Quasi One-dimensional Systems Research Articles

Quantum transport regimes in quartic dispersion materials with Anderson disorder

Mexican-hat-shaped quartic dispersion manifests itself in certain families of single-layer two-dimensional hexagonal crystals such as compounds of groups III–VI and groups IV–V as well as elemental crystals of group V. A quartic band forms the valence band edge in various of these structures, and some of the experimentally confirmed structures are GaS, GaSe, InSe, SnSb, and blue phosphorene. Here, we numerically investigate strictly one-dimensional and quasi-one dimensional (Q1D) systems with quartic dispersion and systematically study the effects of Anderson disorder on their transport properties with the help of a minimal tight-binding model and Landauer formalism. We compare the analytical expression for the scaling function with simulation data to distinguish the domains of diffusion and localization regimes. In one dimension, it is shown that conductance drops dramatically at the quartic band edge compared to the quadratic case. As for the Q1D nanoribbons, a set of singularities emerge close to the band edge, suppressing conductance and leading to short mean-free-paths and localization lengths. Interestingly, wider nanoribbons can have shorter mean-free-paths because of denser singularities. However, the localization lengths sometimes follow different trends. Our results display the peculiar effects of quartic dispersion on transport in disordered systems.

Magnetic relaxation in a Co(II) based quasi-one dimensional Ising spin system

Single crystal study of Co(NCS)2(aniline)2 reveals that this compound orders at 6.49 K into a canted AF magnetic structure that explains the presence of a hysteresis loop along the b crystal direction. Effective s=1/2 spins of Co(II) ions within the ground state doublet create an Ising spin system that can be described by J1−J2 triangular model. Temperature dependence of specific heat yields exchange interactions J1=31.3(4) K and 2J2=−2.23(7) K. Applying magnetic field ≃6 kOe perpendicular to b compensates for the AF exchange J2 decoupling ferromagnetic spin chains. This restores the one-dimensionality of the system and allows for observation of magnetic relaxation of single chains, similar to previously studied pyridine-based Co(NCS)2L2 compounds. The analysis of the relaxation time is performed taking into account single-ion relaxation mechanisms together with the Glauber relaxation. We also show, using Monte Carlo calculations of specific heat, that for ferromagnetic J1≫|J2|, the triangular Ising model can be approximated by the rectangular Ising model for which the analytical Onsager’s solution is available.

Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks

The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks Pergamenshchik [19] provides an analytical description of the thermodynamics and ordering in this system (a pore) as a function of linear density Nd/L where d is the disk diameter. We derive the analytical formulae for the distance dependence of the translational pair distribution function and the distribution function of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for different pore widths and densities shows a non-monotonic dependence with a maximum at Nd/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. Comparison between the theoretical results for an infinite system and the results of a molecular dynamics simulation for a finite system with periodic boundary conditions is presented and discussed.

Pattern Formation and Aggregation in Ensembles of Solitons in Quasi One-Dimensional Electronic Systems

Broken symmetries of quasi one-dimensional electronic systems give rise to microscopic solitons taking roles of carriers of the charge or spin. The double degeneracy gives rise to solitons as kinks of the scalar order parameter A; the continuous degeneracy for the complex order parameter Aexp(iθ) gives rise to phase vortices, amplitudes solitons, and their combinations. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge doping. The long-range ordering in dimensions above one imposes super-long-range confinement forces upon the solitons, leading to a sequence of phase transitions in their ensembles. The higher-temperature T transition enforces the confinement of solitons into topologically bound complexes: pairs of kinks or the amplitude solitons dressed by exotic half-integer vortices. At a second lower T transition, the solitons aggregate into rods of bi-kinks or into walls of amplitude solitons terminated by rings of half-integer vortices. With lowering T, the walls multiply, passing sequentially across the sample. Here, we summarize results of a numerical modeling for different symmetries, for charged and neutral soliton, in two and three dimensions. The efficient Monte Carlo algorithm, preserving the number of solitons, was employed which substantially facilitates the calculations, allowing to extend them to the three-dimensional case and to include the long-range Coulomb interactions.

Cooling low-dimensional electron systems into the microkelvin regime

Two-dimensional electron gases (2DEGs) with high mobility, engineered in semiconductor heterostructures host a variety of ordered phases arising from strong correlations, which emerge at sufficiently low temperatures. The 2DEG can be further controlled by surface gates to create quasi-one dimensional systems, with potential spintronic applications. Here we address the long-standing challenge of cooling such electrons to below 1 mK, potentially important for identification of topological phases and spin correlated states. The 2DEG device was immersed in liquid 3He, cooled by the nuclear adiabatic demagnetization of copper. The temperature of the 2D electrons was inferred from the electronic noise in a gold wire, connected to the 2DEG by a metallic ohmic contact. With effective screening and filtering, we demonstrate a temperature of 0.9 ± 0.1 mK, with scope for significant further improvement. This platform is a key technological step, paving the way to observing new quantum phenomena, and developing new generations of nanoelectronic devices exploiting correlated electron states.

Mechanical response of double-stranded DNA to dynamic excitation

The present work investigates the vibrational properties of a DNA-like structure by means of a harmonic Hamiltonian and the Green’s function formalism. The DNA sequence is considered as a quasi one-dimensional system in which the mass-spring pairs are randomly distributed inside each crystalline unit. The sizes of the units inside the system are increased, in a step-by-step approach, so that the actual condition of the DNA could be modeled more accurately. The linear-elastic forces mimicking the bonds between the pairs are initially considered constant along the entire length of the system. In the next step, these forces are randomly shuffled so as to take into account the inherent randomness of the DNA. The results reveal that increasing the number of mass-spring pairs in the crystalline structure decreases the influence of randomness on the mechanical behavior of the structure. This also holds true for systems with larger crystalline units. The obtained results can be used to investigate the mechanical behavior of similar macro-systems.

Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite (Semi-)classical Chains

This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration, we apply the method to a classical particle chain, to the semiclassical nonlinear Schrödinger (NLS) equation and to a classical system on a cylindrical lattice. A comparison with molecular dynamics simulations performed for the NLS model shows very good agreement.

FORTRESS: FORTRAN programs for solving coupled Gross–Pitaevskii equations for spin–orbit coupled spin-1 Bose–Einstein condensate

Here, we present simple and efficient numerical scheme to study static and dynamic properties of spin-1 Bose–Einstein condensates (BECs) with spin–orbit (SO) coupling by solving three coupled Gross–Pitaevskii equations (CGPEs) in three-, quasi-two and quasi-one dimensional systems. We provide a set of three codes developed in FORTRAN 90/95 programming language with user defined ‘option’ of imaginary and real-time propagation. We present the numerical results for energy, chemical potentials, and component densities for the ground state and compare with the available results from the literature. The results are presented for both the ferromagnetic and antiferromagnetic spin-1 BECs with and without SO coupling. To improve the computational speed, all the codes have the option of OpenMP parallelization. We have also presented the results for speedup and efficiency of OpenMP parallelization for the three codes with both imaginary and real-time propagation. Program summaryProgram Title: FORTRESSCPC Library link to program files:https://doi.org/10.17632/st7md3ss85.1Licensing provisions: MITProgramming language: (OpenMP) FORTRAN 90/95External routines/libraries: FFTW 3.3.8Nature of problem: To solve the coupled Gross–Pitaevskii equations for spin-1 BEC with anisotropic spin–orbit coupling using the time-splitting spectral method.Solution method: We use the time-splitting Fourier spectral method to solve the coupled Gross–Pitaevskii equations. The resulting equations are evolved in imaginary time to obtain the ground state of the system or in real-time to study the dynamics.

Improved effective equation for the Rashba spin-orbit coupling in semiconductor nanowires

Semiconductor Rashba nanowires are quasi-one dimensional systems that have large spin-orbit (SO) coupling arising from a broken inversion symmetry due to an external electric field. There exist parametrized multiband models that can describe accurately this effect. However, simplified single band models are highly desirable to study geometries of recent experimental interest, since they may allow to incorporate the effects of the low dimensionality and the nanowire electrostatic environment at a reduced computational cost. Commonly used conduction band approximations, valid for bulk materials, greatly underestimate the SO coupling in Zinc-blende crystal structures and overestimate it for Wurtzite ones when applied to finite cross-section wires, where confinement effects turn out to play an important role. We demonstrate here that an effective equation for the linear Rashba SO coupling of the semiconductor conduction band can reproduce the behavior of more sophisticated eight-band k$\cdot$p model calculations. This is achieved by adjusting a single effective parameter that depends on the nanowire crystal structure and its chemical composition. We further compare our results to the Rashba coupling extracted from magnetoconductance measurements in several experiments on InAs and InSb nanowires, finding excellent agreement. This approach may be relevant in systems where Rashba coupling is known to play a major role, such as in spintronic devices or Majorana nanowires.

Non-collinear Order and Spin–Orbit Coupling in Sr3ZnIrO6

Sr$_{3}$ZnIrO$_{6}$ is an effective spin one-half Mott insulating iridate belonging to a family of magnets which includes a number of quasi-one dimensional systems as well as materials exhibiting three dimensional order. Here we present the results of an extensive investigation into the magnetism including heat capacity, a.c. susceptibility, muon spin rotation ($\mu$SR), neutron diffraction and inelastic neutron scattering on the same sample. It is established that the material exhibits a transition at about $17$ K into a three-dimensional antiferromagnetic structure with propagation vector $\boldsymbol{k}=(0,\frac{1}{2},1)$ in the hexagonal setting of R$\bar{3}$c and non-collinear moments of $0.87$$\mu_B$ on Ir$^{4+}$ ions. Further we have observed a well defined powder averaged spin wave spectrum with zone boundary energy of $\sim 5$ meV at $5$ K. We stress that a theoretical analysis shows that the observed non-collinear magnetic structure arises from anisotropic inter- and intra- chain exchange which has its origin in significant spin-orbit coupling. The model can satisfactorily explain the observed spin wave excitations.

Bidirectional non-Markovian exclusion processes

Bidirectional transport in (quasi) one-dimensional systems generically leads to cluster-formation and small particle currents. This kind of transport can be described by the asymmetric simple exclusion process (ASEP) with two species of particles. In this work, we consider the effect of non-Markovian site exchange times between particles. Different realizations of the exchange process can be considered: The exchange times can be assigned to the lattice bonds or each particle. In the latter case we specify additionally which of the two exchange times is executed, the earlier one (minimum rule) or the later one (maximum rule). In a combined numerical and analytical approach we find evidence that we recover the same asymptotic behavior as for unidirectional transport for most realizations of the exchange process. Differences in the asymptotic behavior of the system have been found for the minimum rule which is more efficient for fast decaying exchange time distributions.

Order Parameter in Electron System: Its Fluctuations and Oscillations

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to describe in an unified manner diverse physical phenomena including coexisting superconductivity and insulators in (quasi)one-dimensional systems, superconductivity and Coulomb blockade in granular superconductors and Josephson networks, Anderson localization and mesoscopic effects in disordered and chaotic systems, and thermodynamic quantum time-space crystals.

Measuring hole g -factor anisotropies using transverse magnetic focusing

Recent theoretical and experimental results from quasi-one dimensional heavy hole systems have suggested that heavy hole gases have a strongly anisotropic g factor. In this theoretical paper, we propose a method for measuring this anisotropy using transverse magnetic focusing (TMF). We demonstrate that for experimentally accessible fields, the g factor anisotropy leads to a relative variation in the characteristic of spin-splitting of the TMF spectrum which allows for the measurement of the anisotropy of the g factor. We show that this variation is insensitive to additional spin-orbit interactions, and is resolvable with current devices.

ORDER PARAMETER IN ELECTRON SYSTEMS: ITS FLUCTUATIONS AND OSCILLATIONS

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to describe in an unified manner diverse physical phenomena including coexisting superconductivity and insulators in (quasi)one-dimensional systems, superconductivity and Coulomb blockade in granular superconductors and Josephson networks, Anderson localization and mesoscopic effects in disordered and chaotic systems, and thermodynamic quantum time-space crystals.

Critical Exponent of the Anderson Transition Using Massively Parallel Supercomputing

To date the most precise estimations of the critical exponent for the Anderson transition have been made using the transfer matrix method. This method involves the simulation of extremely long quasi one-dimensional systems. The method is inherently serial and is not well suited to modern massively parallel supercomputers. The obvious alternative is to simulate a large ensemble of hypercubic systems and average. While this permits taking full advantage of both OpenMP and MPI on massively parallel supercomputers, a straight forward implementation results in data that does not scale. We show that this problem can be avoided by generating random sets of orthogonal starting vectors with an appropriate stationary probability distribution. We have applied this method to the Anderson transition in the three-dimensional orthogonal universality class and been able to increase the largest $L\times L$ cross section simulated from $L=24$ (New J. Physics, 16, 015012 (2014)) to $L=64$ here. This permits an estimation of the critical exponent with improved precision and without the necessity of introducing an irrelevant scaling variable. In addition, this approach is better suited to simulations with correlated random potentials such as is needed in quantum Hall or cold atom systems.

Localization-Delocalization Transition in Disordered One-Dimensional Exciton-Polariton System

The transition from the delocalized to the localized state has been investigated in a quasi-onedimensional exciton-polariton system excited nonresonantly in GaAs-based microcavity wire with disordered potential. The photoexcited polariton condensate has been found to spread along the wire with а velocity exceeding 1 μm/ps. The propagation along the wire is provided by high energy polaritons. The LP localization length decreases with decreasing blue shift of LPs in the excited spot. The polariton condensate returns to the Bose glass state when the blue shift of the LP resonance at the excitation spot decreases below the critical level that depends on the potential disorder.

An Analytical Approach for Electronic Properties of Semiconductors Quantum Well Wires

In this work a theoretical investigation of the electronic properties of quasi-one dimensional semiconductor systems is presented. An approximately analytical self-consistent approach is used for the calculation of the energy subbands and electron density. The electron – impurity and electron – electron interaction potentials are calculated for a two subband model, for a cylindrical quantum wire. The analytical results for the electron –impurity and electron-electron interaction potentials are in good agreement with the results of the model calculations. With my analytical results I discuss various aspects of the electronic properties of semiconductors quantum well wires, such as the binding energy of shallow impurity, screening, intrasubband Plasmon, and the mobility.

Majorana quasiparticles in semiconducting carbon nanotubes

Engineering effective p-wave superconductors hosting Majorana quasiparticles (MQPs) is nowadays of particular interest, also in view of the possible utilization of MQPs in fault-tolerant topological quantum computation. In quasi one-dimensional systems, the parameter space for topological superconductivity is significantly reduced by the coupling between transverse modes. Together with the requirement of achieving the topological phase under experimentally feasible conditions, this strongly restricts in practice the choice of systems which can host MQPs. Here we demonstrate that semiconducting carbon nanotubes (CNTs) in proximity with ultrathin s-wave superconductors, e.g. exfoliated NbSe$_2$, satisfy these needs. By precise numerical tight-binding calculations in the real space we show the emergence of localized zero-energy states at the CNT ends above a critical value of the applied magnetic field. Knowing the microscopic wave functions, we unequivocally demonstrate the Majorana nature of the localized states. An accurate analytical model Hamiltonian is used to calculate the topological phase diagram.

The influence of the dimensionality of the system on the realization of unconventional Fulde–Ferrell–Larkin–Ovchinnikov pairing in ultra-cold Fermi gases

The recent development of experimental techniques in ultracold atomic Fermi gases is extremely helpful in the progress of the realization of the unconventional Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superfluid phase in quasi-one dimensional systems (Liao et al 2010 Nature 467 567). Due to a Fermi surface nesting, which is enhanced in 1D, the low-dimensional systems are particularly good candidates to find the FFLO phase stable. We investigate the influence of a dimensional crossover (from one dimension (1D) to two dimensions (2D) or three dimensions (3D)) on the stability of the FFLO state in the spin-imbalanced attractive Hubbard model.

Universal spin dynamics in quantum wires

We discuss the universal spin dynamics in quasi one-dimensional systems including the real spin in narrow-gap semiconductors like InAs and InSb, the valley pseudospin in staggered single-layer graphene, and the combination of real spin and valley pseudospin characterizing single-layer transition metal dichalcogenides (TMDCs) such as MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$. All these systems can be described by the same Dirac-like Hamiltonian. Spin-dependent observable effects in one of these systems thus have counterparts in each of the other systems. Effects discussed in more detail include equilibrium spin currents, current-induced spin polarization (Edelstein effect), and spin currents generated via adiabatic spin pumping. Our work also suggests that a long-debated spin-dependent correction to the position operator in single-band models should be absent.