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 field B pointing toward suppression of the topological protection of the electron states against impurity scattering. The temperature dependent term, $ξ_2 T$, indicates increase of the reciprocal velocity of 2D helical electrons suggesting modification of the electron spectrum in magnetic fields.
We study the influence of electron puddles created by doping of a 2D topological insulator on its helical edge conductance. A single puddle is modeled by a quantum dot tunnel-coupled to the helical edge. It may lead to significant inelastic backscattering within the edge because of the long electron dwelling time in the dot. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on temperature and doping level, and compare it with recent experimental data.
Time-reversal symmetry prohibits elastic backscattering of electrons propagating within a helical edge of a two-dimensional topological insulator. However, small band gaps in these systems make them sensitive to doping disorder, which may lead to the formation of electron and hole puddles. Such a puddle -- a quantum dot -- tunnel-coupled to the edge may significantly enhance the inelastic backscattering rate, due to the long dwelling time of an electron in the dot. The added resistance is especially strong for dots carrying an odd number of electrons, due to the Kondo effect. For the same reas…
Non-Hermitian skin effect and critical skin effect are unique features of non-Hermitian systems. In this Letter, we study an open system with its dynamics of single-particle correlation function effectively dominated by a non-Hermitian damping matrix, which exhibits $\mathbb{Z}_2$ skin effect, and uncover the existence of a novel phenomenon of helical damping. When adding perturbations that break anomalous time reversal symmetry to the system, the critical skin effect occurs, which causes the disappearance of the helical damping in the thermodynamic limit although it can exist in small size sy…
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…
The charge and spin patterns of a quantum dot embedded into a spin-orbit coupled quantum wire subject to a magnetic field are investigated. A Luttinger liquid theory is developed, taking into account open boundaries and finite magnetic field. In the quasi-helical regime, when spin-orbit effects dominate over the Zeeman interaction, peculiar states develop at the Fermi surface of the dot. Anomalous Friedel oscillations with twice the expected wavelength develop in the wavefunction of collective excitations of such states, accompanied by peculiar spin patterns in their magnetization. Both effect…
A proposal of electrically controlled spin transistor in helical magnetic field is presented. In the proposed device, the transistor action is driven by the Landau-Zener transitions that lead to a backscattering of spin polarized electrons and switching the transistor into the high-resistance state (off state). The on/off state of the transistor can be controlled by the all-electric means using Rashba spin-orbit coupling that can be tuned by the voltages applied to the side electrodes.
A non-Hermitian extension of a Chern insulator and its bulk-boundary correspondence are investigated. It is shown that in addition to the robust chiral edge states that reflect the nontrivial topology of the bulk (nonzero Chern number), anomalous helical edge states localized only at one edge can appear, which are unique to the non-Hermitian Chern insulator.
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…
In some recent experiments [A. J. Bestwick, et. al., Phys. Rev. Lett. 114, 187201 (2015), Cui-Zu Chang, et. al., Nat. Materials. 14, 473-477 (2015)] it has been shown that in observations of the quantum anomalous Hall (QAH) effect the longitudinal resistance $R_L$ increases as temperature $T$ increases, while Hall resistance $R_H$ loses its quantization with increase in $T$. This behavior was explained due to increased thermal fluctuations as $T$ increases. We show that similar effects arise in QAH samples with quasi-helical edge modes as disorder increases in presence of inelastic scattering …
We report anomalous structure in the magnetoresistance of SiO$_2$/Si(100)/SiO$_2$ quantum wells. When Landau levels of opposite valleys are driven through coincidence at the Fermi level, the longitudinal resistance displays elevations at filling factors that are integer multiples of 4 $(ν=4i)$ accompanied by suppression on either side of $ν=4i$. This persists when either magnetic field or valley splitting is swept leading to resistance ridges running along $ν=4i$. The range of field over which they are observed points to the role of spin degeneracy, which is directly confirmed by their disappe…
We present an experimental study of inverted InAs/GaSb composite quantum wells in the hybridization regime and contacted by superconducting electrodes. A front gate is used to vary the Fermi level into the mini-gap, where recent experiments indicate existence of helical edge modes [arXiv:1105.0137]. Zero bias dips in differential resistance are observed across the mini-gap, suggesting transport dominated by Andreev reflection processes. Evolution of the mini-gap differential resistance with applied bias as well as measured mini-gap excess current of 150 nA are in good agreement with the predic…
We predict by first-principles calculations that thin films of Cr-doped (Bi,Sb)$_2$Te$_3$ magnetic topological insulator have gapless non-chiral edge states coexisting with the chiral edge state. Such gapless non-chiral states are not immune to backscattering, which would explain dissipative transport in the quantum anomalous Hall (QAH) state observed in this system experimentally. Here we study the edge transport with both chiral and non-chiral states by Landaur-Büttiker formalism, and find that the longitudinal resistance is nonzero whereas Hall resistance is quantized to $h/e^2$. In particu…
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 report on the observation of non-metallic electrical conduction, resistive switching, and a negative temperature coefficient of resistance in cluster-assembled nanostructured gold films above the electrical percolation and in strong-coupling regime, from room to cryogenic temperatures (24K). The structure of the films is characterized by an extremely high density of randomly oriented crystalline nanodomains, separated by grain boundaries. The observed behavior can be explained by considering space charge limited conduction and Coulomb blockade phenomena highlighting the influence of the hig…
Local and nonlocal differential resistance measurements on Hall bars defined in AlO$_x$/KTaO$_3$ heterostructures show anomalous behavior that depends on the crystal orientation and the applied back gate voltage. The local differential resistance is asymmetric in the dc bias current, with an antisymmetric component that grows with decreasing gate voltage. More surprisingly, a large nonlocal differential resistance is observed that extends between measurement probes that are separated by 100s of microns. The potential source of this anomalous behavior is discussed.
Electrostatic Control Enables Robust Helical Edge Channel Transport in III-V Quantum Spin Hall Insulators
Julius-Maximilians-Universität Würzburg（维尔茨堡朱利叶斯-马克西米利安大学）；University of British Columbia（不列颠哥伦比亚大学）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群 ctd.qmat）；Laboratoire Charles Coulomb (L2C)（夏尔·库仑实验室 (L2C)）；Université de Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；IES（电子与系统研究所）；Institut Universitaire de France（法兰西学院）；École Normale Supérieure, PSL（巴黎高等师范学院，PSL）
The quantized version of the anomalous Hall effect has been predicted to occur in magnetic topological insulators, but the experimental realization has been challenging. Here, we report the observation of the quantum anomalous Hall (QAH) effect in thin films of Cr-doped (Bi,Sb)2Te3, a magnetic topological insulator. At zero magnetic field, the gate-tuned anomalous Hall resistance reaches the predicted quantized value of h/e^2,accompanied by a considerable drop of the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes whereas the Hall resistance remains…
An intriguing observation on the quantum anomalous Hall effect (QAHE) in magnetic topological insulators (MTIs) is the dissipative edge states, where quantized Hall resistance is accompanied by nonzero longitudinal resistance. We numerically investigate this dissipative behavior of QAHE in MTIs with a three-dimensional tight-binding model and non-equilibrium Greens function formalism. It is found that, in clean samples, the geometric mismatch between the detecting electrodes and the MTI sample leads to additional scattering in the central Hall bar, which is similar to the effect of splitting g…
We report on low-temperature electron transport properties of MnSb2Te4, a candidate of ferrimagnetic Weyl semimetal. Long -range magnetic order is manifested as a nearly square-shaped hysteresis loop in the anomalous Hall resistance, as well as sharp jumps in the magnetoresistance. At temperatures below 4 K, a lnT-type upturn appears in the temperature dependence of longitudinal resistance, which can be attributed to the electron-electron interaction (EEI), since the weak localization can be excluded by the temperature dependence of magnetoresistance. Although the anomalous Hall resistance exh…
A lattice-based model exhibits an unusual conductivity when it is subjected to both a static magnetic field and electromagnetic radiation. This conductivity anomaly may explain some aspects of the recently observed "zero-resistance states". PACS: 72.40+w, 73.40-c, 73.63 Keywords: Zero-resistance states, negative conductivity, lattice model
In this work we report experiments on defined by shallow etching narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the integer quantized Hall effect. We observe a non-monotonic increase of Hall resistance at the low magnetic field ends of the quantized plateaus, known as the overshoot effect. Unexpectedly, for Hall bars that are defined by shallow chemical etching the overshoot effect becomes more pronounced at elevated temperatures. We observe the overshoot effect at odd and…
The measured electric resistance of carbon nanotubes wrapped with DNA molecules depends strongly on the spin of the injected electrons. Motivated by these experiments, we study the effect of helix-shaped potentials on the electronic spectrum of carbon nanotubes. We find that in combination with the curvature-induced spin-orbit coupling inherent to nanotubes, such a perturbation opens helicity-dependent gaps. Within these partial gaps, left-moving electrons carry a fixed spin-projection that is reversed for right-moving electrons, and the probability of electrons to transfer through the nanotub…
We calculate spin transport in two-dimensional waveguides in the presence of spatially modulated Zeeman-split energy bands. We show that in a regime where the spin evolution is predominantly adiabatic the spin backscattering rate can be tuned via diabatic Landau-Zener transitions between the spin-split bands [C. Betthausen et. al., Science 337, 324 (2012)]. This mechanism is tolerant against spin-independent scattering processes. Completely spin-polarized systems show full spin backscattering, and thus current switching. In partially spin-polarized systems a spatial sequence of Landau-Zener tr…
Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（格勒诺布尔阿尔卑斯大学）；LPMMC, Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（物质材料研究所）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料研究所）；Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG-Pheliqs（格勒诺布尔阿尔卑斯大学）；Liaoning Academy of Materials（辽宁省材料研究院）；State Key Laboratory of Quantum Optics Technologies and Devices, Institute of Optoelectronics, Shanxi University（山西大学）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学）
In contrast to the case of ordinary quantum Hall effect, the resistance of ballistic helical edge channels in typical quantum spin-Hall experiments is non-vanishing, additive and poorly quantized. Here we present a simple argument connecting this qualitative difference with a spin relaxation in the current/voltage leads in an experimentally relevant multi-terminal bar geometry. Both the finite lead resistance and the spin relaxation contribute to a non-vanishing four-terminal edge resistance, explaining poor quantization quality. We show that corrections to the four-terminal and two-terminal r…
We explore the robust quantization of the Hall resistance in epitaxial graphene grown on Si-terminated SiC. Uniquely to this system, the dominance of quantum over classical capacitance in the charge transfer between the substrate and graphene is such that Landau levels (in particular, the one at exactly zero energy) remain completely filled over an extraordinarily broad range of magnetic fields. One important implication of this pinning of the filling factor is that the system can sustain a very high nondissipative current. This makes epitaxial graphene ideally suited for quantum resistance me…
Helical symmetry of massive Dirac fermions is broken explicitly in the presence of electric and magnetic fields. Here we present two equations for the divergence of helical and axial-vector currents following the Jackiw-Johnson approach to the anomaly of the neutral axial vector current. We discover the contribution from the helical symmetry breaking is attributed to the occupancy of the two states at the top of the valence band and the bottom of the conduction band. The explicit symmetry breaking fully cancels the anomalous correction from the quantum fluctuation in the band gap. The chiral a…
We investigate experimentally transport in gated microsctructures containing a band-inverted HgTe/Hg_{0.3}Cd_{0.7}Te quantum well. Measurements of nonlocal resistances using many contacts prove that in the depletion regime the current is carried by the edge channels, as expected for a two-dimensional topological insulator. However, high and non-quantized values of channel resistances show that the topological protection length (i.e. the distance on which the carriers in helical edge channels propagate without backscattering) is much shorter than the channel length, which is ~100 micrometers. T…
We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the juncti…
Magnetic induction can be regarded as a negative feedback effect, where the motive-force opposes the change of magnetic flux that generates the motive-force. In artificial electromagnetics emerging from spintronics, however, this is not necessarily the case. By studying the current-induced domain wall dynamics in a cylindrical nanowire, we show that the spin motive-force exerting on electrons can either oppose or support the applied current that drives the domain wall. The switching into the anomalous feedback regime occurs when the strength of the dissipative torque β is about twice the value…
CrAs is a well-known helimagnet with the double-helix structure originating from the competition between the Dzyaloshinskii-Moriya interaction (DMI) and antiferromagnetic exchange interaction $J$. By resonant soft X-ray scattering (RSXS), we observe the magnetic peak (0~0~$q_m$) that emerges at the helical transition with $T_S$ $\approx$ 267.5 K. Intriguingly, the helimagnetic domains significantly shrink on cooling below $\sim$255 K, opposite to the conventional thermal effect. The weakening of DMI on cooling is found to play a critical role here. It causes the helical wave vector to vary, or…
The transversal propagation of the edge states in a two-dimensional quantum spin Hall system are classified by decay characteristic quantity $λ$. Two different modes of the helical edge states exhibit distinct behaviors. The penetration depth is momentum dependent in normal edge states. The finite size gap decays monotonously with sample width, leading to the normal size effect. In contrast, the penetration depth maintains a uniform minimal value in the special edge states with much shorter length. The finite size gap decays non-monotonously with width, leading to the anomalous finite size eff…
Anomalous nematic states, recently discovered in ultraclean two-dimensional electron gas, emerge from quantum Hall stripe phases upon further cooling. These states are hallmarked by a local minimum (maximum) in the hard (easy) longitudinal resistance and by an incipient plateau in the Hall resistance in nearly half-filled Landau levels. Here, we demonstrate that a modest in-plane magnetic field, applied either along $\left < 110 \right >$ or $\left < 1\bar10 \right >$ crystal axis of GaAs, destroys anomalous nematic states and restores quantum Hall stripe phases aligned along their native $\le…
In this work we use electrostatic control of quantum Hall ferromagnetic transitions in CdMnTe quantum wells to study electron transport through individual domain walls (DWs) induced at a specific location. These DWs are formed due to hybridization of two counter-propagating edge states with opposite spin polarization. Conduction through DWs is found to be symmetric under magnetic field direction reversal, consistent with the helical nature of these DWs. We observe that long domain walls are in the insulating regime with localization length 4 - 6~$μ$m. In shorter DWs the resistance saturates to…
We report the magnetic and electronic transport properties of the inversion and time-reversal symmetry breaking Weyl semimetal NdAlGe. This material is analogous to NdAlSi, whose helical magnetism presents a rare example of a Weyl-mediated collective phenomenon, but with a larger spin-orbit coupling. Our neutron diffraction experiments revealed that NdAlGe, similar to NdAlSi, supports an incommensurate Ising spin density wave ($T_{\text{inc}}=6.8$ K) with a small helical spin canting of 3$^\circ$ and a long-wavelength of $\sim$ 35 nm, which transitions to a commensurate ferrimagnetic state bel…
We study the quantum anomalous Hall effect in a strip of stripes model coupled to a magnetic texture with zero total magnetization and in the presence of strong electron-electron interactions. A helical magnetization along the stripes and a spin-selective coupling between the stripes gives rise to a bulk gap and chiral edge modes. Depending on the ratio between the period of the magnetic structure and the Fermi wavelength, the system can exhibit the integer or fractional quantum anomalous Hall effect. In the fractional regime, the quasiparticles have fractional charges and non-trivial Abelian …
Coherent motion of electrons in a twisted quantum ring is considered to explore the effect of torsion inherent to the ring. Internal torsion of the ring composed of helical atomic configuration yields a non-trivial quantum phase shift in the electrons' eigenstates. This torsion-induced phase shift causes novel kinds of persistent current flow and an Aharonov-Bohm like conductance oscillation. The two phenomena can occur even when no magnetic flux penetrates inside the twisted ring, thus being in complete contrast with the counterparts observed in untwisted rings.
We present magnetotransport measurements in HgTe quantum well with inverted band structure, which expected to be a two-dimensional topological insulator having the bulk gap with helical gapless states at the edge. The negative magnetoresistance is observed in the local and nonlocal resistance configuration followed by the periodic oscillations damping with magnetic field. We attribute such behaviour to Aharonov-Bohm effect due to magnetic flux through the charge carrier puddles coupled to the helical edge states. The characteristic size of these puddles is about 100 nm.
In the quantum anomalous Hall effect, the edge states of a ferromagnetically doped topological insulator exhibit quantized Hall resistance and dissipationless transport at zero magnetic field. Up to now, however, the resistance was experimentally assessed with standard transport measurement techniques which are difficult to trace to the von-Klitzing constant R$_K$ with high precision. Here, we present a metrologically comprehensive measurement, including a full uncertainty budget, of the resistance quantization of V-doped (Bi,Sb)$_2$Te$_3$ devices without external magnetic field. We establishe…
Quantum anomalous Hall effect(QAHE) can only be realized at extremely low temperatures in magnetically doped topological insulators(TIs) due to limitations inherent with the doping precess. In an effort to boost the quantization temperature of QAHE, magnetic proximity effect in magnetic insulator/TI heterostructures has been extensively investigated. However, the observed anomalous Hall resistance has never been more than several Ohms, presumably owing to the interfacial disorders caused by the structural and chemical mismatch. Here, we show that, by growing (BixSb1-x)2Te3(BST) thin films on s…
We uncover two anomalous features in the nonlocal transport behavior of two-dimensional metallic materials with spin-orbit coupling. Firstly, the nonlocal resistance can have negative values and oscillate with distance, even in the absence of a magnetic field. Secondly, the oscillations of the nonlocal resistance under an applied in-plane magnetic field (Hanle effect) can be asymmetric under field reversal. Both features are produced by direct magnetoelectric coupling, which is possible in materials with broken inversion symmetry but was not included in previous spin diffusion theories of nonl…
We have studied quantized transport in HgTe wells with inverted band structure corresponding to the two-dimensional topological insulator phase (2D TI) with locally-controlled density allowing n-p-n and n-2D TI-n junctions. The resistance reveals the fractional plateau $2h/e^{2}$ in n-p-n regime in the presence of the strong perpendicular magnetic field. We found that in n-2D TI-n regime the plateaux in resistance in not universal and results from the edge state equilibration at the interface between chiral and helical edge modes. We provided the simple model describing the resistance quantiza…
Semiconductors with strong spin-orbit interactions can exhibit a helical gap with spin-momentum locking opened by a magnetic field. Such a gap is highly spin selective as a result of a topologically protected spin-momentum locking, which can be used for spin filtering. We experimentally demonstrate such a spin filtering effect in a quasi-ballistic p-type germanium/silicon core/shell nanowire (NW), which possesses a pseudo-helical gap without the application of magnetic field. Polarized hole spin injection to the NW is achieved using cobalt ferromagnetic contacts with controlled natural surface…
A study of the resistively detected nuclear magnetic resonance (RDNMR) lineshape in the vicinity of $ν=1$ was performed on a high-mobility 2D electron gas formed in GaAs/AlGaAs. In higher Landau levels, application of an RF field at the nuclear magnetic resonance frequency coincides with an observed minimum in the longitudinal resistance, as predicted by the simple hyperfine interaction picture. Near $ν=1$ however, an anomalous dispersive lineshape is observed where a resistance peak follows the usual minimum. In an effort to understand the origin of this anomalous peak we have studied the res…
In this work, we demonstrate that making a cut (a narrow vacuum regime) in the bulk of a quantum anomalous Hall insulator (QAHI) creates a topologically protected single helical channel with counter-propagating electron modes, and inducing superconductivity on the helical channel through proximity effect will create Majorana zero energy modes (MZMs) at the ends of the cut. In this geometry, there is no need for the proximity gap to overcome the bulk insulating gap of the QAHI to create MZMs as in the two-dimensional QAHI/superconductor (QAHI/SC) heterostructures. Therefore, the topological reg…
Helical metals realized at the surfaces of topological insulators have recently attracted wide attention due to their potential applications in spintronics. In this paper we propose to realize helical metals through the application of THz light on common two-dimensional semiconductors and discuss their observable properties. We show that the application of circularly polarized light enables coherent manipulation of magnetization. Moreover, for a range of chemical potentials the system behaves as a helical metal, exhibiting a large anomalous Hall conductivity and associated magnetoelectric effe…
We present a microscopic theory of the Hall current in the bilayer quantum Hall system on the basis of noncommutative geometry. By analyzing the Heisenberg equation of motion and the continuity equation of charge, we demonstrate the emergence of the phase current in a system where the interlayer phase coherence develops spontaneously. The phase current arranges itself to minimize the total energy of the system, as induces certain anomalous behaviors in the Hall current in the counterflow geometry and also in the drag experiment. They explain the recent experimental data for anomalous Hall resi…
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 …
In a magnetic metal, the Hall resistance is generally taken to be the sum of the ordinary Hall resistance and the anomalous Hall resistance. Here it is shown that this empirical relation is no longer valid when either the ordinary Hall angle or the anomalous Hall angle is not small. Using the proper conductivity relation, we reveal an unexpected magnetoresistance (MR) induced by the anomalous Hall effect (AHE). A $B$-linear MR arises and the sign of the slope depends on the sign of the anomalous Hall angle, giving rise to a characteristic bowtie shape. The Hall resistance in a single-band syst…
In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating 2D bulk, without requiring an external magnetic field. Here, we explore the potential of this effect in magnetic topological insulator thin films for metrological applications. Using a cryogenic current comparator system, we measure quantization of the Hall resistance to within one part per million and longitudinal resistivity under 10 m$Ω$ per square at zero magnetic field. Increasing the curre…
