Helical edge modes of 2D topological insulators are supposed to be protected from time-reversal invariant elastic backscattering. Yet substantial deviations from the perfect conductance are typically observed experimentally down to very low temperatures. To resolve this conundrum we consider the effect of a single magnetic impurity with arbitrary spin on the helical edge transport. We consider the most general structure of the exchange interaction between the impurity and the edge electrons. Moreover, for the first time, we take into the account the local anisotropy for the impurity and show that it strongly affects the backscattering current in a wide range of voltages and temperatures. We show that the sensitivity of the backscattering current to the presence of the local anisotropy is different for half-integer and integer values of the impurity spin. In the latter case the anisotropy can significantly increase the backscattering correction to the current.
We consider the effects of electron scattering off a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance is a non-monotonous function of the voltage with several extrema.
Transport by helical edge states of a quantum spin Hall insulator is experimentally characterized by a weakly temperature-dependent mean free path of a few microns and by reproducible conductance oscillations, challenging proposed theoretical explanations. We consider a model where edge electrons experience spatially random Rashba spin-orbit coupling and couple to a magnetic impurity with spin S >= 1/2. In a finite bias steady state, we find for S > 1/2 an impurity induced resistance with a temperature dependence in agreement with experiments. Since backscattering is elastic, interference betw…
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 …
The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In the absence of superconductivity and magnetism, Rashba coupling is the most relevant single particle perturbation in this system. Since Rashba coupling does not break time reversal symmetry, its influence on transport properties is only visible if processes that do not conserve the single particle energy are included. Paradigmatic examples of such processes are electron-electron interactions and time dependent external drivings. We ana…
Edge states of two-dimensional topological insulators are helical and single-particle backscattering is prohibited by time-reversal symmetry. In this work, we show that an isotropic exchange coupling of helical edge states (HES) to a spin 1/2 impurity subjected to a magnetic field results in characteristic backscattering current noise (BCN) as a function of bias voltage and tilt angle between the direction of the magnetic field and the quantization axis of the HES. In particular, we find transitions from sub-Poissonian (antibunching) to super-Poissonian (bunching) behavior as a direct conseque…
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 $ϕ$ (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 $ϕ$ - with the period 1/2 - in the presence of magnetic impurity. W…
Charge transport in topological insulators is primarily characterised by so-called topologically projected helical edge states, where charge carriers are correlated in spin and momentum. In principle, dissipation-less current can be carried by these edge states as backscattering from impurities and defects is suppressed as long as time-reversal symmetry is not broken. However, applied magnetic fields or underlying nuclear spin-defects in the substrate can break this time reversal symmetry. In particular, magnetic impurities lead to back-scattering by spin-flip processes. We have investigated t…
We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin $S=1/2$ of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poissonian noise of the full current $I$ at high frequencies. If the interaction only flips the impurity spin but conserves those of electrons, the noise at high voltages $eV\gg T$ is frequency-independent. Both the noise and the backscattering current $I_{bs}$ saturate at voltage-independent values. Finally, if the Hami…
A quantum magnetic impurity of spin $S$ at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary $S$. Our full analytical solution reveals that for $S>\frac{1}{2}$ the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for $S=\frac{1}{2}$ the Fano factor is bounded between $1$ and $2$, generalizing earlier studies.
Inevitable for the basic principles of skyrmion racetrack-like applications is not only their confined motion along one-dimensional channels but also their controlled creation and annihilation. Helical magnets have been suggested to naturally confine the motion of skyrmions along the tracks formed by the helices, which also allow for high-speed skyrmion motion. We propose a protocol to create topological magnetic structures in a helical background. We furthermore analyse the stability and current-driven motion of the skyrmions in a helical background with in-plane uniaxial anisotropy fixing th…
Shubnikov de Haas resistance oscillations of highly mobile two dimensional helical electrons propagating on a conducting surface of strained HgTe 3D topological insulator are studied in magnetic fields B tilted by angle $θ$ from the normal to the conducting layer. Strong decrease of oscillation amplitude A is observed with the tilt: $A \sim \exp(-ξ/cos(θ))$, where $ξ$ is a constant. Evolution of the oscillations with temperature T shows that the parameter $ξ$ contains two terms: $ξ=ξ_1+ξ_2 T$. The temperature independent term, $ξ_1$, describes reduction of electron mean free path in magnetic f…
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…
Using an advanced tight-binding approach, we estimate the anisotropy of the tunnel transmission associated with the rotation of the 5/2 spin of a single Mn atom forming an acceptor state in GaAs and located near an AlGaAs tunnel barrier. Significant anisotropies in both in-plane and out-of-plane geometries are found, resulting from the combination of the large spin-orbit coupling associated with the p-d exchange interaction, cubic anisotropy of heavy-hole dispersion and the low C2v symmetry of the chemical bonds.
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 $hc/2e$ …
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…
The interaction of a magnetic insulator with the helical electronic edge of a two-dimensional topological insulator has been shown to lead to many interesting phenomena. One of these is that for a suitable orientation of the magnetic anisotropy axis, the exchange coupling to an easy-plane magnet has no effect on DC electrical transport through a helical edge, despite the fact that it opens a gap in the spectrum of the helical edge [Meng {\em et al.}, Phys.\ Rev.\ B {\bf 90}, 205403 (2014)]. Here, we theoretically consider such a magnet embedded in an interferometer, consisting of a pair of hel…
Finite-frequency admittance and noise of a helical edge coupled to a magnet
Dahlem Center for Complex Quantum Systems, Halle-Berlin-Regensburg Cluster of Excellence CCE, and Physics Department, Freie Universität Berlin（达勒姆复杂量子系统中心、哈雷-柏林-雷根斯堡卓越集群CCE及柏林自由大学物理系）；Institut für Mathematische Physik, Technische Universität Braunschweig（布伦瑞克工业大学数学物理研究所）
We show that higher-harmonics exchange scattering from a magnetic adatom on the surface of a three dimensional topological insulator leads to a magnetic anisotropy whose magnitude and sign may be tuned by adjusting the chemical potential of the helical surface band. As chemical potential moves from the Dirac point towards the surface band edge, the surface normal is found to change from magnetic easy, to hard axis. Hexagonal warping is shown to diminish the region with easy axis anisotropy, and to suppress the anisotropy altogether. This indirect contribution can be comparable in magnitude to …
Although indications are that a single chiral quantum anomalous Hall(QAH) edge mode might have been experimentally detected. There have been very many recent experiments which conjecture that a single chiral QAH edge mode always materializes along with a pair of quasi-helical quantum spin Hall (QSH) edge modes. The reason for this seems to lie in the origin of QAH edge modes. These evolve from QSH edge modes via suppression of one of the spin edge modes by application of a ferromagnet or magnetic impurity. In this work we deal with a substantial 'What If ?' question- in case the QSH edge modes…
Anisotropic charge carrier transport in black phosphorus limited by ionized impurity scattering at finite temperature is explored theoretically. The anisotropic electronic structure enters the calculation for the polarizability (screening), the momentum relaxation time, and the mobility. For finite temperature, scattering is not limited to the Fermi surface and the polarizability is temperature dependent. The impact of screening is investigated in detail with its dependence on carrier density and temperature. Competing with the thermal excitation effects, the temperature dependence of the pola…
We theoretically consider a quantum magnetic impurity coupled to a superconductor, and obtain the local density of states at the position of the impurity taking into account the effect of spin-fluctuations and single-ion magnetic anisotropy. We particularly focus on the spectrum of subgap Yu-Shiba-Rusinov (YSR or Shiba) states induced by a quantum impurity with easy- or hard-axis uniaxial anisotropy. Although this is a relevant experimental situation in, e.g., magnetic adatoms on the surface of clean metals, it is customary that theoretical descriptions assume a classical-spin approximation wh…
We calculate exact zero-temperature real space properties of a substitutional magnetic impurity coupled to the edge of a zigzag silicene-like nanoribbon. Using a Lanczos transformation [Phys. Rev. B 91, 085101 (2015)] and the density matrix renormalization group method, we obtain a realistic description of stanene and germanene that includes the bulk and the edges as boundary one-dimensional helical metallic states. Our results for substitutional impurities indicate that the development of a Kondo state and the structure of the spin correlations between the impurity and the electron spins in t…
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…
The inverse spinel ferrimagnetic NiCo$_2$O$_4$ possesses high magnetic Curie temperature $T_C$, high spin polarization, and strain-tunable magnetic anisotropy. Understanding the thickness scaling limit of these intriguing magnetic properties in NiCo$_2$O$_4$ thin films is critical for their implementation in nanoscale spintronic applications. In this work, we report the unconventional magnetotransport properties of epitaxial (001) NiCo$_2$O$_4$ films on MgAl$_2$O$_4$ substrates in the ultrathin limit. Anomalous Hall effect measurements reveal strong perpendicular magnetic anisotropy for films …
