In this case, the motion of an electron can be considered as a one-electron charge wave.

Stability of the smectic phase in arrays of parallel quantum wires

Using bosonization, we study a microscopic model of parallel quantum wires constructed from two dimensional Dirac fermions in the presence of periodic topological domain walls. The model accounts for the lateral spread of the wavefunctions $\ell$ in the transverse direction to the wires. The gapless modes confined to each domain wall are shown to form Luttinger liquids, which realize a well known smectic non-Fermi liquid fixed point when interwire Coulomb interactions are taken into account. Perturbative studies on phenomenological models have shown that the smectic fixed point is unstable towards a variety of phases such as superconductivity, stripe, smectic and Fermi liquid phases. Here, we show that the considered microscopic model leads to a phase diagram with only smectic metal and Fermi liquid phases. The smectic metal phase is stable in the ideal quantum wire limit $\ell\to0$. For finite $\ell$, we find a critical Coulomb coupling $\alpha_{c}$ separating the strong coupling smectic metal from a weak coupling Fermi liquid phase. We conjecture that the absence of superconductivity should be a generic feature of similar microscopic models. Finally, we discuss the physical realization of this model with moire heterostructures.

The influence of confined acoustic phonon on the Quantum Ettingshausen effect in cylindrical quantum wire with an infinite potential in presence of strong electromagnetic wave

Based on the quantum kinetic equation method, the quantum Ettingshausen effect has been theoretically studied under the influence of confined acoustic phonon in a cylindrical quantum wire (CQW) with infinite potential in the presence of a strong electromagnetic wave. We considered a quantum wire in the presence of a constant electric field, a magnetic field, an electromagnetic wave (EMW) with an assumption that electron – confined acoustic phonon (CAP) scattering is essential. Analytical results obtained show that the EC depends on the amplitude and the frequency of the EMW in a non-linear way. Besides, the impact of phonon confinement on the above effect characterized by m-quantum number in the expression of the EC. The theoretical results have been numerically calculated for the GaAS/AlGaAs cylindrical quantum wire model. The obtained results show that the phonon confinement contributes to the EC quantitatively and qualitatively. On the other hand m is set to zero, the result obtained is similar to the case of unconfined phonon. Furthermore, by considering the quantum size effect, the values of the EC increases, the position of the magnetic-phonon resonance peak changes, and the number of peak resonant peak increases while the radius of quantum wire declines. These obtained results are different from bulk semiconductor and unconfined phonon case which donates to the theory of the Ettingshausen effect in low-dimensional semiconductor systems.

Dissipative Majorana Quantum Wires.

SummaryIn this paper, we formulate and quantitatively examine the effect of dissipation on topological systems. We use a specific model of Kitaev quantum wire with an onsite Ohmic dissipation and perform a numerically exact method to investigate the effect of dissipation on the topological features of the system (e.g., the Majorana edge mode) at zero temperature. We find that even though the topological phase is robust against weak dissipation as it is supposed to be, it will eventually be destroyed by sufficiently strong dissipation via either a continuous quantum phase transition or a crossover depending on the symmetry of the system. The dissipation-driven quantum criticality has also been discussed.

Comment on “Landau quantized dynamics and spectra for group VI dichalcogenides, including a model quantum wire” [AIP Advances 7, 065316 (2017)

Comment on “Landau quantized dynamics and spectra for group VI dichalcogenides, including a model quantum wire” [AIP Advances 7, 065316 (2017)

Analysis of Nonequilibrium Transport Properties of Interacting Quantum Wire Models

We analyze nonequilibrium electronic transport properties of a typical interacting three-site quantum wire model within Hartree-Fock approximation making use of Keldysh formalism. Some rigorous formulas are provided for direct calculations when Coulomb repulsion is present. According to numerical calculations using above formulas, we investigate the conductance, transport currents, and on site electronic charges of the wire on some special occasions in the interacting case, and also compare them with the results in the noninteracting case.

Addendum: “Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire” [AIP Advances 7, 065316 (2017)

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Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction

We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin–orbit (SO) interaction in a magnetic field, using a combination of matrix product state and bosonization techniques. Quantum wires with strong Rashba SO interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with SO interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at k = 0 and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton–antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.

Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

This work is concerned with the derivation of the Green’s function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green’s function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green’s function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function). The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ(x)-potential profile. This retarded Green’s function for propagation directly along the wire is determined exactly in terms of the corresponding Green’s function for the system without the δ(x)-potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green’s function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

Tuning directional dependent metal–insulator transitions in quasi-1D quantum wires with spin–orbit density wave instability

We study directional dependent band gap evolutions and metal–insulator transitions (MITs) in model quantum wire systems within the spin–orbit density wave (SODW) model. The evolution of MIT is studied as a function of varying anisotropy between the intra-wire hopping () and inter-wire hopping () with Rashba spin–orbit coupling. We find that as long as the anisotropy ratio () remains below 0.5, and the Fermi surface nesting is tuned to , an exotic SODW induced MIT easily develops, with its critical interaction strength increasing with increasing anisotropy. As (2D system), the nesting vector switches to , making this state again suitable for an isotropic MIT. Finally, we discuss various physical consequences and possible applications of the directional dependent MIT.

Topological phases of inhomogeneous superconductivity

We theoretically consider the effect of a spatially periodic modulation of the superconducting order parameter on the formation of Majorana fermions induced by a one-dimensional system with magnetic impurities brought into close proximity to an $s$-wave superconductor. When the magnetic exchange energy is larger than the inter-impurity electron hopping we model the effective system as a chain of coupled Shiba states. While in the opposite regime, the effective system is accurately described by a quantum wire model. Upon including a spatially modulated superconducting pairing, we find, for sufficiently large magnetic exchange energy, the system is able to support a single pair of Majorana fermions with one Majorana fermion on the left end of the system and one on the right end. When the modulation of superconductivity is large compared to the magnetic exchange energy, the Shiba chain returns to a trivially gapped regime while the quantum wire enters a new topological phase capable of supporting two pairs of Majorana fermions.

Probing zero modes of a defect in a Kitaev quantum wire

The Kitaev quantum wire (KQW) model with open boundary possesses two Majorana edge modes. When the local chemical potential on a defect site is much higher than that on other sites and than the hopping energy, the electron hopping is blocked at this site. We show that the existence of such a defect on a closed KQW also gives rise to two low-energy modes, which can simulate the edge modes. The energies of the defect modes vanish to zero as the local chemical potential of the defect increase to infinity. We develop a quantum Langevin equation to study the transport of KQW for both open and closed cases. We find that when the lead is contacted with the site beside the defect, we can observe two splitted peaks around the zero-bias voltage in the differential conductance spectrum, whereas if the lead is contacted with the bulk of the quantum wire far from the the defect or the open edges, we cannot observe any zero-bias peak.

Scaling of Geometric Quantum Discord Close to a Topological Phase Transition

Quantum phase transition is one of the most interesting aspects in quantum many-body systems. Recently, geometric quantum discord has been introduced to signature the critical behavior of various quantum systems. However, it is well-known that topological quantum phase transition can not be described by the conventional Landau's symmetry breaking theory, and thus it is unknown that whether previous study can be applicable in this case. Here, we study the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric quantum discord. The derivative of geometric quantum discord is nonanalytic at the critical point, in both zero temperature and finite temperature cases. The scaling behavior and the universality are verified numerically. Therefore, our results clearly show that all the key ingredients of the topological phase transition can be captured by the nearest neighbor and long-range geometric quantum discord.

Scaling of geometric phases close to the topological quantum phase transition in Kitaev's quantum wire model

We present a unified study of the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric phase (GP). We also analyze zero-temperature and finite-temperature scaling parameters, extracted from the GP near the critical point. The derivative of the ground-state GP is nonanalytic at the phase boundary. A finite-size scaling and finite-temperature scaling analysis are carried out and, furthermore, the scaling behavior and universality are verified numerically.

Intrinsic exchange-correlation magnetic fields in exact current density functional theory for degenerate systems

We calculate the exact Kohn-Sham (KS) scalar and vector potentials that reproduce, within current-density functional theory, the steady-state density and current density corresponding to an electron quasiparticle added to the ground state of a model quantum wire. Our results show that, even in the absence of an external magnetic field, a KS description of a steady-state system in general requires a non-zero exchange-correlation magnetic field that is purely mechanical in origin. The KS paramagnetic current density is not, in general, that of the interacting system in any gauge.

Inducing Time-Reversal-Invariant Topological Superconductivity and Fermion Parity Pumping in Quantum Wires

We propose a setup to realize time-reversal-invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is ϕ=π a Kramers pair of Majorana zero modes appears at each edge of the wire. We study the robustness of the phase in the presence of both time-reversal-invariant and time-reversal-breaking perturbations. In addition, we show that the system forms a natural realization of a fermion parity pump, switching the local fermion parity of both edges when the relative phase between the superconductors is changed adiabatically by 2π.

Optical transitions in AlGaAs/GaAs quantum wires on GaAs(6 3 1) substrates studied by photoreflectance spectroscopy

We present the synthesis and characterization of a system of self-assembling GaAs quantum wires (QWRs) embedded in Al x Ga 1− x As barriers grown by molecular beam epitaxy on GaAs(6 3 1)-oriented substrates. We studied the optical transitions in the QWRs as a function of temperature ( T) by photoreflectance (PR) spectroscopy. The energy transitions were extracted from the PR spectra employing the third-derivative functional form, and they were compared with the transitions theoretically calculated from both, a model of QWRs with cylindrical geometry and a model of a conventional square quantum well. The results show a good agreement between experimental and theoretical data in the case of the QWR model, and from this comparison we were able to identify up to 12 different transitions in the PR spectra and to study their behavior dependent on temperature.

Negative magnetoresistance in transverse and longitudinal magnetic fields in Bi nanowires

In this work the measurements of longitudinal (LMR) and transverse magnetoresistance (TMR) in Bi wires with 50<d<500 nm in the interval 4.2 - 300 K and magnetic field up to 14 T were carried out. Was shown that, the maximum on LMR at H||I is suppressed due to quantum size effect. For the first time it was found that the field dependence of TMR R(H) at I⊥H) in Bi wires with d<80 nm contains the negative region R(H) > R0 at T<5 K. This result was unexpected, because it is known that in bulk Bi samples the "giant" increase of magnetoresistance in the case H⊥I is observed. We calculate the conductivity of nanowires in longitudinal and transverse magnetic fields on the basis of the Cubo formula for the conductivity. We use the model of quantum wires with a parabolic potential in the plane orthogonal to the axis of the size-quantized system. According to the model of such TMR and LMR were experimentally observed in the Bi quantum wires (QW) with d<80nm.

Nonequilibrium transport properties for a three‐site quantum wire model

AbstractWe derive nonequilibrium electronic transport properties for a three‐site quantum wire model within Hartree‐Fock approximation making use of Keldysh formalism. Some rigorous formulas are provided for direct calculations when Coulomb repulsion is present. According to numerical calculations using these formulas, we investigate the conductance, transport current, and on site electronic charges of the wire in some special occasions. In noninteracting case, when site‐site couplings in the wire are tougher than wire‐electrode couplings, the resonant tunneling transport takes place and the phenomenon of conductance quantization can be easily observed. The transport properties of up‐spin are identical with those of down‐spin. When the Coulomb interaction is present, the line shapes of transport characteristics are changed because of electron‐electron repulsions. With the increase of U, the Coulomb blockade and metal‐insulator transition (Mott transition) phenomena are obvious if the self‐energies Γ have small values compared with U. The transport properties of the up‐spin also become quite different from those of the down‐spin indicating that the spin polarization takes place in the wire. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)