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. Our theory provides a systematic description of the spectroscopic signals in the MRTS measurement and we hope will stimulate future experimental studies on the two-dimensional time-reversal invariant topological insulator.
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 study the localization-driven correlated states among two isolated dirty interacting helical edges as realized at the boundaries of two-dimensional $\mathbb{Z}_2$ topological insulators. We show that an interplay of time-reversal symmetric disorder and strong interedge interactions generically drives the entire system to a gapless localized state, preempting all other intraedge instabilities. For weaker interactions, an antisymmetric interlocked fluid, causing a negative perfect drag, can emerge from dirty edges with different densities. We also find that the interlocked fluid states of hel…
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 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…
One-dimensional (1D) electron systems in the presence of Coulomb interaction are described by Luttinger liquid theory. The strength of Coulomb interaction in the Luttinger liquid, as parameterized by the Luttinger parameter K, is in general difficult to measure. This is because K is usually hidden in powerlaw dependencies of observables as a function of temperature or applied bias. We propose a dynamical way to measure K on the basis of an electronic time-of-flight experiment. We argue that the helical Luttinger liquid at the edge of a 2D topological insulator constitutes a preeminently suited…
We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and exact Emery-Luther mapping. The gapless glassy edge state spontaneously breaks time-reversal symmetry in a `spin glass' fashion, and may be viewed as a localized state of solitons which carry half integer charge. Such a qualitatively distinct edge state provides a simple explanation for heretofore puzzling experimental observations. This phase exhibits a str…
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…
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 consider the interacting, spin conserving, extended Kane-Mele-Hubbard model, and we rigorously establish the exact quantization of the edge spin conductance and the validity of the Helical Luttinger liquid relations for Drude weights and susceptibilities. Our analysis fully takes into account lattice effects, typically neglected in the Helical Luttinger model approximation, which play an essential role for universality. The analysis is based on exact renormalization group methods and on a combination of lattice and emergent Ward identities, which allow to relate the emergent chiral anomaly …
In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter $K$, characterising the competition between the electrons' kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show th…
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 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…
The helical edge states of time-reversal invariant two-dimensional topological insulators are protected against backscattering in idealized models. In more realistic scenarios with a shallow confining potential at the sample boundary, additional strongly interacting edge states may arise, that could interfere with the topological protection of edge conduction. We find that interaction effects within the reconstructed edges are well described by the Luttinger liquid model. While interactions between this Luttinger liquid and the helical edge states can in principle give rise to dynamical spin p…
In the context of one-dimensional fermionic systems, helical Luttiger liquids are not only characterized by intriguing spin properties, but also by the possibility to be manipulated by means of electrostatic gates, exploiting finite Rashba coupling. We use this property to show that a heterostructure composed of a helical Luttinger liquid, contacted to two metallic leads and supplemented by top gates, can be used as a tunable thermal valve. By relying on bosonization techniques and scattering of plasmonic modes, we investigate the performance of this valve with respect to electron-electron int…
We study the effect of localized magnetic moments on the conductance of a helical edge. Interaction with a local moment is an effective backscattering mechanism for the edge electrons. We evaluate the resulting differential conductance as a function of temperature $T$ and applied bias $V$ for any value of $V/T$. Backscattering off magnetic moments, combined with the weak repulsion between the edge electrons results in a power-law temperature and voltage dependence of the conductance; the corresponding small positive exponent is indicative of insulating behavior. Local moments may naturally app…
We discuss a platform for the synthetic realization of key physical properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly correlated metallic state where spin polarization and propagation direction of the itinerant particles are locked to each other. We propose an unconventional one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the HTLL in the long wavelength limit, as we demonstrate with a combination of analytical (bosonization) and numerical (density matrix renormalization gr…
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…
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 …
Topological insulators are frequently also one of the best known thermoelectric materials. It has been recently discovered that in 3D topological insulators each skew dislocation can host a pair of 1D topological states a helical TLL. We derive exact analytical formulas for thermoelectric Seebeck coefficient in TLL and investigate up to what extent one can ascribe the outstanding thermoelectric properties of Bi 2 Te 3 to these 1D topological states. To this end we take a model of a dense dislocation network and find an analytic formula for an overlap between 1D (the TLL) and 3D electronic stat…
