Ballistic transport of helical edge modes in two-dimensional topological insulators is protected by time-reversal symmetry. Recently it was pointed out [1] that coupling of non-interacting helical electrons to an array of randomly anisotropic Kondo impurities can lead to a spontaneous breaking of the symmetry and, thus, can remove this protection. We have analyzed effects of the interaction between the electrons using a combination of the functional and the Abelian bosonization approaches. The suppression of the ballistic transport turns out to be robust in a broad range of the interaction strength. We have evaluated the renormalization of the localization length and have found that, for strong interaction, it is substantial. We have identified various regimes of the dc transport and discussed its temperature and sample size dependencies in each of the regimes.
We develop a theory of finite-temperature momentum-resolved tunneling spectroscopy (MRTS) for disordered, interacting two-dimensional topological-insulator edges. The MRTS complements conventional electrical transport measurement in characterizing the properties of the helical Luttinger liquid edges. Using standard bosonization technique, we study low-energy spectral function and the MRTS tunneling current, providing a detailed description controlled by disorder, interaction, and temperature, taking into account Rashba spin orbit coupling, interedge interaction and distinct edge velocities. Ou…
We provide analytic expressions for the Green's functions in position-frequency space as well as for the tunneling density of states of various Luttinger liquids at zero temperature: the standard spinless and spinful Luttinger liquids, the helical Luttinger liquid at the edge of a topological insulator, and the Luttinger liquid that appears either together with an ordering transition of nuclear spins in a one-dimensional conductor, or in spin-orbit split quantum wires in an external magnetic field. The latter system is often used to mimic a helical Luttinger liquid, yet we show here that it ex…
We show that the paradigmatic Ruderman-Kittel-Kasuya-Yosida (RKKY) description of two local magnetic moments coupled to propagating electrons breaks down in helical Luttinger Liquids when the electron interaction is stronger than some critical value. In this novel regime, the Kondo effect overwhelms the RKKY interaction over all macroscopic inter-impurity distances. This phenomenon is a direct consequence of the helicity (realized, for instance, at edges of a time-reversal invariant topological insulator) and does not take place in usual (non-helical) Luttinger Liquids.
We analyze the time evolution of spin-polarized electron wave packets injected into the edge states of a two-dimensional topological insulator. In the presence of electron interactions, the system is described as a helical Luttinger liquid and injected electrons fractionalize. However, because of the presence of metallic detectors, no evidences of fractionalization are encoded in dc measurements, and in this regime the system do not show deviations from its non-interacting behavior. Nevertheless, we show that the helical Luttinger liquid nature emerges in the transient dynamics, where signatur…
The combined effect of Rashba and Dresselhaus spin-orbit interactions on the physics of a helical Luttinger liquid coupled to a Kondo impurity is studied. A Rashba coupling can potentially destroy the Kondo singlet formation in certain parameter regimes [Phys. Rev. B 86, 161103(R) (2012)]. This effect is here shown to vanish for sufficiently strong Dresselhaus interaction. The transport properties of the system are investigated by calculating electrical conductance, current and current fluctuations, and thermal conductance.
Helical Luttinger liquids, appearing at the edge of two-dimensional topological insulators, represent a new paradigm of one-dimensional systems, where peculiar quantum phenomena can be investigated. Motivated by recent experiments on charge fractionalization, we propose a setup based on helical Luttinger liquids that allows to time-resolve, in addition to charge fractionalization, also spin-charge separation and pure spin fractionalization. This is due to the combined presence of spin-momentum locking and interactions. We show that electric time-resolved measurements can reveal both charge and…
We propose and study the charge transport through single and double quantum point contacts setup between helical Majorana modes and an interacting helical Luttinger liquid. We show that the differential conductance decreases for stronger repulsive interactions and that the point contacts become insulating above a critical interaction strength. For a single point contact, the differential conductance as a function of bias voltage shows a series of peaks due to Andreev reflection of electrons in the Majorana modes. In the case of two point contacts, interference phenomena make the structure of t…
We propose a three terminal spin polarized stm setup for probing the helical nature of the Luttinger liquid edge state that appears in the quantum spin Hall system. We show that the three-terminal tunneling conductance strongly depends on the angle ($θ$) between the magnetization direction of the tip and the local orientation of the electron spin on the edge while the two terminal conductance is independent of this angle. We demonstrate that chiral injection of an electron into the helical Luttinger liquid (which occurs when $θ$ is zero or $π$) is associated with fractionalization of the spin …
We demonstrate the possibility to induce and control peculiar spin textures in a helical Luttinger liquid, by means of a time-dependent magnetic scatterer. The presence of a perturbation that breaks the time-reversal symmetry opens a gap in the spectrum, inducing single-particle backscattering and a peculiar spin response. We show that in the weak backscattering regime asymmetric spin textures emerge at the left and right side of the scatterer, whose spatial oscillations are controlled by the ratio between the magnetization frequency and the Fermi energy and by the electron interaction. This p…
The tunnel current of a Luttinger liquid with a finite density of strong impurities is calculated using an instanton approach. For very low temperatures $T$ or electric fields $E$ the (nonlinear) conductivity is of variable range hopping (VRH) type as for weak pinning. For higher temperatures or fields the conductivity shows power law behavior corresponding to a crossover from multi- to single-impurity tunneling. For even higher $T$ and not too strong pinning there is a second crossover to weak pinning. The determination of the position of the various crossover lines both for strong and weak p…
We investigate the low-energy properties of (quasi) helical and fractional helical Luttinger liquids. In particular, we calculate the Drude peak of the optical conductivity, the density of states, as well as charge transport properties of the interacting system with and without attached Fermi liquid leads at small and large (compared to the gap) frequencies. For fractional wires, we find that the low energy tunneling density of states vanishes. The conductance of a fractional helical Luttinger liquid is non-integer. It is independent of the Luttinger parameters in the wire, despite the intrica…
A Cooper-pair or electron-hole splitter is a device capable of spatially separating entangled fermionic quasiparticles into mesoscopic solid-state systems such as quantum dots or quantum wires. We theoretically study such a splitter based on a pair of helical Luttinger liquids, which arise naturally at the edges of a quantum spin Hall insulator. Equipping each helical liquid with a beam splitter, current-current cross correlations can be used to construct a Bell inequality whose violation would indicate nonlocal orbital entanglement of the injected electrons and/or holes. Due to Luttinger-liqu…
The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.
We report on quantum interference between a pair of counterpropagating quantum Hall edge states that are separated by a high quality tunnel barrier. Observed Aharonov-Bohm oscillations are analyzed in terms of resonant tunneling between coupled Luttinger liquids that creates bound electronic states between pairs of tunnel centers that act like interference slits. We place a lower bound in the range of 20-40 $μ$m for the phase coherence length and directly confirm the extended phase coherence of quantum Hall edge states.
We theoretically study Coulomb drag between two helical edges with broken spin-rotational symmetry, such as would occur in two capacitively coupled quantum spin Hall insulators. For the helical edges, Coulomb drag is particularly interesting because it specifically probes the inelastic interactions that break the conductance quantization for a single edge. Using the kinetic equation formalism, supplemented by bosonization, we find that the drag resistivity $ρ_D$ exhibits a nonmonotonic dependence on the temperature $T$. In the limit of low $T$, $ρ_D$ vanishes with decreasing $T$ as a power law…
We study the quantum point contact between the topological superconductor and the helical Luttinger liquid. The effects of the electron-electron interactions in the helical Luttinger liquid on the low-energy physics of this system are analyzed by the renormalization group. Among the various couplings at the point contact which arise from the tunneling via the Majorana edge channel, the induced backscattering in the helical Luttinger liquid is the most relevant for repulsive interactions. Hence, at low temperatures, the helical Luttinger liquid is effectively cut into two separated half wires. …
We study a steady state non-equilibrium transport between two interacting helical edge states of a two dimensional topological insulator, described by helical Luttinger liquids, through a quantum dot. For non-interacting dot the current is obtained analytically by including the self-energy correction to the dot Green's function. For interacting dot we use equation of motion method to study the influence of weak on-site Coulomb interaction on the transport. We find the metal-to-insulator quantum phase transition for attractive or repulsive interactions in the leads when the magnitude of the int…
We calculate the finite-temperature local spectral weight (LSW) of a Luttinger liquid with an "open" (hard wall) boundary. Close to the boundary the LSW exhibits characteristic oscillations indicative of spin-charge separation. The line shape of the LSW is also found to have a Fano-like asymmetry, a feature originating from the interplay between electron-electron interaction and scattering off the boundary. Our results can be used to predict how edges and impurities influence scanning tunneling microscopy (STM) of one-dimensional electron systems at low temperatures and voltage bias. Applicati…
We derive and analyze the effective low-energy theory for interacting electrons in a cylindrical nanowire made of a strong topological insulator. Three different approaches provide a consistent picture for the band structure, where surface states forming inside the bulk gap correspond to one-dimensional bands indexed by total angular momentum. When a half-integer magnetic flux pierces the nanowire, we find a strongly correlated helical Luttinger liquid topologically protected against weak disorder. We describe how transport experiments can detect this state.
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…
The weakly interacting helical Luttinger liquid, due to spin momentum locking, is characterized by extremely peculiar local observables: we show that the density-density correlation functions do not exhibit signatures of Friedel and Wigner oscillations, and that spin-spin correlation functions, which are strongly anisotropic, witness the formation of a planar spin wave. Moreover, we demonstrate that the most relevant scattering potentials involving a localized impurity are not able to modify the electron density, while only magnetic impurities can pin the planar spin density wave.
Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations. Here we investigate transport properties of hDWs in the $ν=2/3$ fractional QH regime. Experimentally we found that current carried by hDWs is substantially smalle…
We study the problem of underscreened Kondo physics in an interacting electronic system modeled by a Luttiger Liquid (LL). We find that the leading temperature dependence of thermodynamical quantities like the specific heat, spin susceptibility are Fermi Liquid like in nature. However, anomalous power law exponents are seen in the subleading terms. We also discuss possible realizations through single and double quantum dot configurations coupled to LL leads and its consequences for electronic transport. The leading low temperature transport behavior is seen to exhibit in general, non Fermi liq…
We consider a four-terminal Aharonov-Bohm interference setup formed out of two edges of a quantum spin Hall insulator, supporting helical Luttinger liquids (HLLs). We show that the temperature and bias dependence of the interference oscillations are linked to the amount of spin flips in tunneling between two HLLs which is a unique signature of a HLL. We predict that spin dephasing depends on the electron-electron (e-e) interaction but differently from the charge dephasing due to distinct dominant tunneling excitations. In contrast, in a spinful Luttinger liquid with SU(2) invariance, uncharged…
We improve the recently developed functional renormalization group (fRG) for impurities and boundaries in Luttinger liquids by including renormalization of the two-particle interaction, in addition to renormalization of the impurity potential. Explicit flow-equations are derived for spinless lattice fermions with nearest neighbor interaction at zero temperature, and a fast algorithm for solving these equations for very large systems is presented. We compute spectral properties of single-particle excitations, and the oscillations in the density profile induced by impurities or boundaries for ch…
We report on the observation of a helical Luttinger-liquid in the edge of InAs/GaSb quantum spin Hall insulator, which shows characteristic suppression of conductance at low temperature and low bias voltage. Moreover, the conductance shows power-law behavior as a function of temperature and bias voltage. The results underscore the strong electron-electron interaction effect in transport of InAs/GaSb edge states. Because of the fact that the Fermi velocity of the edge modes is controlled by gates, the Luttinger parameter can be fine tuned. Realization of a tunable Luttinger-liquid offers a one-…
We study the statistics of charge transfer through an impurity in a chiral Luttinger liquid (realized experimentally as a quantum point contact in a fractional quantum Hall edge state device). Taking advantage of the integrability we present a procedure for obtaining the cumulant generating function of the probability distribution to transfer a fixed amount of charge through the constriction. Using this approach we analyze in detail the behaviour of the third cumulant C_3 as a function of applied voltage, temperature and barrier height. We predict that C_3 can be used to measure the fractional…
We demonstrate the equivalence between two distinct Luttinger liquid impurity problems. The first concerns a one-dimensional topological superconductor coupled at one end to the ends of two single channel Luttinger liquids. The second concerns a point contact in the quantum spin Hall effect, where four helical Luttinger liquids meet at a point. Both problems have been studied previously and exhibit several stable phases depending on the Luttinger parameter K, that can be characterized in terms of simple conformally invariant boundary conditions describing perfect normal (or Andreev) transmissi…
We study the DC spin current induced into an unbiased quantum spin Hall system through a two-point contacts setup with time dependent electron tunneling amplitudes. By means of two external gates, it is possible to drive a current with spin-preserving and spin-flipping contributions showing peculiar oscillations as a function of pumping frequency, electron-electron interaction and temperature. From its interference patterns as a function of the Fabry-Perot and Aharonov-Bohm phases, it is possible to extract information about the helical nature of the edge states and the intensity of the electr…
We theoretically investigate the tunneling spectroscopy of a system of two parallel one-dimensional helical conductors in the interacting, Luttinger liquid regime. We calculate the non-linear differential conductance as a function of the voltage bias between the conductors and the orbital momentum shift induced on tunneling electrons by an orthogonal magnetic field. We show that the conductance map exhibits an interference pattern which is characteristic to the interacting helical liquid. This can be contrasted with the different interference pattern from tunneling between regular Luttinger li…
Electron backscattering in a Luttinger liquid with an impurity is investigated in the presence of zero point motion of the phonon lattice. The impurity can mean either a mass defect, an elastic defect or a pinning defect. The phonon spectrum is then affected by the presence of the defect, which enters in the renormalization group equations for backscattering. The RG equation becomes dependent on the energy cutoff for finite Debye frequency $ω_D$ giving rise to finite energy effects. We compute the local density of states and show how the renormalization group flow is affected by a finite $ω_D$…
Elastic backscattering of electrons moving along the helical edge is prohibited by time-reversal symmetry (TRS). We demonstrate, however, that an ensemble of magnetic impurities may cause TRS-preserving quasi-elastic backscattering, resulting in interference effects in the conductance. The characteristic energy transferred in a backscattering event is suppressed due to the RKKY interaction of localized spins (the suppression is exponential in the total number of magnetic impurities). We predict the statistics of conductance fluctuations to differ from those in the conventional case of a one-di…
Dynamical magnetic impurities (MI) are considered as a possible origin for suppression of the ballistic helical transport on edges of 2D topological insulators. The MIs provide a spin-flip backscattering of itinerant helical electrons. Such a backscattering reduces the ballistic conductance if the exchange interaction between the MI and the electrons is anisotropic and the Kondo screening is unimportant. It is well-known that the isotropic MIs do not suppress the helical transport in systems with axial spin symmetry of the electrons. We show that, if this symmetry is broken, the isotropic MI a…
We investigate the response of 3D Luttinger semimetals to localized charge and spin impurities as a function of doping. The strong spin-orbit coupling of these materials strongly influences the Friedel oscillations and RKKY interactions. This can be seen at short distances with an $1/r^4$ divergence of the responses, and anisotropic behavior. Certain of the spin-orbital signatures are robust to temperature, even if the charge and spin oscillations are smeared out, and give an unusual diamagnetic Pauli susceptibility. We compare our results to the experimental literature on the bismuth-based ha…
We consider the superconducting proximity effect in a helical Luttinger liquid at the edge of a 2D topological insulator, and derive the low-energy Hamiltonian for an edge state tunnel-coupled to a s-wave superconductor. In addition to correlations between the left and right moving modes, the coupling can induce them inside a single mode, as the spin axis of the edge modes is not necessarily constant. This can be induced controllably in HgTe/CdTe quantum wells via the Rashba spin-orbit coupling, and is a consequence of the 2D nature of the edge state wave function. The distinction of these two…
Coulomb interaction has important consequences on the physics of quantum spin Hall edge states, weakening the topological protection via two-particle scattering and renormalizing both the velocity and charge of collective plasmon modes compared to that of free electrons. Despite these effects, interactions remain difficult to quantify. We propose here simple and robust edge resonator geometries to characterize Coulomb interaction by means of high-frequency measurements. They rely on a transmission line approach, and take advantage of the impedance mismatch between the edge states and their mic…
The local density of states (LDOS) in a one-dimensional helical channel of finite length is studied within a Tomonaga-Luttinger model at zero temperature. Two particular cases of loop and Josephson junction geometries are considered. The LDOS, as a function of energy $ω$ measured from the Fermi level, consists of equally spaced spikes of the $δ$-function type, and electron-electron interactions modify their relative height. It is shown that, in the loop geometry, the height of spikes decreases as $ω\to 0$ everywhere in the system. It is also shown that, in the Josephson junction, the behavior …
We consider a superconductor-two dimensional topological insulator- superconductor junction (S-2DTI-S) and study how the 2π- and 4π-periodic Josephson currents are affected by the electron-electron interaction. In the long-junction limit the supercurrent can by evaluated by modeling the system as a helical Luttinger liquid coupled to superconducting reservoirs. After having introduced bosonization in the presence of the parity constraint we turn to consider the limit of perfect and poor interfaces. For transparent interfaces, where perfect Andreev reflections occur at the boundaries, the Josep…
The indirect exchange interaction between magnetic impurities located in the bulk of a two-dimensional topological insulator decays exponentially with the distance. The indirect exchange interaction for magnetic impurities mediated by the helical states at the edge of the topological insulator demonstrates behaviour which is typical for the Ruderman-Kittel-Kasuya-Yosida interaction in a one-dimensional metal. We have shown that interference between the bulk and edge states in the two-dimensional topological insulator results in existence of the unusual contribution to the indirect exchange int…
Helical edge states appear at the surface of two dimensional topological insulators and are characterized by spin up traveling in one direction and the spin down traveling in the opposite direction. Such states are protected by time reversal symmetry and no backscattering due to scalar impurities can occur. However, magnetic impurities break time reversal symmetry and lead to backscattering. Often their presence is unintentional, but in some cases they are introduced into the sample to open up gaps in the spectrum. We investigate the influence of random impurities on helical edge states, speci…
We analyze the Ruderman-Kettel-Kasuya-Yosida(RKKY) interaction between magnetic impurities embedded in the helical metal on the surface of three-dimensional topological insulators. Apart from the conventional RKKY terms, the spin-momentum locking of conduction electrons also leads to a significant Dzyaloshinskii-Moriya (DM) interaction between impurity spins. For a chain of magnetic impurities, the DM term can result in single-handed spin helix on the surface. The handedness of spin helix is locked with the sign of Fermi velocity of the emergent Dirac fermions on the surface. We also show the …
Non-equilibrium transport properties of charge and spin sector of two edges of a quantum spin Hall insulator are investigated theoretically in a four-terminal configuration. A simple duality relation between charge and spin sector is found for two helical Tomonaga Luttinger liquids (hTTLs) connected to non-interacting electron reservoirs. If the hTLLs on opposite edges are coupled locally or non-locally, the mixing between them yields interesting physics where spin information can be easily detected by a charge measurement and vice versa. Particularly, we show how a pure spin density in the ab…
In this work, analytical expressions for the Green function of a Luttinger liquid are derived with one and two mobile impurities (heavy particles) using a combination of bosonization and perturbative approaches. The calculations are done in the random phase approximation (RPA) limit using the powerful non-chiral bosonization technique (NCBT) which is nothing but the resummation of the most singular parts of the RPA terms of the Green function expanded out in powers of the forward scattering between fermions with the source of inhomogeneities treated exactly. The force acting on the heavy parti…
We study the quasiparticle interference (QPI) patterns caused by scattering off nonmagnetic, magnetic point impurities, and edge impurities, separately, in a two dimensional helical liquid, which describes the surface states of a topological insulator. The unique features associated with hexagonal warping effects are identified in the QPI patterns of charge density with nonmagnetic impurities and spin density with magnetic impurities. The symmetry properties of the QPI patterns can be used to determine the symmetry of microscopic models. The Friedel oscillation is calculated for edge impuritie…
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 study a quantum phase transition which occurs in a system composed of two impurities (or quantum dots) each coupled to a different interacting (Luttinger-liquid) lead. While the impurities are coupled electrostatically, there is no tunneling between them. Using a mapping of this system onto a Kondo model, we show analytically that the system undergoes a Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the Luttinger liquid parameter in the leads and the dot-lead interaction. The phase with low values of the Luttinger-liquid parameter is characterized by an abrupt switc…
We develop a continuous-time quantum Monte Carlo (CTQMC) method for quantum impurities coupled to interacting quantum wires described by a Tomonaga-Luttinger liquid. The method is negative-sign free for any values of the Tomonaga-Luttinger parameter, which is rigorously proved, and thus, efficient low-temperature calculations are possible. Duality between electrons and bosons in one dimensional systems allows us to construct a simple formula for the CTQMC algorithm in these systems. We show that the CTQMC for Tomonaga-Luttinger liquids can be implemented with only minor modifications of previo…
We study transport properties in a Tomonaga-Luttinger liquid in the presence of two time-dependent point like weak impurities, taking into account finite-length effects. By employing analytical methods and performing a perturbation theory, we compute the backscattering pumping current (I_bs) in different regimes which can be established in relation to the oscillatory frequency of the impurities and to the frequency related to the length and the renormalized velocity (by the electron-electron interactions) of the charge density modes. We investigate the role played by the spatial position of th…
We investigate theoretically indirect exchange interaction between magnetic impurities mediated by one-dimensional gapped helical states. Such states, containing massive Dirac fermions, may be realized on the edge of a two-dimensional topological insulator when time-reversal symmetry is weakly broken. We find that the indirect exchange interaction consists of Heisenberg, Dzyaloshinsky-Moriya, in-plane and out-of-plane Ising terms. These terms decay exponentially when Fermi level lies inside the bandgap whereas the Dzyaloshinsky-Moriya term has smallest amplitude. Outside the energy gap the mas…
We consider chiral electrons moving along the 1D helical edge of a 2D topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.
We study how a Luttinger liquid of spinless particles in one dimension approaches thermal equilibrium. Full equilibration requires processes of backscattering of excitations which occur at energies of order of the bandwidth. Such processes are not accounted for by the Luttinger liquid theory. We treat the high-energy excitations as mobile impurities and derive an expression for the equilibration rate in terms of their spectrum. Our results apply at any interaction strength.
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.
We demonstrate that electrostatic interactions between helical electrons at the edge of a quantum spin Hall insulator and a dynamical impurity can induce quasi-elastic backscattering. Modelling the impurity as a two-level system, we show that transitions between counterpropagating Kramers-degenerate electronic states can occur without breaking time-reversal symmetry, provided that the impurity also undergoes a transition. The associated electrical resistance has a weak temperature dependence down to a non-universal temperature scale. Our results extend the range of known backscattering mechani…
Magnetic impurities with sufficient anisotropy could account for the observed strong deviation of the edge conductance of 2D topological insulators from the anticipated quantized value. In this work we consider such a helical edge coupled to dilute impurities with an arbitrary spin $S$ and a general form of the exchange matrix. We calculate the backscattering current noise at finite frequencies as a function of the temperature and applied voltage bias. We find that in addition to the Lorentzian resonance at zero frequency, the backscattering current noise features Fano-type resonances at non-z…
We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium, within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate $γ_E$. Remarkably, for not too low temperature and bias voltage, $γ_E$ is given by the elastic backscattering rate, independent of the strength of electron-electron interaction, temperature, and bias.
We theoretically investigate the non-equilibrium current through a quantum dot coupled to one- dimensional electron leads, utilizing a controlled frequency-dependent renormalization group (RG) approach. We compute the non-equilibrium conductance for large bias voltages and address the interplay between decoherence, Kondo entanglement and Luttinger physics. The combined effect of large bias voltage and strong interactions in the leads, known to stabilize two-channel Kondo physics, leads to non-trivial modifications of the conductance. For weak interactions, we build an analogy to a dot coupled …
