Motivated by recent high-resolution scanning tunneling microscopy (STM) experiments in the quantum Hall regime both on massive two-dimensional electron gas and on graphene, we consider theoretically the disorder averaged nonlocal correlations of the local density of states (LDoS) for electrons moving in a smooth disordered potential in the presence of a high magnetic field. The intersection of two quantum cyclotron rings around the two different positions of the STM tip, correlated by the local disorder, provides peaks in the spatial dispersion of the LDoS-LDoS correlations when the intertip distance matches the sum of the two quantum Larmor radii. The energy dependence displays also complex behavior: for the local LDoS-LDoS average (i.e., at coinciding tip positions), sharp positive correlations are obtained for tip voltages near Landau level, and weak anticorrelations otherwise.
We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic approximation still holds for large skyrmions as well as for few atomic size-nanoskyrmions. Finally, we te…
We study nonlocal resistance in an H-shaped two-dimensional HgTe/CdTe quantum well consist of injector and detector, both of which can be tuned in the quantum spin Hall or metallic spin Hall regime. Because of strong spin-orbit interaction, there always exist spin Hall effect and the nonlocal resistance in HgTe/CdTe quantum well. We find that when both detector and injector are in the quantum spin Hall regime, the nonlocal resistance is quantized at $0.25\frac{h}{e^2}$, which is robust against weak disorder scattering and small magnetic field. While beyond this regime, the nonlocal resistance …
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elu…
Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley hall effect (VHE) that can be detected in nonlocal transport measurements. We provide a theory of the strain-induced VHE starting from the quantum Boltzmann equation. This allows us to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only pa…
In most cases, to observe quantized Hall plateaux, an external magnetic field is applied in intrinsic magnetic topological insulators $\mathrm{MnBi_2Te_4}$. Nevertheless, whether the nonzero Chern number ($C\neq 0$) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed $C=2$ phase [Deng \textit{et al}., Science \textbf{367}, 895 (2020)]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaux in disordered $\mathrm{MnBi_2Te_4…
We investigate the electric and thermal transport properties in a disordered Weyl ferromagnet on an equal footing by using the Keldysh formalism in curved spacetime. In particular, we calculate the anomalous thermal Hall conductivity, which consists of the Kubo formula and the heat magnetization, without relying on the Wiedemann-Franz law. We take nonmagnetic impurities into account within the self-consistent $T$-matrix approximation and reproduce the Wiedemann-Franz law for the extrinsic Fermi-surface and intrinsic Fermi-sea terms, respectively. This is the first step towards a unified theory…
Recent experiments reporting unexpectedly large spin Hall effect (SHE) in graphene decorated with adatoms have raised a fierce controversy. We apply numerically exact Kubo and Landauer- Buttiker formulas to realistic models of gold-decorated disordered graphene (including adatom clustering) to obtain the spin Hall conductivity and spin Hall angle, as well as the nonlocal resistance as a quantity accessible to experiments. Large spin Hall angles of 0.1 are obtained at zero-temperature, but their dependence on adatom clustering differs from the predictions of semiclassical transport theories. F…
Spin accumulation generated by the anomalous Hall effects (AHE) in mesoscopic ferromagnetic Ni81Fe19 (permalloy or Py) films is detected electrically by a nonlocal method. The reciprocal phenomenon, inverse spin Hall effects (ISHE), can also be generated and detected all-electrically in the same structure. For accurate quantitative analysis, a series of nonlocal AHE/ISHE structures and supplementary structures are fabricated on each sample substrate to account for statistical variations and to accurately determine all essential physical parameters in-situ. By exploring Py thicknesses of 4 nm, …
The magnetotransport properties of disordered ferromagnetic kagome layers are investigated numerically. We show that a large domain-wall magnetoresistance or negative magnetoresistance can be realized in kagome layered materials (e.g. Fe$_3$Sn$_2$, Co$_3$Sn$_2$S$_2$, and Mn$_3$Sn), which show the quantum anomalous Hall effect. The kagome layers show a strong magnetic anisotropy and a large magnetoresistance depending on their magnetic texture. These domain-wall magnetoresistances are expected to be robust against disorder and observed irrespective of the domain-wall thickness, in contrast to c…
The possibility of realizing fractional quantum Hall liquids in photonic systems has attracted a great deal of interest of late. Unlike electronic systems, interactions in photonic systems must be engineered from non-linear elements and are thus subject to positional disorder. The stability of the topological liquid relies on repulsive interactions. In this paper we investigate the stability of fractional quantum Hall liquids to impurities which host attractive interactions. We find that for sufficiently strong attractive interactions these impurities can destroy the topological liquid. Howeve…
Berry curvature hot spots in two-dimensional materials with broken inversion symmetry are responsible for the existence of transverse valley currents, which give rise to giant nonlocal dc voltages. Recent experiments in high-quality gapped graphene have highlighted a saturation of the nonlocal resistance as a function of the longitudinal charge resistivity $ρ_{{\rm c}, xx}$, when the system is driven deep into the insulating phase. The origin of this saturation is, to date, unclear. In this work we show that this behavior is fully compatible with bulk topological transport in the regime of lar…
We study the dissipative and Hall viscosity of a disordered noninteracting 2D electrons, both analytically and numerically. Analytically, we employ the self-consistent Born approximation, explicitly taking into account the modification of the single-particle density of states and the elastic transport time due to the Landau quantization. The reported results interpolate smoothly between the limiting cases of weak (strong) magnetic field and strong (weak) disorder. In the regime of weak magnetic field, our results describes the quantum (de Haas-van Alphen type) oscillations of the dissipative a…
A non-local Hall bar geometry is used to detect neutral-current Hall effects in graphene on silicon dioxide. Disorder is tuned by the addition of Au or Ir adatoms in ultra-high vacuum. A reproducible neutral-current Hall effect is found in both as-fabricated and adatom-decorated graphene. The Hall angle exhibits a complex but reproducible dependence on gate voltage and disorder, and notably breaks electron-hole symmetry. An exponential dependence on length between Hall and inverse-Hall probes indicates a neutral current relaxation length of approximately 300 nm. The short relaxation length and…
The observation of large nonlocal resistances near the Dirac point in graphene has been related to a variety of intrinsic Hall effects, where the spin or valley degrees of freedom are controlled by symmetry breaking mechanisms. Engineering strong spin or valley Hall signals on scalable graphene devices could stimulate further practical developments of spin- and valleytronics. Here we report on scale-invariant nonlocal transport in large-scale chemical vapour deposition graphene under an applied external magnetic field. Contrary to previously reported Zeeman spin Hall effect, our results are ex…
Chiral integer quantum Hall (QH) edge modes are immune to backscattering and therefore are non-localized and show a vanishing longitudinal as well as non-local resistance along with quantized 2-terminal and Hall resistance even in the presence of sample disorder. However, this is not the case for contact disorder, which refers to the possibility that a contact can reflect edge modes either partially or fully. This paper shows that when all contacts are disordered in a N-terminal quantum Hall bar, then transport via chiral QH edge modes can have a significant localization correction. The Hall a…
We study the effects of spatial dispersion in disordered noncentrosymmetric metals. These include the kinetic magnetoelectric effect, natural optical activity of metals, as well as the so-called dynamic chiral magnetic effect as a particular case of the latter. These effects are determined by the linear in the wave vector of an electromagnetic perturbation contribution to the conductivity tensor of a material, and stem from the magnetic moments of quasiparticles near the Fermi surface. We identify new disorder-induced contributions to these magnetic moments that come from the skew scattering a…
Quantum coherence and its dephasing in the giant spin Hall effect and nonlocal voltage generated by magnetotransport through multiterminal graphene bars
受近期实验观察的启发[D. A. Abanin等人，Science 323，328（2011）]中的六端石墨烯霍尔棒中的狄拉克点附近的磁输运中的非定域性，对于宽范围的温度和磁场，我们开发了该现象的非平衡格林函数（NEGF）理论。在相位相干区和强磁场中，我们发现四端桥中存在大的自旋霍尔（SH）电导，其中SH电流仅在狄拉克点（DP）处是纯的，而六端棒中的正、逆SH效应同时作用，在远处的位置处存在非局域电压.“动量松弛”的失相减少了两个数量级的DP的值，同时洗出任何功能远离DP。我们的理论是基于Meir-Wingreen公式，通过现象学的多体自能，然后线性化的多端几何形状，以提取电流和电压的失相。
Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论物理研究所）；Institute of Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Department of Physics, Nagoya University（名古屋大学物理学系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
We calculate the Hall viscosity and the nonlocal (i.e., dependent on wave vector $\bm q$) Hall conductivity of "gapped graphene" (a non-topological insulator with two valleys) in the presence of a strong perpendicular magnetic field. Using the linear-response theory at zero temperature within the Dirac approximation for the Landau levels, we present analytical expressions for both valley and total Hall viscosity and conductivity up to $\bm q^2$ at all frequencies. Although the final formulas for total Hall viscosity and conductivity are similar to the ones previously obtained for gapless graph…
It is well known that quantum spin Hall (QSH) edge modes being helical are immune to backscattering due to non-magnetic disorder within the sample. Thus, quantum spin Hall edge modes are non-localized and show a vanishing Hall resistance along with quantized 2-terminal, longitudinal and non-local resistances even in presence of sample disorder. However, this is not the case for contact disorder. This paper shows that when all contacts are disordered in an N-terminal quantum spin Hall sample, then transport via these helical QSH edge modes can have a significant localization correction. All the…
We investigate theoretically the phase coherence of electron transport in edge states of the integer quantum Hall effect at filling factor $ν=2$, in the presence of disorder and inter-edge state Coulomb interaction. Within a Fokker-Planck approach, we calculate analytically the visibility of the Aharonov-Bohm oscillations of the current through an electronic Mach-Zehnder interferometer. In agreement with recent experiments, we find that the visibility is independent of the energy of the current-carrying electrons injected high above the Fermi sea. Instead, it is the amount of disorder at the e…
The discovery of the integer quantum Hall effect in the early eighties of the last century, with highly precise quantization values for the Hall conductance in multiples of $e^2/h$, has been the first fascinating manifestation of the topological state of matter driven by magnetic field and disorder, and related to the formation of non-dissipative current flow. In 2005, several new phenomena such as the spin Hall effect and the quantum spin Hall effect were predicted in the presence of strong spin-orbit coupling and vanishing external magnetic field. More recently, the Zeeman spin Hall effect a…
We study the intrinsic and extrinsic Hall effects in disordered magnetic Weyl semimetals numerically. We show that in Weyl metals, where the Fermi energy deviates from the Weyl point, the Hall and longitudinal conductances exhibit a specific relation, which is distinguished from the well-known relation in integer quantum Hall systems. Around the Weyl point, the Hall conductance increases with increasing longitudinal conductance. This increasing behavior indicates the existence of additional contributions to the Hall conductance from the subbands of Weyl cones besides that from the bulk Berry c…
Impurities and defects are ubiquitous in topological insulators (TIs) and thus understanding the effects of disorder on electronic transport is important. We calculate the distribution of the random conductance fluctuations $P(G)$ of disordered 2D TI wires modeled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian with realistic parameters. As we show, the disorder drives the TIs into different regimes: metal (M), quantum spin-Hall insulator (QSHI), and ordinary insulator (OI). By varying the disorder strength and Fermi energy, we calculate analytically and numerically $P(G)$ across the entire pha…
We consider a disordered topological insulator thin film placed on the top of a ferromagnetic insulator with a perpendicular exchange field $M$ and subjected to a perpendicular electric field. The presence of ferromagnetic insulator causes that bottom surface states of the topological insulator thin film become spin polarized and the electric field provides a potential difference $V$ between the two surface states, resulting in breaking of time-reversal and inversion symmetry in the system. Using Kubo formalism and employing the first Born approximation as well as the self-consistent Born appr…
Under more consideration, it seems that bulk valley current mediated nonlocal resistance is inconsistent with Landau-Buttiker formalism. We believe Landau-Buttiker formalism is right and the declared bulk valley current mediated nonlocal resistance is questionable and the experimental signal should be attributed to other origins.
The robustness of the anomalous Hall conductance, $σ_{yx}^{}= σ_{H}^{}$, quantization in the model of a~two-dimensional disordered gas of massive Dirac electrons subjected to an external orthogonal magnetic field is investigated in the framework of Kubo--Středa formalism. Using the momentum representation for the averaged one-electron Green functions in a~magnetic field, an explicit analytical expression for the Středa term of $σ_{H}^{}$ is obtained. It is shown that this term is proportional to the topological Chern number, ${\rm Ch}=\pm 1/2$, if the Fermi level is in the energy gap. In this …
Recent experiments have studied the temperature and gate voltage dependence of nonlocal transport in bilayer graphene, identifying features thought to be associated with the two-dimensional semiconductor's bulk intrinsic valley Hall effect. Here, we use both simple microscopic tight-binding ribbon models and phenomenological bulk transport equations to emphasize the impact of sample edges on the nonlocal voltage signals. We show that the nonlocal valley Hall response is sensitive to electronic structure details at the sample edges, and that it is enhanced when the local longitudinal conductivi…
