One-dimensional (1D) quantum wires, which are functionalized by magnetic ad-atoms, can host ballistic helical transport. Helicity protects transport from an undesirable influence of material imperfections, and it makes the magnetically doped wire a very promising element for nanoelectronics and spintronics. However, fabricating purely 1D conductors is experimentally very challenging and not always feasible. In this paper, we show that the protected helical transport can exist even in quasi-1D wires. We model the quasi-1D magnetically doped wire as two coupled dense 1D Kondo chains. Each chain consists of itinerant electrons interacting with localized quantum magnetic moments -- Kondo impurities. We have analyzed the regimes of weak-, intermediate-, and strong inter-chain coupling, and we found conditions necessary for the origin of the aforementioned protected transport. Our results may pave the way for experimental realizations of helical states in magnetically doped wires.
We study the plasmon excitations and the electromagnetic response of the magnetically doped single layer and multilayer of ``helical metals'', which emerge at the surfaces of topological insulators. For the single layer case, we find a ``spin-plasmon'' mode with the rotating spin texture due to the combination of the spin-momentum locking of ``helical metals'' and the Hall response from magnetization. For the multilayers case, we investigate the electromagnetic response due to the plasmon excitations, including the Faraday rotation for the light propagating normal to the helical metal layers a…
We show that the combination of a Dresselhaus interaction and a spatially periodic Rashba interaction leads to the formation of a helical liquid in a quantum wire when the electron-electron interaction is weakly screened. The effect is sustained by a helicity-dependent effective band gap which depends on the size of the Dresselhaus and Rashba spin-orbit couplings. We propose a design for a semiconductor device in which the helical liquid can be realized and probed experimentally.
We study the phase diagram and transport properties of arbitrarily doped quantum wires functionalized by magnetic adatoms. The appropriate theoretical model for these systems is a dense one-dimensional Kondo Lattice (KL) which consists of itinerant electrons interacting with localized quantum magnetic moments. We discover the novel phase of the locally helical metal where transport is protected from a destructive influence of material imperfections. Paradoxically, such a protection emerges without a need of the global helicity, which is inherent in all previously studied helical systems and re…
We study one dimensional wires with spin-orbit coupling. We show that in the presence of Zeeman field and strong electron-electron interaction a clean wire may form fractional helical liquid states with phenomenology similar to fractional quantum Hall liquids. Most notably, the wire's two terminal conductance is predicted to show fractional quantized conductance plateaus at low electron density. When the system is proximity-coupled to a superconductor, fractional Majorana bound states may be stabilized. We discuss how disorder destabilizes these fractional phases. Possible experimental realiza…
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 den…
We develop a theory of the correlated magnetically ordered insulating state at the edge of a two-dimensional topological insulator. We demonstrate that the gapped spin-polarized state, induced by the application of the magnetic field $B$, is naturally facilitated by electron interactions, which drive the critical easy-plane ferromagnetic correlations in the helical liquid. As the key manifestation, the gap $\De$ in the spectrum of collective excitations, which carry both spin and charge, is enhanced and exhibits a scaling dependence $\De \propto B^{1/(2-K)}$, controlled by the Luttinger liquid…
We propose and analyze inter-edge tunneling in a quantum spin Hall corner junction as a means to probe the helical nature of the edge states. We show that electron-electron interactions in the one-dimensional helical edge states result in Luttinger parameters for spin and charge that are intertwined, and thus rather different than those for a quantum wire with spin rotation invariance. Consequently, we find that the four-terminal conductance in a corner junction has a distinctive form that could be used as evidence for the helical nature of the edge states.
Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems like the B-phase of superfluid helium He$_3$, where vortices are associated with low energy excitations in the cores. Similarly, cosmic strings may be tied to propagating fermion modes. Can analogous phenomena occur in crystalline solids that host a plethora of topological defects? Here we show that indeed dislocation lines are associated with one dimensional fermionic excitations in a `topological insulator', a novel band insulator believed to be realized in the b…
We study four-terminal junction of spinless Luttinger liquid wires, which describes either a corner junction of two helical edges states of topological insulators or the tunneling from the spinful wire into the helical edge state. We use the fermionic representation and the scattering state formalism, in order to compute the renormalization group (RG) equations for the linear response conductances. We establish our approach by considering a junction between two possibly non-equivalent helical edge states and find an agreement with the earlier analysis of this situation. Tunneling from the tip …
We show that edges of Quantum Spin Hall topological insulators represent a natural platform for realization of exotic supersolid phase. On one hand, fermionic edge modes are helical due to the nontrivial topology of the bulk. On the other hand, a disorder at the edge or magnetic adatoms may produce a dense array of localized spins interacting with the helical electrons. The spin subsystem is magnetically frustrated since the indirect exchange favors formation of helical spin order and the direct one favors (anti)ferromagnetic ordering of the spins. At a moderately strong direct exchange, the c…
The dehydration of CuCl2*2(H2O) to CuCl2 leads to a dramatic change in magnetic behavior and ground state. Combining density functional electronic structure and model calculations with thermodynamical measurements we reveal the microscopic origin of this unexpected incident -- a crystal water driven switching of the magnetically active orbitals. This switching results in a fundamental change of the coupling regime from a three-dimensional antiferromagnet to a quasi one-dimensional behavior. CuCl2 can be well described as a frustrated J1-J2 Heisenberg chain with ferromagnetic exchange J1 and J2…
We study the exchange interaction and the subsequent collective behavior of magnetic impurities embedded in a disordered two-dimensional (2D) helical metal. The exchange coupling follows a statistical distribution whose moments are calculated to the lowest order in $\left(p_F\ell\right)^{-1}$, where $p_F$ is the Fermi momentum of itinerant electrons and $\ell$ is the mean free path. We find that i) the first moment of the distribution decays exponentially, and ii) the variance of the interaction is long-range, however, it becomes independent of the orientation of the localized magnetic moments…
We show that for a quantum wire with a local asymmetric scattering potential the principal channels for charge and heat rectification decouple and renormalise differently under electron interactions, with heat rectification generally being more relevant. The polarisation of the rectification results from quantum interference and is tuneable through external gating. Furthermore, for spin polarised or helical electrons and sufficiently strong interactions a regime can be obtained in which heat transport is strongly rectified but charge rectification is very weak.
We theoretically study tunneling of Cooper pairs from an s-wave superconductor into two semiconductor quantum wires with strong spin-orbit interaction under magnetic field, which approximate helical Luttinger liquids. The entanglement of electrons within a Cooper pair can be detected by the electric current cross correlations in the wires. By controlling the relative orientation of the wires, either lithographically or mechanically, on the substrate, the current correlations can be tuned, as dictated by the initial spin entanglement. This proposal of a spin-to-charge readout of quantum correla…
Magnetic Brightening and Nanoscale Imaging of Spin-Polarized Helical Edge Modes
Ames National Laboratory（艾姆斯国家实验室）；Department of Physics and Astronomy, Iowa State University（爱荷华州立大学物理与天文系）；Condensed Matter Physics and Materials Sciences Department, Brookhaven National Laboratory（布鲁海文国家实验室凝聚态物理与材料科学系）；Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文系）
One-dimensional lattice with strong spin-orbit interactions (SOI) and Zeeman magnetic field is shown to lead to the formation of a helical charge-density wave (CDW) state near half-filling. Interplay of the magnetic field, SOI constants and the CDW gap seems to support Majorana bound states under appropriate value of the external parameters. Explicit calculation of the quasi-particles' wave functions supports a formation of the localized zero-energy state, bounded to the sample end-points. Symmetry classification of the system is provided. Relative value of the density of states shows a precis…
We study the temperature dependence of the electrical conductance of a clean strongly interacting quantum wire in the presence of a helical nuclear spin order. The nuclear spin helix opens a temperature-dependent partial gap in the electron spectrum. Using a bosonization framework we describe the gapped electron modes by sine-Gordon-like kinks. We predict an internal resistivity caused by an Ohmic-like friction these kinks experience via interacting with gapless excitations. As a result, the conductance rises from $G=e^2/h$ at temperatures below the critical temperature when nuclear spins are …
We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum spin Hall system. This problem arose in context of the spin and charge fractionalization of an injected electron. Renormalization of the dc conductances of the system is calculated in the fermionic approach and scattering states formalism. In lowest order of tunneling amplitude we confirm previous results for the scaling dependence of conductances. Going beyond the lowest order we show that interaction affects not only the total tunneling rate, but also the asymmetry of the injected current. The h…
Fe3PO4O3 forms a non-centrosymmetric lattice structure (space group R3m) comprising triangular motifs of Fe^{3+} coupled by strong antiferromagnetic interactions (|Θ_{CW}| > 900 K). Neutron diffraction from polycrystalline samples shows that strong frustration eventually gives way to an ordered helical incommensurate structure below T_N = 163 K, with the helical axis in the hexagonal ab plane and a modulation length of ~ 86 Å. The magnetic structure consists of an unusual needle-like correlation volume that extends past 900 Åalong the hexagonal c-axis but is limited to ~ 70 Åin the ab plane, d…
SrCo2As2 is a peculiar itinerant magnetic system that does not order magnetically, but inelastic neutron scattering experiments observe the same stripe-type antiferromagnetic (AF) fluctuations found in many of the Fe-based superconductors along with evidence of magnetic frustration. Here we present results from neutron diffraction measurements on single crystals of Sr(Co1-xNix)2As2 that show the development of long-range AF order with Ni-doping. However, the AF order is not stripe-type. Rather, the magnetic structure consists of ferromagnetically-aligned (FM) layers (with moments laying in the…
The competing magnetic ground states of the itinerant magnet EuCuSb, which has a hexagonal layered structure, were studied via magnetization, resistivity, and neutron diffraction measurements on single-crystal samples. EuCuSb has a three-dimensional semimetallic band structure as confirmed by band calculation and angle-resolved photoelectron spectroscopy, consistent with the nearly isotropic metallic conductivity in the paramagnetic state. However, below the antiferromagnetic transition temperature of TN1 (8.5 K), the resistivity, especially along the hexagonal axis, increases significantly. T…
In frustrated spinel antiferromagnets, dilution with non-magnetic ions can be a powerful strategy for probing unconventional spin states or uncovering interesting phenomena. Here, we present X-ray, neutron scattering and thermodynamic studies of the effects of magnetic dilution of the tetragonally-distorted A-site spinel antiferromagnet, CuRh$_2$O$_4$, with non-magnetic Zn$^{2+}$ ions. Our data confirm the helical spin order recently identified at low-temperatures in this material, and further demonstrate a systematic suppression of the associated Néel temperature with increasing site dilution…
We study one-dimensional Kondo Lattices (KL) which consist of itinerant electrons interacting with Kondo impurities (KI) - localized quantum magnetic moments. We focus on KL with isotropic exchange interaction between electrons and KI and with a high KI density. The latter determines the principal róle of the indirect interaction between KI for the low energy physics. Namely, the Kondo physics becomes suppressed and all properties are governed by spin ordering. We present a first-ever comprehensive analytical theory of such KL at an arbitrary doping and predict a variety of regimes with differ…
Below a temperature of approximately 29 K the manganese magnetic moments of the cubic binary compound MnSi order to a long-range incommensurate helical magnetic structure. Here, we quantitatively analyze a high-statistic zero-field muon spin rotation spectrum recorded in the magnetically ordered phase of MnSi by exploiting the result of representation theory as applied to the determination of magnetic structures. Instead of a gradual rotation of the magnetic moments when moving along a <111> axis, we find that the angle of rotation between the moments of certain subsequent planes is essentiall…
We propose a platform for engineering helical fermions in a hybridized double-quantum-wire setup. When our setup is proximity coupled to an $s$-wave superconductor it can become a class $D$ topological superconductor exhibiting Majorana zero modes. The goal of this proposal is to expand the group of available Hamiltonians to those without strong Rashba spin-orbit interactions which are essential to many other approaches. Furthermore, we show that there exist electron-electron interactions that stabilize fractional excitations which obey $\mathbb{Z}^{\,}_{3}$ parafermionic algebra.
Magnetic properties of the $S = 1/2$ antiferromagnet $α$-Cu$_{2}$V$_{2}$O$_{7}$ have been studied using magnetization, Quantum Monte Carlo (QMC) simulations, and neutron diffraction. Magnetic susceptibility shows a broad peak at $\sim50$~K followed by an abrupt increase indicative of a phase transition to a magnetically ordered state at $T_{N}$ = 33.4(1) K. Above $T_N$, a fit to the Curie-Weiss law gives a Curie-Weiss temperature of $Θ=-73(1)$~K suggesting the dominant antiferromagnetic coupling. The result of the QMC calculations on the helical-honeycomb spin network with two antiferromagneti…
The magnetic system of the pseudobinary compound Mn$_{1-x}$Co$_{x}$Ge has been studied using small-angle neutron scattering and SQUID-measurements. It is found that Mn$_{1-x}$Co$_{x}$Ge orders magnetically at low temperatures in the whole concentration range of $x \in [0 ÷0.9]$. Three different states of the magnetic structure have been found: a short-periodic helical state at $x \leq 0.45$, a long-periodic helical state at $0.45 < x \leq 0.8$, and a ferromagnetic state at $x \sim 0.9$. Taking into account that the relatively large helical wavevector $k \gg 1$ nm$^{-1}$ is characteristic for s…
The physical properties of single-crystalline SmBe$_{13}$ with a NaZn$_{13}$-type cubic structure have been studied by electrical resistivity ($ρ$), specific heat ($C$), and magnetization ($M$) measurements in magnetic fields of up to 9 T. The temperature ($T$) dependence of $ρ$ shows normal metallic behavior without showing the Kondo -ln$T$ behavior, suggesting the weak hybridization effect in this system. Analyses of the temperature dependence of $C$ suggest that the Sm ions of this compound are trivalent and that the crystalline-electric-field (CEF) ground state is a $Γ_8$ quartet with a fi…
We have performed muon spin rotation/relaxation (muSR) measurements on single crystals of the chiral helimagnet Cr1/3NbS2 at zero to low magnetic field. The transition from the paramagnetic to helical magnetically ordered phase at zero field is marked by the onset of a coherent oscillation of the zero-field muon spin polarization below a critical temperature Tc. An enhancement of the muon spin precession frequency is observed below T ~ 50K, where anomalous behavior has been observed in bulk transport measurements. The enhanced precession frequency indicates a low-temperature modification of th…
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimension (2D) and three-dimension (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted …
We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit 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 …
In this work, we present a collection of three-dimensional higher-order symmetry protected topological phases (HOSPTs) with gapless hinge modes that exist only in strongly interacting systems subject to subsystem symmetry constraints. We use a coupled wire construction to generate three families of microscopic lattice models: insulators with helical hinge modes, superconductors with chiral Majorana hinge modes, and fractionalized insulators with helical hinge modes that carry fractional charge. In particular, these HOSPTs do not require spatial symmetry protection, but are instead protected by…
We have determined the terahertz spectrum of the chiral langasite Ba$_3$NbFe$_3$Si$_2$O$_{14}$ by means of synchrotron-radiation measurements. Two excitations are revealed that are shown to have a different nature. The first one, purely magnetic, is observed at low temperature in the magnetically ordered phase and is assigned to a magnon. The second one persits far into the paramagnetic phase and exhibits both an electric and a magnetic activity at slightly different energies. This magnetoelectric excitation is interpreted in terms of atomic rotations and requires a helical electric polarizati…
Neutron diffraction and 7Li-NMR have been applied to determine the multiferroic system LiCu2O2, which has four chains (ribbon chains) of edge-sharing CuO4 square planes in a unit cell. We have confirmed that there are successive magnetic transitions at TN1=24.5 K and TN2=22.8 K. In the T region between TN1 and TN2, the quasi one-dimensional spins (S=1/2) of Cu2+ ions within a chain have a collinear and sinusoidally modulated structure with Cu-moments parallel to the c-axis and with the modulation vector along the b-axis. At T < TN2, an ellipsoidal helical spin structure with the incommensurate…
