We study the Kondo Lattice and Hubbard models on a triangular lattice for band filling factor 3/4. We show that a simple non-coplanar chiral spin ordering (scalar spin chirality) is naturally realized in both models due to perfect nesting of the Fermi surface. The resulting triple-Q magnetic ordering is a natural counterpart of the collinear Neel ordering of the half-filled square lattice Hubbard model. We show that the obtained chiral phase exhibits a spontaneous quantum Hall-effect with sigma_{xy}= e^2/h.
We show that the chirality of triangular antiferromagnetic clusters can be used as a qubit even if it is entirely decoupled from the total spin of the cluster. In particular, we estimate the orbital moment associated to the chirality, and we show that it can be large enough to allow a direct measurement of the chirality with a field perpendicular to the cluster. Consequences for molecular magnets are discussed, and an alternative implementation with Cu atoms on a surface is proposed, for which one- and two-qubit gates are worked out in detail. Decoherence effects are also discussed.
Much has been learned about the topological transport in real materials. We investigate the interplay between magnetism and topology in the magneto-transport of PrRhC$_2$. The four-fold degeneracy reduces to two-fold followed by non-degenerate Weyl nodes when the orientation of the magnetic quantization axis is changed from easy axis to body-diagonal through face-diagonal. This engenders chirality imbalance between positive and negative chirality Weyl nodes around the Fermi energy. We observe a significant enhancement in the chiral anomaly mediated response such as planar Hall conductivity and…
We present a theoretical proposal for the Herzberg circuit and controlled accumulation of Berry's phase in a chirality-based coded qubit in a triangular triple quantum dot molecule with one electron spin each. The qubit is encoded in the two degenerate states of a three spin complex with total spin $S=1/2$. Using a Hubbard and Heisenberg model the Herzberg circuit encircling the degeneracy point is realized by adiabatically tuning the successive on-site energies of quantum dots and tunnel couplings across a pair of neighbouring dots. It is explicitly shown that encircling the degeneracy point …
Anomalous Hall effect arising from non-trivial spin configuration (chirality) is studied based on the $s$-$d$ model. Considering a weak coupling case, the interaction is treated perturbatively. Scattering by normal impurities is included. Chirality is shown to drive locally Hall current and leads to overall Hall effect if there is a finite uniform chirality. This contribution is independent of the conventional spin-orbit contribution and shows distinct low temperature behavior. In mesoscopic spin glasses, chirality-induced anomalous Hall effect is expected below the spin-glass transition tempe…
We study theoretically the anomalous Hall effect due to the vector spin chirality carried by the local spins in the $s$-$d$ model. We will show that the vector spin chirality indeed induces local Hall effect in the presence of the electron spin polarization, while the global Hall effect vanishes if electron transport is homogeneous. This anomalous Hall effect can be interpreted in terms of the rotational component of the spin current associated with the vector chirality.
We show that the $ν=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a…
The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidos located on the sites of the square lattice. In a such system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values o…
In this Letter, we study the magnetic transport in AA-stacked bilayer honeycomb chiral magnets coupled either ferromagnetically or antiferromagnetically. For both couplings, we observe chirality-induced gaps, chiral protected edge states, magnon Hall and magnon spin Nernst effects of magnetic spin excitations. For ferromagnetically coupled layers, thermal Hall and spin Nernst conductivities do not change sign as function of magnetic field or temperature similar to single-layer honeycomb ferromagnetic insulator. In contrast, for antiferromagnetically coupled layers, we observe a sign change in …
We generalize a semiclassical theory and use the argument of angular momentum conservation to examine the ballistic transport in lightly-doped Weyl semimetals, taking into account various phase-space Berry curvatures. We predict universal transverse shifts of the wave-packet center in transmission and reflection, perpendicular to the direction in which the Fermi energy or velocities change adiabatically. The anomalous shifts are opposite for electrons with different chirality, and can be made imbalanced by breaking inversion symmetry. We discuss how to utilize local gates, strain effects, and …
Scattering by multiple scatterers sometimes gives rise to nontrivial consequences such as anomalous Hall effect. We here study a mechanism for anomalous Hall effect which originates from the correlation of nonmagnetic impurities and localized moments; a Hall effect induced by vector spin chirality. Using a scattering theory approach, we study the skew scattering induced by the scattering processes that involve two magnetic moments and a non-magnetic impurity, which is proportional to the vector spin chirality of the spins in the vicinity of the non-magnetic impurity. Furthermore, we show that …
We consider a Weyl semimetal (WSM) with finite doping and tilt within a continuum model Hamiltonian with both broken time reversal and inversion symmetry. We calculate the absorptive part of the anomalous AC Hall conductivity as a function of photon energy ($Ω$) for both type I and type II Weyl semimetal. For a given Weyl node, changing the sign of its chirality or of its tilt changes the sign of its contribution to the absorptive Hall conductivity with no change in magnitude. For a noncentrosymmetric system we find that there are ranges of photon energies for which only the positive or only t…
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…
We study current-current correlation in an electronic analog of a beam splitter realized with edge channels of a fractional quantum Hall liquid at Laughlin filling fractions. In analogy with the known result for chiral electrons, if the currents are measured at points located after the beam splitter, we find that the zero frequency equilibrium correlation vanishes due to the chiral propagation along the edge channels. Furthermore, we show that the current-current correlation, normalized to the tunneling current, exhibits clear signatures of the Laughlin quasi-particles' fractional statistics.
We investigate hyperfine-induced decoherence in a triangular spin-cluster for different qubit encodings. Electrically controllable eigenstates of spin chirality (C_z) show decoherence times that approach milliseconds, two orders of magnitude longer than those estimated for the eigenstates of the total spin projection (S_z) and of the partial spin sum (S_{12}). The robustness of chirality is due to its decoupling from both the total- and individual-spin components in the cluster. This results in a suppression of the effective interaction between C_z and the nuclear spin bath.
Chiral Magnetism and Quantum Anomalous Hall Effect in a Low-energy Kondo Model on the Triangular Lattice
University of California Santa Barbara（加州大学圣塔芭芭拉分校）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara, California（法国美国理论科学中心）；Canadian Institute for Advanced Research（加拿大高级研究院）
We report on the fate of the quantum Hall effect in graphene under strong laser illumination. By using Floquet theory combined with both a low energy description and full tight-binding models, we clarify the selection rules, the quasienergy band structure, as well as their connection with the two-terminal and multi-terminal conductance in a device setup as relevant for experiments. We show that the well-known dynamical gaps that appear in the Floquet spectrum at $\pm\,\hbarΩ/2$ lead to a switch-off of the quantum Hall edge transport for different edge terminations except for the armchair one, …
Higher-order Hall response arises from octupole order and scalar spin chirality in a noncollinear antiferromagnet
Johannes Gutenberg-University Mainz（约翰内斯·古腾堡美因茨大学）；Forschungszentrum Jülich（于利希研究中心）；Yeshiva University（叶史瓦大学）；Universidad de Salamanca（萨拉曼卡大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
The fractional quantum Hall state at Landau level (LL) filling factor 5/2 is extremely interesting because it is likely the first non-Abelian state, but its precise nature remains unclear after decades of study. We demonstrate this can be resolved by studying the chirality of its graviton excitations, using circularly polarized Raman scattering. We discuss the advantage of this bulk probe over the existing edge probes.
We study the many-body ground states of two-component hardcore bosons in topological triangular lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations, we demonstrate that at commensurate two-thirds filling per lattice site, two-component bosonic integer quantum hall (BIQH) effect emerges with the associated $\mathbf{K}=\begin{pmatrix} 0 & 1\\ 1 & 0\\ \end{pmatrix}$ matrix under strong intercomponent Hubbard repulsion. The topological nature is further elucidated by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a quantized …
We study corrections to the Heisenberg interaction between several lateral, single-electron quantum dots. We show, using exact diagonalization, that three-body chiral terms couple triangular configurations to external sources of flux rather strongly. The chiral corrections impact single qubit encodings utilizing loops of three or more Heisenberg coupled quantum dots.
The fractional quantum Hall effect is a very particular manifestation of electronic correlations in two-dimensional systems in a strong perpendicular magnetic field. It arises as a consequence of a strong Coulomb repulsion between electrons in the same Landau level that conspires with a particular chirality of the electronic states. This chirality is inherited from the classical cyclotron motion, i.e. a particular sense of electronic rotation due to the orientation of the magnetic field. The specificity of the FQHE in graphene consists of a four-fold spin-valley degeneracy inherited from the e…
A Hall effect due to spin chirality in mesoscopic systems is predicted. We consider a 4-terminal Hall system including local spins with geometry of a vortex domain wall, where strong spin chirality appears near the center of vortex. The Fermi energy of the conduction electrons is assumed to be comparable to the exchange coupling energy where the adiabatic approximation ceases to be valid. Our results show a Hall effect where a voltage drop and a spin current arise in the transverse direction. The similarity between this Hall effect and the conventional spin Hall effect in systems with spin-orb…
We propose a tight binding model for the quantum spin Hall system on triangular optical lattice and we determined the edge state spectrum which contains gap traversing states as the hallmark of $\mathds{Z}_{2}$ topological insulator. The advantage of this system is the possibility of implementing it in the fermionic ultracold atomic system whose nearly free electron limit is proposed by B. Béri and N. R. Cooper, Phys. Rev. Lett. {\bf 107}, 145301 (2011).
In a magnetic texture, the spin of a conduction electron is forced to be aligned to the localized moment. As a result, the topology of the magnetic texture affects the electron dynamics in nontrivial ways. A representative example is the topological Hall effect in noncoplanar spin textures with finite spin chirality. While propagating in the noncoplanar spin texture, electrons acquire Berry phase, and their motion is deflected as if they were in a magnetic field. Here, we report a distinct Berry phase effect in a coplanar helimagnet: the spin moment of the conduction electron is polarized unde…
Generic classical electron motion in a strong perpendicular magnetic field and random potential reduces to the bond percolation on a square lattice. Here we point out that for certain smooth 2D potentials with 120 degrees rotational symmetry this problem reduces to the site percolation on a triangular lattice. We use this observation to develop an approximate analytical description of the integer quantum Hall transition. For this purpose we devise a quantum generalization of the real-space renormalization group (RG) treatment of the site percolation on the triangular lattice. In quantum case, …
The non-trivial magnon band topology and its consequent responses have been extensively studied in two-dimensional magnetisms. However, the triangular lattice antiferromagnet (TLAF), the best-known frustrated two-dimensional magnet, has received less attention than the closely related Kagome system, because of the spin-chirality cancellation in the umbrella ground state of the undistorted TLAF. In this work, we study the band topology and the thermal Hall effect (THE) of the TLAF with (anti-)trimerization distortion under the external perpendicular magnetic field using the linearized spin wave…
We present a detailed study of the spin Hall conductivity on a two-dimensional triangular lattice in the presence of Rashba spin-orbit coupling. In particular, we focus part of our attention on the effect of the anisotropy of the nearest neighbor hopping amplitude. It is found that the presence of anisotropy has drastic effects on the spin Hall conductivity, especially in the hole doped regime where a significant increase or/and reversed sign of the spin Hall conductivity has been obtained. We also provide a systematic analysis of the numerical results in terms of Berry phases. The changes of …
This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor compo…
We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.
Quantum Hall (QH) interferometry provides an archetypal platform for the experimental realization of braiding statistics of fractional QH states. However, the complexity of observing fractional statistics requires phase coherence over the length of the interferometer, as well as suppression of Coulomb charging energy. Here, we demonstrate a new type of QH interferometer based on marginally twisted bilayer graphene (mtBLG), with a twist angle $θ$ $\approx$ $0.16$ $^{\circ}$. With the device operating in the QH regime, we observe distinct signatures of electronic Fabry-Pérot (FP) and Aharonov-Bo…
We used micromagnetic simulations to investigate the spatial distributions of the effective magnetic fields induced by spin chirality in crossed nanowires with three characteristic magnetic structures: a radiated-shape, an antivortex, and a uniform-like states. Our results indicate that, unlike the anomalous Hall effect, the topological Hall effect (which is related to the spin chirality) depends on both the polarity and the vorticity. Therefore, measuring the topological Hall effect can detect both the polarity and the vorticity simultaneously in crossed nanowires. This approach may be suitab…
Recent advances in the understanding of spin orbital effects in ultrathin magnetic heterostructures have opened new paradigms to control magnetic moments electrically. The Dzyaloshinskii-Moriya interaction (DMI) is said to play a key role in forming a Neel-type domain wall that can be driven by the spin Hall torque, a torque resulting from the spin current generated in a neighboring non-magnetic layer via the spin Hall effect. Here we show that the sign of the DMI, which determines the direction to which a domain wall moves with current, can be changed by modifying the adjacent non-magnetic la…
We investigate the dependence of band dispersion of the quantum spin Hall effect (QSHE) edge states in the Kane-Mele model on crystallographic orientation of the edges. Band structures of the one-dimensional honeycomb lattice ribbons show the presence of the QSHE edge states at all orientations of the edges given sufficiently strong spin-orbit interactions. We find that the Fermi velocities of the QSHE edge-state bands increase monotonically when the edge orientation changes from zigzag (chirality angle $θ= 0^\circ$) to armchair ($θ= 30^\circ$). We propose a simple analytical model to explain …
We have discussed here the Magnus force acting on the vortices and skyrmions in the quantum Hall systems. We have found that it is generated by the chirality of the system which is associated with the Berry phase and is same for both the cases.
We study the chiral electric separation effect (CESE) in Weyl semimetals (WSM). Within the model based on the kinetic equation we show that there is a non-zero chirality current in external electric and magnetic fields. We distinguish longitudinal, in-plane transverse, Hall, and anomalous Hall components of the CESE. It is shown that the first two components are quadratic in electric field and linear in magnetic field, while the Hall component is quadratic in both the electric and magnetic fields. All three are due to the chiral anomaly. In WSMs the chirality current can be associated with the…
The optical modes of photonic structures are the so-called TE and TM modes which bring intrinsic spin-orbit coupling and chirality to these systems. This, combined with the unique flexibility of design of the photonic potential, and the possibility to mix photon states with excitonic resonances, sensitive to magnetic field and interactions, allows to achieve many phenomena, often analogous to other solid state systems. In this contribution, we review in a qualitative and comprehensive way several of these realizations, namely the optical spin Hall effect, the creation of spin currents protecte…
For two dimensional Schroedinger Hamiltonians we formulate boundary conditions that split the Hilbert space according to the chirality of the eigenstates on the boundary. With magnetic fields, and in particular, for Quantum Hall Systems, this splitting corresponds to edge and bulk states. Applications to the integer and fractional Hall effect and some open problems are described.
Antiparallel spin polarizations as quadratic response in chiral systems
Graduate School of Science, Hokkaido University（北海道大学理学研究科）；Department of Applied Physics, The University of Tokyo（东京大学应用物理系）；Department of Physics, Meiji University（明治大学物理学系）
