Magnetically doped topological insulators have been extensively studied over the past decade as a material platform to exhibit quantum anomalous Hall effect. Most material realizations are magnetically doped and despite material advances suffer from large disorder effects. In such systems, it is believed that magnetic disorder leads to a spatially varying Dirac mass gap and chemical potential fluctuations, and hence quantized conductance is only observed at very low temperatures. Here, we use a recently developed high-precision time-domain terahertz (THz) polarimeter to study the low-energy electrodynamic response of Cr-doped (Bi,Sb)$_2$Te$_3$ thin films. These films have been recently shown to exhibit a dc quantized anomalous Hall response up to T = 2 K at zero gate voltage. We show that the real part of the THz range Hall conductance $σ_{xy}(ω)$ is slightly smaller than $e^2/h$ down to T = 2 K with an unconventional decreasing dependence on frequency. The imaginary (dissipative) part of $σ_{xy}(ω)$ is small, but increasing as a function of omega. We connect both aspects of our data to a simple model for effective magnetic gap disorder. Our work highlights the different effect that disorder can have on the dc vs. ac quantum anomalous Hall effect.
The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report the anomalous Hall effect studies in Mn- and Cr-doped Bi$_2$Te$_3$ topological insulators with varied thickness and doping content. By tracing the chirality of the Hall loops, we find that the Mn-type anomalous Hall effect with clockwise chirality is strengthened by the reduction of film thickness, which is opposite to that of the Cr-type anomalous Hall effect with counterclockwise chirality. We provide a phenomen…
One-dimensional (1D) quantum wires, which are functionalized by magnetic ad-atoms, can host ballistic helical transport. Helicity protects transport from an undesirable influence of material imperfections, and it makes the magnetically doped wire a very promising element for nanoelectronics and spintronics. However, fabricating purely 1D conductors is experimentally very challenging and not always feasible. In this paper, we show that the protected helical transport can exist even in quasi-1D wires. We model the quasi-1D magnetically doped wire as two coupled dense 1D Kondo chains. Each chain …
We report magnetotransport measurements on magnetically doped (Bi,Sb)$_2$Te$_3$ films grown by molecular beam epitaxy. In Hallbar devices, logarithmic dependence on temperature and bias voltage are obseved in both the longitudinal and anomalous Hall resistance. The interplay of disorder and electron-electron interactions is found to explain quantitatively the observed logarithmic singularities and is a dominant scattering mechanism in these samples. Submicron scale devices exhibit intriguing quantum oscillations at high magnetic fields with dependence on bias voltage. The observed quantum osci…
The quantum anomalous Hall effect has recently been observed experimentally in thin films of Cr doped (Bi,Sb)$_2$Te$_3$ at a low temperature ($\sim$ 30mK). In this work, we propose realizing the quantum anomalous Hall effect in more conventional diluted magnetic semiconductors with doped InAs/GaSb type II quantum wells. Based on a four band model, we find an enhancement of the Curie temperature of ferromagnetism due to band edge singularities in the inverted regime of InAs/GaSb quantum wells. Below the Curie temperature, the quantum anomalous Hall effect is confirmed by the direct calculation …
We study disorder induced topological phase transitions in magnetically doped (Bi, Sb)$_2$Te$_3$ thin films, by using large scale transport simulations of the conductance through a disordered region coupled to reservoirs in the quantum spin Hall regime. Besides the disorder strength, the rich phase diagram also strongly depends on the magnetic exchange field, the Fermi level, and the initial topological state in the undoped and clean limit of the films. In an initially trivial system at non-zero exchange field, varying the disorder strength can induce a sequence of transitions from a normal in…
We examine the transport properties of magnetically doped topological insulator (TI) thin films subject to correlated non-magnetic disorder. For the disorder we choose a quasi-periodic potential with a random phase. We restrict the disorder to a central region, which is coupled to two leads in a clean quantum spin Hall insulator (QSHI) state and concentrate on different orientations of the quasi-periodicity in the two-dimensional central region. In the case of a diagonally oriented or purely longitudinal quasi-periodicity we find different topological Anderson insulator (TAI) phases, with a qu…
Proximity induced superconducting states in the surface of magnetically doped topological insulators can host chiral Majorana modes. We consider a Josephson junction in that system with changing the chemical potential, which drives a topological phase transition in the induced superconducting states as well as a metal-insulator transition in the surface states. The local density of states and the Josephson current are analytically calculated by McMillan's Green's function method in terms of the Andreev reflection coefficient. We show that although the magnitude of the Josephson current is grea…
Electric-field manipulation of magnetic order has proved of both fundamental and technological importance in spintronic devices. So far, electric-field control of ferromagnetism, magnetization and magnetic anisotropy has been explored in various magnetic materials, but the efficient electric-field control of spin-orbit torque (SOT) still remains elusive. Here, we report the effective electric-field control of a giant SOT in a Cr-doped topological insulator (TI) thin film using a top-gate FET structure. The SOT strength can be modulated by a factor of 4 within the accessible gate voltage range,…
We study the electron transport in a magnetically doped three dimensional topological insulator (TI) by taking the effects of impurity-impurity exchange interactions into account. The interactions between magnetic impurities give rise to the formation of {\it magnetic clusters} with temperature dependent mean sizes, randomly distributed on the surface of the TI. Instead of dealing with single magnetic impurities, we consider surface Dirac electrons to be scattered off magnetic clusters, and define the scattering potential in terms of clusters mean sizes. Within the semiclassical Boltzmann appr…
We use time-resolved Kerr rotation to demonstrate the optical and electronic tuning of both the electronic and local moment (Mn) spin dynamics in electrically gated parabolic quantum wells derived from II-VI diluted magnetic semiconductors. By changing either the electrical bias or the laser energy, the electron spin precession frequency is varied from 0.1 to 0.8 THz at a magnetic field of 3 T and at a temperature of 5 K. The corresponding range of the electrically-tuned effective electron g-factor is an order of magnitude larger compared with similar nonmagnetic III-V parabolic quantum wells.…
We study the phase diagram and transport properties of arbitrarily doped quantum wires functionalized by magnetic adatoms. The appropriate theoretical model for these systems is a dense one-dimensional Kondo Lattice (KL) which consists of itinerant electrons interacting with localized quantum magnetic moments. We discover the novel phase of the locally helical metal where transport is protected from a destructive influence of material imperfections. Paradoxically, such a protection emerges without a need of the global helicity, which is inherent in all previously studied helical systems and re…
Twin domains are naturally present in the topological insulator \BiSe{} and affect strongly its properties. While studies of its behavior for ideal \BiSe{} structure exist, little is known about their possible interaction with other defects. Extra information are needed especially for the case of artificial perturbation of topological insulator states by magnetic doping, which has attracted a lot of attention recently. Employing ab initio calculations based on layered Green's function formalism, we study the interaction between twin planes in \BiSe{}. We show the influence of various magnetic …
We study the superconducting properties of the thin film BCS superconductor proximity coupled to a magnetically doped topological insulator(TI). Using the mean field theory, we show that Fulde-Ferrell(FF) pairing can be induced in the conventional superconductor by having inverse proximity effect(IPE). This occurs when the IPE of the TI to the superconductor is large enough that the normal band of the superconductor possesses a proximity induced spin-orbit coupling and magnetization. We find that the energetics of the different pairings are dependent on the coupling strength between the TI and…
We use magneto-conductivity to study the magnetic proximity effect on surface states of doped topological insulators. Our bilayers consist of a layer of Fe$_7$Se$_8$, which is a metallic ferrimagnet and a layer of Bi$_{0.8}$Sb$_{1.2}$Te$_{3}$ which is a highly hole-doped topological insulator. Using transport measurements and a modified Hikami-Larkin-Nagaoka model, we show that the ferromagnet shortens significantly the effective coherence length of the surface states, suggesting that a gap is opened at the Dirac point. We show that the magnetically induced gap persists on surface states which…
As a promising candidate system to realize topological superconductivity, the system of a 3D topological insulator (TI) grown on top of the s-wave superconductor has been extensively studied. To access the topological superconductivity experimentally, the 3D TI sample must be thin enough to allow for Cooper pair tunneling to the exposed surface of TI. The use of magnetically ordered dopants to break time-reversal symmetry may allow the surface of a TI to host Majorana fermion, which are believed to be a signature of topological superconductivity. In this work, we study a magnetically-doped thi…
Starting from a three dimensional Hamiltonian, we study the optical properties of ultra-thin topological insulator slabs for which the coupling between Dirac fermions on opposite surfaces results in two degenerated gapped hyperbolic bands. The gap is a threshold for the optical absorption and translates in a peak in the imaginary part of the optical conductivity. An exchange field applied perpendicular to the slab splits the degenerated hyperbolic bands and a double step structure come out in the optical absorption, whereas a double peak structure appears in the imaginary part of the longitudi…
Anomalous Localization in Magnetically Doped Two-Dimensional Topological Insulators
Instituto de Física Teórica, São Paulo State University（圣保罗州立大学理论物理研究所）；School of Physics, Trinity College Dublin（都柏林三一学院物理学院）；Advanced Materials and Bioengineering Research (AMBER) Centre, Trinity College Dublin（都柏林三一学院先进材料与生物工程研究中心）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）
By generalizing the Kubo-Streda formula for calculating electrical conductivities to the thermoelectric coefficients, we theoretically study the anomalous Nernst effect (ANE) on the surface of a topological insulator induced by a finite concentration of magnetic impurities. The ANE is found to be modulated by the impurity scattering and thermal fluctuations, simultaneously, and so exhibits rich structures in the energy space. While the anomalous Hall conductivity is half-integer quantized with the Fermi level across the magnetic-impurity-induced gap, the anomalous Nernst signal (ANS) is fully …
We study the photon-dressed electronic band structure of topological insulator thin films which could be also doped doped by magnetic impurities in response to an off-resonance time-periodic electromagnetic field. The thin films irradiated by a circularly polarized light undergo phase transition, in a driven system made by and a fascinating feature of distinct phases emerges in the phase diagram depending on the parameters such as frequency, intensity and polarization of the light. As a particular case, quantum anomalous Hall insulator phase is induced purely by the light-induced mass term wit…
We study the electronic and transport properties of a topological insulator nanowire including selective magnetic doping of its surfaces. We use a model which is appropriate to describe materials like Bi$_2$Se$_3$ within a k.p approximation and consider nanowires with a rectangular geometry. Within this model the magnetic doping at the (111) surfaces induces a Zeeman field which opens a gap at the Dirac cones corresponding to the surface states. For obtaining the transport properties in a two terminal configuration we use a recursive Green function method based on a tight-binding model which i…
In magnetically doped thin-film topological insulators, aligning the magnetic moments generates a quantum anomalous Hall phase supporting a single chiral edge state. We show that as the system de-magnetizes, disorder from randomly oriented magnetic moments can produce a `quantum anomalous parity Hall' phase with \emph{helical} edge modes protected by a unitary reflection symmetry. We further show that introducing superconductivity, combined with selective breaking of reflection symmetry by a gate, allows for creation and manipulation of Majorana zero modes via purely electrical means and at ze…
We present cavity QED experiments with an Er:YSO crystal magnetically coupled to a 3D cylindrical sapphire loaded copper resonator. Such waveguide cavities are promising for the realization of a superconducting quantum processor. Here, we demonstrate the coherent integration of a rare-earth spin ensemble with the 3D architecture. The collective coupling strength of the Er$^{3+}$ spins to the 3D cavity is 21 MHz. The cylindrical sapphire loaded resonator allowed us to explore the anisotropic collective coupling between the rare-earth doped crystal and the cavity. This work shows the potential o…
The experimental realization of the quantum anomalous Hall (QAH) effect in magnetically-doped (Bi, Sb)2Te3 films stands out as a landmark of modern condensed matter physics. However, ultra-low temperatures down to few tens of mK are needed to reach the quantization of Hall resistance, which is two orders of magnitude lower than the ferromagnetic phase transition temperature of the films. Here, we systematically study the band structure of V-doped (Bi, Sb)2Te3 thin films by angle-resolved photoemission spectroscopy (ARPES) and show unambiguously that the bulk valence band (BVB) maximum lies hig…
Magnetotransport measurements are presented on paramagnetic (Hg,Mn)Te quantum wells (QWs) with an inverted band structure. Gate-voltage controlled density dependent measurements reveal an unusual behavior in the transition regime from n- to p-type conductance: A very small magnetic field of approximately 70 mT is sufficient to induce a transition into the nu = -1 quantum Hall state, which extends up to at least 10 Tesla. The onset field value remains constant for a unexpectedly wide gate-voltage range. Based on temperature and angle-dependent magnetic field measurements we show that the unusua…
We present data on the electrical transport properties of highly-doped silicon-on-insulator quantum dots under the effect of pulsed magnetic fields up to 48 T. At low field intensities, B<7 T, we observe a strong modification of the conductance due to the destruction of weak localization whereas at higher fields, where the magnetic field length becomes comparable to the effective Bohr radius of phosphorous in silicon, a strong decrease in conductance is demonstrated. Data in the high and low electric field bias regimes are then compared to show that close to the Coulomb blockade edge magnetica…
We demonstrate that spin-orbit coupled electrons in a magnetically doped system exert a spin torque on the local magnetization, without a flowing current, when the chemical potential is modulated in a magnetic field. The spin torque is proportional to the anomalous Hall conductivity, and its effective field strength may overcome the Zeeman field. Using this effect, the direction of the local magnetization is switched by gate control in a thin film. This charge-induced spin torque is essentially an equilibrium effect, in contrast to the conventional current-induced spin-orbit torque, and, thus,…
We investigate surface plasmons at a planar interface between a normal dielectric and a topological insulator, where the Fermi-energy lies inside the bulk gap of the topological insulator and gives rise to a two-dimensional charge distribution of free Dirac electrons. We develop the methodology for the calculation of plasmon dispersions, using the framework of classical electrodynamics, with modified constituent equations due to Hall currents in the topological insulator, together with a Lindhard-type description for the two-dimensional charge distribution of free Dirac electrons. For a system…
Magnetic quantum oscillations (MQOs) have been widely used as a tool for probing Fermi surfaces. The shape and topology of the Fermi surface and the related physical parameters, such as the cyclotron mass and relaxation time, can be verified by carefully analyzing the frequency, amplitude, and phase of MQOs. In particular, phase analysis, from which we can obtain the Berry phase, has received much attention with the growing interest in the topology of condensed matter physics. Here, beyond the conventional uses of MQOs, we show that MQOs can be used to determine the Fermi surface magnetization…
We consider the competition between the conventional s-wave and the triplet Balian-Werthamer or the B-phase pairings in the doped three dimensional narrow gap semiconductors, such as $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$. When the coupling constants of the two contending channels are comparable, we find a simultaneously time-reversal and parity violating $p + is$ state at low temperatures, which provides an example of dynamic axionic state of matter. In contradistinction to the time-reversal invariant, topological B-phase, the $p + is$ state …
Quantum light-matter interfaces (QLMIs) connecting stationary qubits to photons will enable optical networks for quantum communications, precise global time keeping, photon switching, and studies of fundamental physics. Rare-earth-ion (REI) doped crystals are state-of-the-art materials for optical quantum memories and quantum transducers between optical photons, microwave photons and spin waves. Here we demonstrate coupling of an ensemble of neodymium REIs to photonic nano-cavities fabricated in the yttrium orthosilicate host crystal. Cavity quantum electrodynamics effects including Purcell en…
