A key concept in the emerging field of spintronics is the electric field control of spin precession via the effective magnetic field generated by the Rashba spin orbit interaction (RSOI). Here, by extensive Density Matrix Renormalization Group computations, we demonstrate the presence of alternating spin current order in the gapped phases of a quantum wire with spatially modulated RSOI and repulsive electron-electron interactions. Our results are analytically supported by bosonization and by a mapping to a locally rotated spin basis.
We propose a spin valve device based on the interplay of a modulated spin-orbit interaction and a uniform external magnetic field acting on a quantum wire. Half-metal phases, where electrons with only a selected spin polarization exhibit ballistic conductance, can be tuned by varying the magnetic field. These half-metal phases are proven to be robust against electron-electron repulsive interactions. Our results arise from a combination of explicit band diagonalization, bosonization techniques and extensive DMRG computations.
We study a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in a two-dimensional array in the absence of a magnetic field. We analyze whether nearest-neighbor inter-wire interactions, stabilize the SLL phase. We construct an analogue of a Su-Schriefer-Heeger (SSH) model (allowing alternating couplings between wires). Calculating the scaling dimensions of the two most relevant perturbations, charge-density wave, and superconducting inter-wire couplings, but excluding the inter-wire single-particle hybridization, we find a finite stability regi…
We study the p-wave superconducting wire with a periodically modulated chemical potential and show that the Majorana edge states are robust against the periodic modulation. We find that the critical amplitude of modulated potential, at which the Majorana edge fermions and topological phase disappear, strongly depends on the phase shifts. For some specific values of the phase shift, the critical amplitude tends to infinity. The existence of Majorana edge fermions in the open chain can be characterized by a topological $Z_2$ invariant of the bulk system, which can be applied to determine the pha…
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with spatially modulated Dzyaloshinskii-Moriya interaction in the presence of applied along with the $\hat{z}$ axis alternating magnetic field. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of the magnetic field, the ground-state phase diagram of the model includes besides the ferromagnetic and gapless Luttiger-Liquid (LL) phases two gapped phases, the composite (C1) phase characterized by the coexistence of the long-range-ord…
We suggest a construction of a large class of topological states using an array of quantum wires. First, we show how to construct a Chern insulator using an array of alternating wires that contain electrons and holes, correlated with an alternating magnetic field. This is supported by semi-classical arguments and a full quantum mechanical treatment of an analogous tight-binding model. We then show how electron-electron interactions can stabilize fractional Chern insulators (Abelian and non-Abelian). In particular, we construct a relatively stable non-Abelian $\mathbb{Z}_{3}$ parafermion state.…
We study the ground-state properties of electrons confined to a quantum wire and subject to a smoothly modulated Rashba spin-orbit coupling. When the period of the modulation becomes commensurate with the band filling, the Rashba coupling drives a quantum phase transition to a nonmagnetic insulating state. Using bosonization and a perturbative renormalization group approach, we find that this state is robust against electron-electron interactions. The gaps to charge- and spin excitations scale with the amplitude of the Rashba modulation with a common interaction-dependent exponent. An estimate…
We study two-component fermions in optical lattices with spatially alternating on-site interactions using dynamical mean-field theory. Calculating the quasi-particle weight, double occupancy, and order parameters for each sublattice, we discuss the low-temperature properties of the system. When both interactions are repulsive, the magnetically ordered state is realized at half-filling. In the attractive case, the superfluid state is, in general, realized with a particle number imbalance. On the other hand, when repulsive and attractive interactions are comparable in the half-filled system, the…
It was recently shown that a spatially modulated Rashba spin-orbit coupling in a quantum wire drives a transition from a metallic to an insulating state when the wave number of the modulation becomes commensurate with the Fermi wave length of the electrons in the wire. It was suggested that the effect may be put to practical use in a future spin transistor design. In the present article we revisit the problem and present a detailed analysis of the underlying physics. First, we explore how the build-up of charge density wave correlations in the quantum wire due to the periodic gate configuratio…
We study a one-dimensional spin-1/2 XXZ Heisenberg model with alternating Dzyaloshinskii- Moriya interaction, using the numerical Lanczos method. Recently, the ground state (GS) phase diagram of this model has been established using the bosonization approach and extensive density matrix renormalization group computations. Four quantum phases - saturated ferromagnetic (FM), Luttinger liquid (LL), and two (C1 and C2) gapped phases with composite structure of GS order, characterized by the coexistence of long-range alternating dimer, chirality and antiferromagnetic order have been identified. Her…
The ground state phase diagram of a spin $S=1/2$ $XXZ$ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya (DM) interaction $ {\cal H}= \sum_n J\left[\left(S^x_n S^x_{n+1} +S^y_n S^y_{n+1}+ΔS^z_n S^z_{n+1}\right)+(D_0+(-1)^n D_1)\left(S^x_n S^y_{n+1} -S^y_n S^{x}_{n+1} \right) \right] $ is studied using the continuum-limit bosonization approach and extensive density matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double frequency sine-Gordon model (DSG) where the frequences i.e. the scaling dime…
We study the ground-state magnetic phase diagram of a spin S=1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin $σ=1/2$ XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes int…
Quantum wires with spin-orbit coupling provide a unique opportunity to simultaneously control the coupling strength and the screened Coulomb interactions where new exotic phases of matter can be explored. Here we report on the observation of an exotic spin-orbit density wave in Pb-atomic wires on Si(557) surfaces by mapping out the evolution of the modulated spin-texture at various conditions with spin- and angle-resolved photoelectron spectroscopy. The results are independently quantified by surface transport measurements. The spin polarization, coherence length, spin dephasing rate, and the …
We describe a strategy for using resonant soft x-ray scattering (RSXS) to study the electronic structure of transition metal oxide quantum wires. Using electron beam lithography and ion milling, we have produced periodic, patterned arrays of colossal magnetoresistance (CMR) phase La(1-x)Sr(x)MnO(3) consisting of ~ 5000 wires, each of which is 80 nm in width. The scattered intensity exhibits a series of peaks that can be interpreted as Bragg reflections from the periodic structure or, equivalently, diffraction orders from the grating-like structure. RSXS measurements at the Mn L(2,3) edge, whic…
We grow a tiled structure of insulating two dimensional LaAlO3/SrTiO3 interfaces composed of alternating one and three LaAlO3 unit cells. The boundary between two tiles is conducting. At low temperatures this conductance exhibits quantized steps as a function of gate voltage indicative of a one dimensional channel. The step size of half the quantum of conductance is an evidence for absence of spin degeneracy.
We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpaired Majorana zero-energy modes, using an all-electric setup with a spin-orbit coupled quantum wire in proximity to an s-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. While an implementation in a hybrid superconductor-semiconductor dev…
Two-leg spin-$\frac12$ ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to a sum of two (even/odd) XY quantum chains in the alternating transverse fields. The mapping between the effective Hamiltonian of the ladder and the pair of the dual XY chains considerably simplifies calculations the order parameters and analysis of the hidden symmetry brea…
We discuss the Luttinger Liquid behaviour of a semiconducting Quantum Wire. We show that the measured value of the bulk critical exponent, $α_{bulk}$, for the tunneling density of states can be easily calculated. Then, the problem of the transport through a Quantum Dot formed by two Quantum Point Contacts along the Quantum Wire, weakly coupled to spinless Tomonaga-Luttinger liquids is studied, including the action of a strong transverse magnetic field $B$. The known magnetic dependent peaks of the conductance, $G(B)$, in the ballistic regime at a very low temperature, $T$, have to be reflected…
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 …
