We investigate the topological properties of one-dimensional weakly interacting topological insulators using bosonization. To do that we study the topological edge states that emerge at the edges of a model realized by a strong impurity or at the boundary between topologically distinct phases. In the bosonic model, the edge states are manifested as degenerate bosonic kinks at the boundaries. We first illustrate this idea on the example of the interacting Su-Schrieffer-Heeger (SSH) chain. We compute the localization length of the edge states as the width of an edge soliton that occurs in the SSH model in the presence of a strong impurity. Next, we examine models of two capacitively coupled SSH chains that can be either identical or in distinct topological phases. We find that weak Hubbard interaction reduces the ground state degeneracy in the topological phase of identical chains. We then prove that similarly to the non-interacting model, the degeneracy of the edge states in the interacting case is protected by chiral symmetry. We then study topological insulators built from two SSH chains with inter-chain hopping, that represent models of different chiral symmetric universality classes. We demonstrate in bosonic language that the topological index of a weakly coupled model is determined by the type of inter-chain coupling, invariant under one of two possible chiral symmetry operators. Finally, we show that a general one-dimensional model in a phase with topological index $ν$ is equivalent at low energies to a theory of at least $ν$ SSH chains. We illustrate this idea on the example of an SSH model with longer-range hopping.
The strong time-reversal symmetric (TRS) topological insulator (TI) in three space dimensions features gapless surface states in the form of massless Dirac fermions. We study these surface states with the method of bosonization, and find that the resulting bosonic theory has a topological contribution due to the parity anomaly of the surface Dirac fermions. We argue that the presence of a quantum anomaly is, in fact, the main reason for the existence of a surface state, by the principle that anomalies of a surface and bulk must cancel. Inspecting other classes of topological insulators, we arg…
Edge excitations of a fractional quantum Hall system can be derived as surface excitations of an incompressible quantum droplet using one dimensional chiral bosonization. Here we show that an analogous approach can be developed to characterize surface states of three-dimensional time reversal invariant topological insulators. The key ingredient of our theory is the Luther's multidimensional bosonization construction.
We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron term is the π-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band $Z_2$ topological insulator). We generalize for flat-band Ch…
We propose a model of three-dimensional topological insulators consisting of weakly coupled electron- and hole-gas layers with Rashba spin-orbit interaction stacked along a given axis. We show that in the presence of strong electron-electron interactions the system realizes a fractional strong topological insulator, where the rotational symmetry and condensation energy arguments still allow us to treat the problem as quasi-one-dimensional with bosonization techniques. We also show that if Rashba and Dresselhaus spin-orbit interaction terms are equally strong, by doping the system with magnetic…
The phase Hamiltonian of armchair carbon nanotubes at half-filling and away from it is derived from the microscopic lattice model by taking the long range Coulomb interaction into account. We investigate the low energy properties of the system using the renormalization group method. At half-filling, the ground state is a Mott insulator with spin gap, in which the bound states of electrons at different atomic sublattices are formed. The difference from the recent results [Phys. Rev. Lett. 79, 5082 (1997)] away half-filling is clarified.
Strong nonmagnetic impurities on the surface of three-dimensional topological insulators (TIs) generate localized resonance peaks close to the Dirac point. We show that this results in a strongly reduced critical Coulomb interaction strength to reach a magnetic surface state, following a Stoner-like criterion. Thus even weakly interacting TIs host a finite (local) magnetization around strong nonmagnetic impurities. The local magnetization gives rise to a global energy gap, linearly dependent on the maximum value of the magnetization but decreasing with reduced impurity concentration.
We report the observation of a parallel magnetic field induced metal-insulator transition (MIT) in a high-mobility two-dimensional electron gas (2DEG) for which spin and localization physics most likely play no major role. The high-mobility metallic phase at low field is consistent with the established Fermi liquid transport theory including phonon scattering, whereas the insulating phase at higher field shows a large negative temperature dependence at resistances much smaller than the quantum of resistance, $h/e^2$. We argue that this observation is a direct manifestation of a quantum-classic…
We show that gated bilayer graphene zigzag ribbons possess a fast and a slow edge, characterized by edge state velocities that differ due to non-negligible next-nearest-neighbor hopping elements. By applying bosonization and renormalization group methods, we find that the slow edge can acquire a sizable interaction-induced gap, which is tunable via an external gate voltage V_{g}. In contrast to the gate-induced gap in the bulk, the interaction-induced gap depends non-monotonously on the on-site potential V.
We introduce the topological mirror excitonic insulator as a new type of interacting topological crystalline phase in one dimension. Its mirror-symmetry-protected topological properties are driven by exciton physics, and it manifests in the quantized bulk polarization and half-charge modes on the boundary. And the bosonization analysis is performed to demonstrate its robustness against strong correlation effects in one dimension. Besides, we also show that Rashba nanowires and Dirac semimetal nanowires could provide ideal experimental platforms to realize this new topological mirror excitonic …
We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter $0<K<1$. The model has been studied in Ref. 21, and was mapped onto an anisotropic two-channel Kondo model via bosonization. For K<1, the strong coupling 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between dot and the 2DTI based on a simple scaling dimensional analysis[21]. We re-examine this model beyond…
We study the boundary physics of bulk insulators by considering three coupled Hubbard chains in a linear confining potential. In the Hartree-Fock approximation, the ground state at and slightly off the particle-hole symmetric point remains insulating even at large slopes of the confining potential. By contrast, accounting for quantum fluctuations and correlations through a combination of bosonization and RG methods, we find that there is always a gapless dipole mode, but it does not contribute to a finite compressibility. Moreover, when increasing the slope of the confining potential at half f…
Potential steps exceeding 1 eV are regularly formed at metal|insulator interfaces, even when the interaction between the materials at the interface is weak physisorption. From first-principles calculations on metal|h-BN interfaces we show that these potential steps are only indirectly sensitive to the interface bonding through the dependence of the binding energy curves on the van der Waals interaction. Exchange repulsion forms the main contribution to the interface potential step in the weakly interacting regime, which we show with a simple model based upon a symmetrized product of metal and …
We compute the energy absorbed by a one dimensional system of cold bosonic atoms in an optical lattice subjected to lattice amplitude modulation periodic with time. We perform the calculation for the superfluid and the Mott insulator created by a weak lattice, and the Mott insulator in a strong lattice potential. For the latter case we show results for 3D systems as well. Our calculations, based on bosonization techniques and strong coupling methods, go beyond standard Bogoliubov theory. We show that the energy absorption rate exhibits distinctive features of low dimensional systems and Luttin…
In this paper we study a non-equilibrium resonant tunnelling problem where a non-interacting quantum dot is connected to two leads, one being the edge of an interacting 2-D topological insulator (Luttinger liquid) and the other being a usual Fermi liquid. We show that the current passing through the system can be expressed in terms of a non-equilibrium local single-particle Green's function of the Luttinger liquid lead which can be analysed using standard bosonization- Renormalization Group (RG) technique. In particular, some exact results can be extracted in the small bias limit with repulsiv…
In two dimensions chaotic level-statistics is expected for massless Dirac fermions in the presence of disorder. For weakly disordered graphene flakes with zigzag edges the obtained level-spacing distribution in the Dirac region is neither chaotic (Wigner) nor localized (Poisson) but similar to that at the critical point of the Anderson metal-insulator transition. The quantum transport in finite graphene can occur via critical edge states as in topological insulators, for strong disorder the Dirac region vanishes and graphene behaves as ordinary Anderson insulator.
The magnetic properties of the van der Waals magnetic topological insulators MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$ are investigated by magneto-transport measurements. We evidence that the relative strength of the inter-layer exchange coupling J to the uniaxial anisotropy K controls a transition from an A-type antiferromagnetic order to a ferromagnetic-like metamagnetic state. A bi-layer Stoner-Wohlfarth model allows us to describe this evolution, as well as the typical angular dependence of specific signatures, such as the spin-flop transition of the uniaxial antiferromagnet and the switching fiel…
We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological crystalline insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled layer construction.
We present an effective low-energy theory of electron-phonon coupling effects for clean cylindrical topological insulator nanowires. Acoustic phonons are modelled by isotropic elastic continuum theory with stress-free boundary conditions. We take into account the deformation potential coupling between phonons and helical surface Dirac fermions, and also include electron-electron interactions within the bosonization approach. For half-integer values of the magnetic flux $Φ_B$ along the wire, the low-energy theory admits an exact solution since a topological protection mechanism then rules out p…
We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence of (d + 1) local unitary transformations parametrized by angles $θ_i$. Without loss of generality, we consider the case of two flat bands separated by a finite gap $Δ$. The perturbed states originating from the flat bands are described by an effective tight binding network with finite on- and off-diagonal disorder strength which depends on the manifold angles $θ_i$. The original infinitesimal onsite disorder strength W is only affect…
We propose a quantum state readout mechanism of a weakly coupled qubit in dispersive regime. The hybrid system consists of ferromagnetic insulator and a superconducting qubit in a microwave cavity. The enhancement of the measurement sensitivity is achieved by exerting torque on the ferromagnetic insulator magnetization, which compensates the damping of the system leading to an exceptional point. The proposed machanism allows to measure the qubit state either via the transmission of the cavity or the FMR signal of the magnetic material.
A theory of combined interference and interaction effects on the diffusive transport properties of 3D topological insulator surface states is developed. We focus on a slab geometry (characteristic for most experiments) and show that interactions between the top and bottom surfaces are important at not too high temperatures. We treat the general case of different surfaces (different carrier densities, uncorrelated disorder, arbitrary dielectric environment, etc.). In order to access the low-energy behavior of the system we renormalize the interacting diffusive sigma model in the one loop approx…
Topological insulators can exhibit strong magnetoelectric effects when their time-reversal symmetry is broken. In this Letter we consider the magneto-optical Kerr and Faraday effects of a topological insulator thin film weakly exchange-coupled to a ferromagnet. We find that its Faraday rotation has a universal value at low-frequencies, $θ_{\mathrm{F}} = \mathrm{tan}^{-1}\,α$ where $α$ is the vacuum fine structure constant, and that it has a giant Kerr rotation $θ_{\mathrm{K}} = π/2$. These properties follow from a delicate interplay between thin-film cavity confinement and the surface Hall con…
Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well-understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. …
Electrical currents at the surface or edge of a topological insulator are intrinsically spin-polarized. We show that such surface/edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface/edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. …
We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to open…
The tunneling junction between one-dimensional topological superconductor and integer (fractional) topological insulator (TI), realized via point contact, is investigated theoretically with bosonization technology and renormalization group methods. For the integer TI case, in a finite range of edge interaction parameter, there is a non-trivial stable fixed point which corresponds to the physical picture that the edge of TI breaks up into two sections at the junction, with one side coupling strongly to the Majorana fermion and exhibiting perfect Andreev reflection, while the other side decouple…
We investigate the transport properties of neutral, fermionic atoms passing through a one-dimensional quantum wire containing a mesoscopic lattice. The lattice is realized by projecting individually controlled, thin optical barriers on top of a ballistic conductor. Building an increasingly longer lattice, one site after another, we observe and characterize the emergence of a band insulating phase, demonstrating control over quantum-coherent transport. We explore the influence of atom-atom interactions and show that the insulating state persists as contact interactions are tuned from moderately…
We study the phase structure and Hall conductance quantization in weakly coupled multi-layer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation. It is shown that (i) finite interlayer tunnelings (however small) give rise to successive metallic and insulating phases and metal-insulator transitions in the unitary universality class. (ii) The Hall conductivity is not renormalized in the metallic phases in the 3D regime. (iii) The Hall conductances are quantized in the insulating phases. In the bulk quan…
A three-dimensional weak topological insulator (WTI) can be regarded as stacked layers of two-dimensional quantum spin-Hall insulators, each of which accommodates a one-dimensional helical edge mode. Massless Dirac electrons emerge on a side surface of WTIs as a consequence of the hybridization of such helical edge modes. We study the energy spectrum and transport of Dirac electrons on a side surface in the presence of step edges, which significantly modify the way of hybridization. It is shown that pseudo-helical modes with a nearly gapless linear dispersion can be created by manipulating ste…
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crystalline insulators, obtained as a stack of weakly-coupled two-dimensional layers. The system has tunable and robust surface Dirac cones even though the mirror Chern numbers of the Floquet bulk bands vanish. The number of surface Dirac cones is given by a new topological invariant determined from the scattering matrix of the system. Further, we find…
To understand the seemingly absent temperature dependence in the conductance of two-dimensional topological insulator edge states, we perform a numerical study which identifies the quantitative influence of the combined effect of dephasing and elastic scattering in charge puddles close to the edges. We show that this mechanism may be responsible for the experimental signatures in HgTe/CdTe quantum wells if the puddles in the samples are large and weakly coupled to the sample edges. We propose experiments on artificial puddles which allow to verify this hypothesis and to extract the real dephas…
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 consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperatute $T$ does not exceed some finite value $T_c$. At the same time, it can be also proven that at high enough $T$ the conductivity is finite. These two statements imply that the system undergoes a finite temperature Metal-to-Insulator transition, which can be viewed as …
We propose a device that allows for the emission of pairs of spin-polarized electrons into the edge-states of a two dimensional topological insulator. Charge and spin emission is achieved using a periodically driven quantum dot weakly coupled to the edge states of the host topological insulator. We present calculations of the emitted time-dependent charge and spin currents of such a dynamical scatterer using the Floquet scattering matrix approach. Experimental signatures of spin-polarized two-particle emission can be found in noise measurements. Here a new form of noise suppression, named $\ma…
We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with non-linear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature $T$ or weakly interacting bosons at high $T$. We calculate the equilibration rate which is found to scale with temperature as $T^5$ and $T^{14}$ in the high-temperatu…
Although the magnetic order is suppressed by a strong magnetic frustration, it is maintained but appears in complex order forms such as a cycloid or spin density wave in weakly frustrated systems. Herein, we report a weakly magnetic-frustrated two-dimensional van der Waals material CrPSe$_3$. Polycrystalline CrPSe$_3$ was synthesized at an optimized temperature of 700$^\circ$C to avoid the formation of any secondary phases (e.g., Cr$_2$Se$_3$). The antiferromagnetic transition appeared at $T_N\sim 126$ K with a large Curie-Weiss temperature $T_{\rm CW} \sim -371$ via magnetic susceptibility me…
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry. In this work we systematically study another class of topological phases of weakly interacting electrons protected by spatial inversion symmetry, which generally don't support stable gapless boundary states. We classify these inversion-symmetric topological insulators and superconductors in the framework of K-theory, and construct their lattice models. We a…
We report the observation of a re-entrant insulator--metal--insulator transition at B=0 in a two dimensional (2D) hole gas in GaAs at temperatures down to 30mK. At the lowest carrier densities the holes are strongly localised. As the carrier density is increased a metallic phase forms, with a clear transition at σ= ~5e^2/h. Further increasing the density weakens the metallic behaviour, and eventually leads to the formation of a second insulating state for σ> ~50e^2/h. In the limit of high carrier densities, where k_F.l is large and r_s is small, we thus recover the results of previous work on …
We study precursor states of fractional topological insulators (FTIs) in interacting fermionic ladders with spin-orbit coupling. Within a microscopically motivated bosonization approach, we investigate different competing phases depending on same-spin and interspin interactions at fractional effective filling $ν=1/3$ per spin. In the spin-decoupled limit, we find that strong repulsive interactions of already moderate range may lead to a partially gapped state with two time-reversed copies of a quasi-one dimensional Laughlin phase. This FTI precursor competes with an interleg partially gapped p…
We reanalyze some of the critical transport experiments and provide a coherent understanding of the current generation of topological insulators (TIs). Currently TI transport studies abound with widely varying claims of the surface and bulk states, often times contradicting each other, and a proper understanding of TI transport properties is lacking. According to the simple criteria given by Mott and Ioffe-Regel, even the best TIs are not true insulators in the Mott sense, and at best, are weakly-insulating bad metals. However, band-bending effects contribute significantly to the TI transport …
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $θ$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $θ$ is the same parameter that appears in the "axion electrodynamics" Lagrangian $Δ{\cal L}_{EM} = (θe^2 / 2 πh) {\bf E} \cdot {\bf B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($θ=π$). We compute $θ$ for a simple model that accesses the topological insulator and discu…
Three-dimensional topological insulators feature Dirac-like surface states which are topologically protected against the influence of weak quenched disorder. Here we investigate the effect of surface disorder beyond the weak-disorder limit using large-scale numerical simulations. We find two qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and induces diffusive metallic behavior at the surface. Even more remarkably, for strong surface disorder a Dirac cone reappears, as new weakly disordered "surface" states emerge in the sample beneath the disordered surface layer, wh…
The Hall coefficient $R_H$ and resistivity $ρ$ of the topological insulator Bi$_2$Te$_2$Se display a number of puzzling features vs. temperature $T$. We propose a model that describes well the non-monotonic variation of $R_H(T)$. A key feature of the model is a chemical potential that is weakly $T$-dependent. From the fit to the model, we infer a "transport" gap $Δ_T$ of 50 mV. We find that hydrostatic pressure $P$ (0-27 kbar) has a pronounced effect on both $R_H$ and $ρ$. We show that these changes arise from decreases in both $Δ_T$ and the hole effective mass under pressure.
We present analysis of a single channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low-energy theory is then a two band model with a difference of Fermi velocities $δv$. Using bosonization and a two-loop renormalization group procedure we show that electron-electron interactions can open a gap in the spin sector of the theory when the interaction strength $U$ is smaller than $δv$ in appropriate units. For repulsive interactions, the resulting strong…
When a ferromagnet is deposited on the surface of a topological insulator the topologically protected surface state develops a gap and becomes a 2-dimensional quantum Hall liquid. We demonstrate that the Hall current in such a liquid, induced by an external electric field, can have a large effect on the magnetization dynamics of the ferromagnet by changing the effective anisotropy field. This change is dissipationless and may be substantial even in weakly spin-orbit coupled ferromagnets. We study the possibility of dissipationless current-induced magnetization reversal in monolayer-thin, insul…
We study a Majorana-carrying quantum wire, driven into a trivial phase by breaking the spatial inversion symmetry with a tilted external magnetic field. Interestingly, we predict that a supercurrent applied in the proximate superconductor is able to restore the topological phase and therefore the Majorana end-states. Using Abelian bosonization, we further confirm this result in the presence of electron-electron interactions and show a profound connection of this phenomenon to the physics of a one-dimensional doped Mott-insulator. The present results have important applications in e.g., realizi…
Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that describes an interacting yet exactly solvable 2D topological insulator. We explicitly show that both the gapped and gapless boundaries of our model are consistent with those of band-theoretic, weakly interacting topological insulators. Interestingly, on certain lattices our time-reversal-symmetric models also enjoy $\mathcal{CP}$ symmetry, leading to intuitive…
We study the interaction between a ferromagnetically ordered medium and the surface states of a topological insulator with a general surface termination. This interaction is strongly crystal face dependent and can generate chiral states along edges between crystal facets even for a uniform magnetization. While magnetization parallel to quintuple layers shifts the momentum of Dirac point, perpendicular magnetization lifts the Kramers degeneracy at any Dirac points except on the side face where the spectrum remains gapless and the Hall conductivity switches sign. Chiral states can be found at an…
