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We study interaction-induced backscattering mechanism for helical edge states of a two dimensional topological insulator which is tunnel-coupled to a puddle located near the edge channel. The mechanism does not involve inelastic scattering and is due to the zero-mode fluctuations in a puddle. We discuss in detail a simple model of a puddle - a cavity in the bulk of the topological insulator. Such a cavity also has helical edge states which are tunnel-coupled with helical states encompassing the topological insulator. We analyze effect of the edge current in the puddle. Although averaged value of this current is equal to zero, its zero-mode fluctuations act, in the presence of electron-electron interaction, similar to magnetic flux thus allowing backscattering processes, which involve tunneling through the puddle. Rectification of these fluctuations leads to a finite probability of backscattering. This effect is further enhanced due to dephasing process which is also dominated by zero-mode fluctuations. Remarkably, for temperature exceeding level spacing in the puddle, the rate of backscattering does not depend on temperature in a good agreement with recent experiments., Comment: 7 pages, 2 figures

We study the shot noise of current through the edge states of a two-dimensional topological insulator placed in magnetic field and compare the obtained results with the shot noise in conventional single-channel spinless Aharonov-Bohm interferometer. We find general formulas for the Fano factors of these setups, assuming that temperature exceeds level spacing in the system. We demonstrate that both in helical and in conventional case the interference effects dramatically change the Fano factor and its magnetic field dependence. For weak tunneling coupling with leads, the Fano factors of both setups exhibit a periodic series of sharp Aharonov-Bohm peaks with variation of magnetic flux piercing the system. Our key finding is that the Fano factor in the helical interferometer provides information about the presence of backscattering defects violating topological protection. In particular, the amplitude of Aharonov-Bohm peaks in the helical setup is proportional to the strength of the defect in contrast to conventional setup, where peaks have finite amplitude even in the ballistic case., Comment: 16 pages, 10 figures

We study a superlattice formed by tunnel-coupled identical antidots periodically situated in a two-dimensional topological insulator placed in a magnetic field. The superlattice spectrum can be controlled by gate electrodes or by changing the magnetic flux through the antidots. We demonstrate that a topologically protected qubit appears at the boundary between two regions with different fluxes. The qubit properties depend on the value of the flux jump on the boundary and can be controlled by the gate voltage. We derive the effective Hamiltonian of such a qubit and analyze the dependence of its properties on the main parameters of the superlattice: the tunnel coupling between antidots, and the probability of jumps with the spin flip., Comment: 8 pages, 2 figures

We consider a superlattice formed by tunnel-connected identical holes, periodically placed in a two-dimensional topological insulator. We study tunneling transport through helical edges of these holes and demonstrate that the band structure of such helical crystal can be controlled by both gate electrodes and external magnetic filed. For integer and half-integer values of dimensionless magnetic flux through the holes, the spectrum possesses Dirac points whose positions and velocities can be tuned by gates. The deviation of magnetic flux from these special values by $\delta \phi$ makes the Dirac cones massive, with the gap value $\Delta \propto |\delta \phi|$. At certain gate-dependent values of $\delta \phi$ different Dirac points converge to a double Dirac point and then disappear with further increase of $\delta \phi.$ Interaction between carriers may lead to strong renormalization of parameters $\alpha$ and $\beta$ controlling total tunnel coupling between holes and spin flip tunneling processes, respectively. We plot the renormalization flow in the plane $(\alpha,\beta)$ and demonstrate multicritical behavior of the crystal -- there is a multicritical fully unstable fixed point separating three different phases: independent rings, independent shoulders, and perfect spin-flip channels. We also find that defects in the crystal may lead to a formation of topologically protected qubits which are not destroyed by temperature and can be also manipulated both by gates and by magnetic field. The possibility of purely electrical high-temperature control of the qubits opens a wide avenue for applications in the area of quantum computing., Comment: 15 pages, 11 figures

We discuss transport through an interferometer formed by helical edge states of the quantum spin Hall insulator. Focusing on effects induced by a strong magnetic impurity placed in one of the arms of interferometer, we consider the experimentally relevant case of relatively high temperature as compared to the level spacing. We obtain the conductance and the spin polarization in the closed form for arbitrary tunneling amplitude of the contacts and arbitrary strength of the magnetic impurity. We demonstrate the existence of quantum effects which do not show up in previously studied case of weak magnetic disorder. We find optimal conditions for spin filtering and demonstrate that the spin polarization of outgoing electrons can reach 100%., Comment: 6 pages, 4 figures

The renormalization of conductances in a Y junction of spinless Luttinger-liquid wires additionally coupled to acoustic longitudinal phonons is investigated in fermionic representation. This system corresponds to geometry of a tunneling experiment and exhibits the interplay between the Coulomb repulsion and the attractive retarded interaction mediated by phonons. The retardation effects related to the propagation of phonons through the junction with arbitrary transmission and reflection amplitudes are taken into account. The appearing logarithmic corrections to conductances of the junction are treated in a renormalization group approach, and scaling exponents are calculated up to infinite order in the interaction after RPA-type summation. The fixed points and corresponding scaling exponents are considered in various non-equilibrium regimes. We show that the boundary exponent and the bulk anomalous dimension of fermion operator are characterized by two different Luttinger parameters, referring to the main wire, thanks to non-local character of phonon-mediated interaction. In the limiting case of the junction of only two wires, the scaling exponents found by our method are in exact correspondence with previous bosonization analysis., Comment: 20 pages, 10 figures

We study coherent spin transport through helical edge states of topological insulator tunnel-coupled to metallic leads. We demonstrate that unpolarized incoming electron beam acquires finite polarization after transmission through such a setup provided that edges contain at least one magnetic impurity. The finite polarization appears even in the fully classical regime and is therefore robust to dephasing. There is also a quantum magnetic field-tunable contribution to the polarization, which shows sharp identical Aharonov-Bohm resonances as a function of magnetic flux - with the period $hc/2e$ - and survives at relatively high temperature. We demonstrate that this tunneling interferometer can be described in terms of ensemble of flux-tunable qubits giving equal contributions to conductance and spin polarization. The number of active qubits participating in the charge and spin transport is given by the ratio of the temperature and the level spacing. The interferometer can effectively operate at high temperature and can be used for quantum calculations. In particular, the ensemble of qubits can be described by a single Hadamard operator. The obtained results open wide avenue for applications in the area of quantum computing., Comment: 15 pages, 9 figures

We discuss transport through interferometer formed by helical edge states tunnel-coupled to metallic leads. We focus on the experimentally relevant case of relatively high temperature as compared to the level spacing and discuss a response of the setup to the external magnetic flux $\phi$ (measured in units of flux quantum) piercing the area encompassed by edge states. We demonstrate that tunneling conductance of the interferometer is structureless in ballistic case but shows a sharp antiresonances, as a function of magnetic flux $\phi$ - with the period 1/2 - in the presence of magnetic impurity. We interpret the resonance behavior as a coherent enhancement of backward scattering off magnetic impurity at integer and half-integer values of flux, which is accompanied by suppression of the effective scattering at other values of flux. Both enhancement and suppression are due to the interference of processes with multiple returns to magnetic impurity after a number of clockwise and counterclockwise revolutions around setup. This phenomenon is similar to the well-known weak-localization-induced enhancement of backscattering in disordered systems. The quantum correction to the tunneling conductance is shown to be proportional to flux-dependent "ballistic Cooperon". The obtained results can be used for flux-tunable control of the magnetic disorder in Aharonov-Bohm interferometers built on helical edge states., Comment: 13 pages, 7 figures

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 helical edge state forbids the backscattering, which leads to the possibility of two stable fixed points in renormalization group sense, in contrast to the Y-junction between the usual quantum wires., Comment: 9 pages, 5 figures

Light scattering in a magnetic medium with uncorrelated inclusions is theoretically studied in the approximation of ladder diagram. Correlation between polarizations of electromagnetic waves that are produced by infinitely-distant dipole source is considered. Here white noise disorder model with Gaussian distribution is taken into account. In such a medium the magneto-optical interaction leads to correlation between perpendicular light polarizations. Spatial field correlation matrix with nonzero nondiagonal elements is obtained in the first order on gyration., Comment: 6 pages, 3 figures

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 of the spinful wire to the edge state is further analyzed which requires some modification of our formalism. In the latter case we demonstrate i) the existence of both fixed lines and conventional fixed points of RG equations, and ii) certain proportionality relations holding for conductances during renormalization. The scaling exponents and phase portraits are obtained in all cases., Comment: 10 pages, 6 figures

We study four-lead junction of semi-infinite wires by using fermionic representation in the scattering state formalism. The model of spinless fermions with short-range Luttinger liquid type interaction is used. We find the renormalization group (RG) equations for the conductances of the system in the first order of fermionic interaction. In contrast to the well-known cases of two-lead and three-lead junctions, we show that the RG equations cannot be expressed solely in terms of conductances. The appearing ambiguity is resolved by choosing a certain sign defined at the level of S-matrix, but hidden in conductances. The origin of this Z_2 symmetry is traced back to the particle-hole symmetry of our Hamiltonian. We demonstrate two distinct RG flows from any point in the space of conductances. The scaling exponents at the fixed points are not affected by these observations., Comment: 13 pages, 3 figures

We have measured the 3He(e,e'pp)n reaction at 2.2 GeV over a wide kinematic range. The kinetic energy distribution for `fast' nucleons (p > 250 MeV/c) peaks where two nucleons each have 20% or less, and the third nucleon has most of the transferred energy. These fast pp and pn pairs are back-to-back with little momentum along the three-momentum transfer, indicating that they are spectators. Experimental and theoretical evidence indicates that we have measured distorted two-nucleon momentum distributions by striking the third nucleon and detecting the spectator correlated pair., Comment: 6 pages, 5 figures, submitted to PRL

We have measured the $^3$He(e,e$'$pp)n{} reaction in the Jefferson Lab CLAS with 2.2 and 4.4 GeV electrons. We looked at the energy distribution of events with all three nucleons at high momentum (p > 250 MeV/c). This distribution has peaks where two nucleons each have 20% or less of the energy transfer (ie: the third or `leading' nucleon carries most of the kinetic energy). The angular distribution of these two `fast' nucleons shows a very large back-to-back peak, indicating the effect of correlations. While there is some theoretical disagreement, experimental evidence, plus calculations at lower energy by W. Glockle, indicates that these events are primarily sensitive to NN correlations., Comment: 4 pages, 4 included figures, invited talk at the Conference on Electron-Nucleus Scattering VII, Elba, Italy, June 2002 Version 2: corrected references