Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors (original) (raw)
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Quantized Anomalous Hall Effect in Magnetic Topological Insulators
Science, 2010
The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin Hall effect have been discovered in recent years.
Cornell University - arXiv, 2022
We study the suppression of the conductance quantization in quantum spin Hall systems by a combined effect of electronic interactions and edge disorder, that is ubiquitous in exfoliated and CVD grown 2D materials. We show that the interplay between the electronic localized states due to edge defects and electron-electron interactions gives rise to local magnetic moments, that break time-reversal symmetry and the topological protection of the edge states in 2D topological systems. Our results suggest that edge disorder leads to small deviations of a perfect quantized conductance in short samples and to a strong conductance suppression in long ones. Our analysis is based on on the Kane-Mele model, an unrestricted Hubbard mean field Hamiltonian and on a self-consistent recursive Green's functions technique to calculate the transport quantities.
Quantum spin Hall effect in two-dimensional metals without spin-orbit coupling
Bulletin of the American Physical Society, 2021
The quantum spin Hall effect has been observed in topological insulators using spin-orbit coupling as the probe, but it has not yet been observed in a metal. An experiment is proposed to measure the quantum spin Hall effect of an electron or hole in a two-dimensional (2D) metal by using the previously unexplored but relativistically generated 2D quantum spin Hall Hamiltonian, but without using spin-orbit coupling. A long cylindrical solenoid lies normally through the inner radius of a 2D metallic Corbino disk. The current IS surrounding the solenoid produces an azimuthal magnetic vector potential but no magnetic field in the disk. In addition, a radial electric field is generated across the disk by imposing either (a) a potential difference ∆v or (b) a radial charge current I across its inner and outer radii. Combined changes in IS and in either ∆v or I generate spontaneously quantized azimuthal charge and spin currents. The experiment is designed to measure these quantized azimuthal charge and spin currents in the disk consistently. The quantum Hamiltonians for experiments (a) and (b) are both solved exactly. A method to control the Joule heating is presented, which could potentially allow the quantum spin Hall measurements to be made at room temperature. Extensions of this design to an array of thermally-managed solenoids, each surrounded by thermally-managed stacks of 2D metallic Corbino disks, could function as a quantum computer that could potentially operate at room temperature.
Spin quantum Hall effects in a spin-1 topological paramagnet
AKLT state (or Haldane phase) in a spin-1 chain represents a large class of gapped topological paramagnets, which hosts symmetry-protected gapless excitations on the boundary. In this work we show how to realize this type of featureless spin-1 states on a generic two-dimensional lattice. These states have a gapped spectrum in the bulk but supports gapless edge states protected by spin rotational symmetry along a certain direction, and are featured by spin quantum Hall effect. Using fermion representation of integer-spins we show a concrete example of such spin-1 topological paramagnets on kagome lattice, and suggest a microscopic spin-1 Hamiltonian which may realize it.
Nature Physics, 2014
A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport signatures predicted for such topological surface states (TSS) is a well-defined half-integer quantum Hall effect (QHE) in a magnetic field, where the surface Hall conductivities become quantized in units of (1/2)e 2 /h (e being the electron charge, h the Planck constant) concomitant with vanishing resistance. Here, we observe well-developed QHE arising from TSS in an intrinsic TI of BiSbTeSe 2 . Our samples exhibit surface dominated conduction even close to room temperature, while the bulk conduction is negligible. At low temperatures and high magnetic fields perpendicular to the top and bottom surfaces, we observe well-developed integer quantized Hall plateaus, where the two parallel surfaces each contributing a half integer e 2 /h quantized Hall (QH) conductance, accompanied by vanishing longitudinal resistance. When the bottom surface is gated to match the top surface in carrier density, only odd integer QH plateaus are observed, representing a half-integer QHE of two degenerate Dirac gases. This system provides an excellent platform to pursue a plethora of exotic physics and novel device applications predicted for TIs, ranging from magnetic monopoles and Majorana particles to dissipationless electronics and fault-tolerant quantum computers.
Topological Surface States in Three-Dimensional Magnetic Insulators
Physical Review Letters, 2008
An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these "Hopf insulators" are characterized by a topological invariant as in quantum Hall states and Z2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the 3-sphere to the 2-sphere. This paper gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model. PACS numbers: 73.20.At, 03.65.Vf Recent theoretical and experimental work has shown that there exist nonmagnetic band insulators in which spin-orbit coupling plays a role similar to that of the magnetic field in the integer quantum Hall effect (IQHE). In two dimensions [1], these "topological insulators" have robust edge states, observed in HgTe/(Hg,Cd)Te heterostructures , and are predicted to show a spin quantum Hall effect. The existence of a genuinely threedimensional topological insulator phase [3, 4, 5] with protected surface states, recently observed in Bi 0.9 Sb 0.1 [6], is rather surprising because the IQHE does not have a fully three-dimensional version, but only layered versions of the 2D case. Both 2D and 3D topological insulators are nonmagnetic, and in fact unbroken time-reversal invariance is required for the edge state to remain gapless. The edge or surface states of topological insulators and IQHE states exist because there are topological invariants that distinguish these insulating states from ordinary insulators, and across a boundary between one of these states and an ordinary insulator, the energy gap must close.
Anomalous Landau quantization in intrinsic magnetic topological insulators
Nature Communications
The intrinsic magnetic topological insulator, Mn(Bi1−xSbx)2Te4, has been identified as a Weyl semimetal with a single pair of Weyl nodes in its spin-aligned strong-field configuration. A direct consequence of the Weyl state is the layer dependent Chern number, CC.PreviousreportsinMnBi2Te4thinfilmshaveshownhigherC . Previous reports in MnBi2Te4 thin films have shown higherC.PreviousreportsinMnBi2Te4thinfilmshaveshownhigherCCstateseitherbyincreasingthefilmthicknessorcontrollingthechemicalpotential.AclearpictureofthehigherChernstatesisstilllackingasdatainterpretationisfurthercomplicatedbytheemergenceofsurface−bandLandaulevelsundermagneticfields.Here,wereportatunablelayer−dependentC states either by increasing the film thickness or controlling the chemical potential. A clear picture of the higher Chern states is still lacking as data interpretation is further complicated by the emergence of surface-band Landau levels under magnetic fields. Here, we report a tunable layer-dependentCstateseitherbyincreasingthefilmthicknessorcontrollingthechemicalpotential.AclearpictureofthehigherChernstatesisstilllackingasdatainterpretationisfurthercomplicatedbytheemergenceofsurface−bandLandaulevelsundermagneticfields.Here,wereportatunablelayer−dependentC$$ C = 1 state with Sb substitution by performing a detailed analysis of the quantization states in Mn(Bi1−xSbx)2Te4 dual-gated devices—consistent with calculations of the bulk Weyl point separation in the doped thin films. The observed Hall quantization plateaus for our thicker Mn(Bi1−xSbx)2Te4 films under strong magnetic fields can be interpreted b...
Magnetic topological insulators and quantum anomalous hall effect
When the magnetic order is introduced into topological insulators (TIs), the time-reversal symmetry (TRS) is broken, and the non-trivial topological surface is driven into a new massive Dirac fermions state. The study of such TRS-breaking systems is one of the most emerging frontiers in condensed-matter physics. In this review, we outline the methods to break the TRS of the topological surface states. With robust out-of-plane magnetic order formed, we describe the intrinsic magnetisms in the magnetically doped 3D TI materials and the approach to manipulate each contribution. Most importantly, we summarize the theoretical developments and experimental observations of the scale-invariant quantum anomalous Hall effect (QAHE) in both the 2D and 3D Cr-doped (BiSb) 2 Te 3 systems; at the same time, we also discuss the correlations between QAHE and other quantum transport phenomena. Finally, we highlight the use of TI/Cr-doped TI heterostructures to both manipulate the surface-related ferromagnetism and realize electrical manipulation of magnetization through the giant spin-orbit torques.
A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
2010
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern number, even if it is defined for a non-conserved quantity such as spin in the case of the spin Hall effect, one can always infer the existence of gapless edge states under certain twisted boundary conditions that allow tunneling between edges. This relation is robust against disorder and interactions, and it provides a unified topological classification of both the quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it reconciles the apparent conflict between the stability of bulk topological order and the instability of gapless edge states in systems with open boundaries (as known happening in the spin Hall case). The consequences of time reversal invariance for bulk topological order and edge state dynamics are further ...