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. However, the quantized anomalous Hall (QAH) effect has not yet been realized experimentally. In a QAH insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically non-trivial electronic structure, leading to the quantized Hall effect without any external magnetic field. In this work, based on state-of-art first principles calculations, we predict that the tetradymite semiconductors Bi$_2$Te$_3$, Bi$_2$Se$_3$, and Sb$_2$Te$_3$ form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in sharp contrast to conventional dilute magnetic semiconductor where free carriers are necessary to mediate the magnetic coupling. Magnetic order in two-dimensional thin films gives rise to a topological electronic structure characterized by a finite Chern number, with quantized Hall conductance $e^{2}/h$. Experimental realization of the long sought-after QAH insulator state could enable robust dissipationless charge transport at room temperature.
Intrinsic magnetic topological insulator ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ is believed to be an axion insulator in its antiferromagnetic ground state. However, direct identification of axion insulators remains experimentally elusive because the observed vanishing Hall resistance, while indicating the onset of the axion field, is inadequate to distinguish the system from a trivial normal insulator. Using numerical Green's functions, we theoretically demonstrate the quantized magnetoelectric current in a tunnel junction of atomically thin ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ sandwiched be…
In this paper we propose that, quantized and nearly half-quantized intrinsic anomalous Hall effect can be induced by in-plane external magnetic field through the Zeeman coupling in non-magnetic 2D systems with sizeable spin-orbital coupling but without two-fold rotational symmetry. An analytical result is derived for 2D electron gas model with $C_{3v}$ symmetry. Based on the $\boldsymbol{k\cdot p}$ Hamiltonian derived from first principle calculations, we find that quantized and nearly half-quantized conductance can be observed in $\mathrm{Sb_2Te_3}$ thin film in the clean limit with strong in…
We propose that a quantum anomalous Hall insulator (QAHI) can be realized in a nanopatterned two-dimensional electron gas (2DEG) with a small in-plane magnetic field and a high carrier density. The Berry curvatures originating from the in-plane magnetic field and Rashba and Dresselhaus spin-orbit coupling, in combination with a nanoscale honeycomb lattice potential modulation, lead to topologically nontrivial insulating states in the 2DEG without Landau levels. In the bulk insulating gaps, the anomalous Hall conductivity is quantized $-e^{2}/h$, corresponding to a finite Chern number -1. There…
One-dimensional (1D) topologically protected states are usually formed at the interface between two-dimensional (2D) materials with different topological invariants. Therefore, 1D chiral interface channels (CICs) can be created at the boundary of two quantum anomalous Hall (QAH) insulators with different Chern numbers. Such a QAH junction can function as a chiral edge current distributer at zero magnetic field, but its realization remains challenging. Here, by employing an in-situ mechanical mask, we use molecular beam epitaxy (MBE) to synthesize QAH insulator junctions, in which two QAH insul…
The half-quantized Hall conductance is characteristic of quantum systems with parity anomaly. Here we investigate topological and transport properties of a class of parity anomalous semimetals, in which massive Dirac fermions coexist with massless Dirac fermions in momentum space or real space, and uncovered a distinct bulk-edge correspondence that the half-quantized Hall effect is realized via the bulk massless Dirac fermions while the nontrivial Berry curvature is provided by the massive Dirac fermions. The spatial distribution of the edge current decays away from the boundary in a power law…
Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric H…
In magnetic topological insulators, quantized electronic transport is interwined with spontaneous magnetic ordering, as magnetization controls band gaps, hence band topology, through the exchange interaction. We show that considering the exchange gaps at the mean-field level is inadequate to predict phase transitions between electronic states of distinct topology. Thermal spin fluctuations disturbing the magnetization can act as frozen disorders that strongly scatter electrons, reducing the onset temperature of quantized transport appreciably even in the absence of structural impurities. This …
The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing puzzle of how to calculate dipole moments in crystals, but also lies at the core of the theory of topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator [3, 4] and the quantum spin Hall insulator [5-7], as well as quantized adiabatic pumping processes [8-10]. A recent theoretical proposal extended the Berry…
We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of ferromagnetic insulator Cr2Ge2Te6 and topological insulator (Bi,Sb)2Te3. Despite small magnetization in the (Bi,Sb)2Te3 layer, the anomalous Hall conductivity reaches a large value of 0.2e2/h in accord with a ferromagnetic response of the Cr2Ge2Te6. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr2Ge2Te6 layer is effective and strong enough to open the sizable exchange gap in the surface state.
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 identify topological aspects of the subextensive magnetic moment contributed by the surfaces of a three-dimensional crystallite -- assumed to be insulating in the bulk as well as on all surface facets, with trivial Chern invariants in the bulk. The geometric component of this subextensive moment is given by its derivative with respect to the chemical potential, at zero temperature and zero field, per unit surface area, and hence corresponds to the surface magnetic compressibility. The sum of the surface compressibilities contributed by two opposite facets of a cube-shaped crystallite is qua…
An anomalous Hall effect and rectification of a Hall voltage are observed by applying a radio-frequency (rf) current through a single-layered ferromagnetic wire located on a coplanar waveguide. The components of the magnetization precession, both in and perpendicular to the plane, can be detected via the Hall voltage rectification of the rf current by incorporating an additional direct (dc) current. In this paper, we propose a phenomenological model, which describes the time-dependent anisotropic magnetoresistance and time-dependent planer Hall effect. The nonlinearity of the spin dynamics acc…
Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized non-local property commonly manifests through exotic bulk phenomena and corresponding robust boundary effects. In our work, we report a new type of topological insulator exhibiting spectral bands with non-quantized topological properties, but with a quantization that arises in a corresponding system where the square of the Hamiltonian is taken. We provide a thorough theoretical analysis as well as an experimental demonstration based on photonic Ah…
We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the longitudinal and Hall resistivities are derived. In agreement with recent numerical studies, we find that the Hall resistivity is quantized in the metallic phase but diverges in the insulating phase. This suggests that the characteristics of a quantized Hall insulator can occur only in the presence of a strong dephasing mechanism.
We propose a surface-edge state theory for half quantized Hall conductance of surface states in topological insulators. The gap opening of a single Dirac cone for the surface states in a weak magnetic field is demonstrated. We find a new surface state resides on the surface edges and carries chiral edge current, resulting in a half-quantized Hall conductance in a four-terminal setup. We also give a physical interpretation of the half quantized conductance by showing that this state is the product of splitting of a boundary bound state of massive Dirac fermions which carries a conductance quant…
The quantized conductance plateaus and zero conductance fluctuation are the general consequence of electron transport in chiral edge states of Hermitian Chern insulators. Here we show that the physics of electron transport through chiral or helical edge channels becomes much richer when the non-Hermicity is allowed. In the presence of an unbalanced non-Hermicity where the chiral edge states have finite-lifetime, the conductance of the edge channels is not quantized, but its conductance fluctuation is zero. For the balanced non-Hermicity, however, the chiral edge states have infinite-lifetime, …
Quite generally, an insulator is theoretically defined by a vanishing conductivity tensor at the absolute zero of temperature. In classical insulators, such as band insulators, vanishing conductivities lead to diverging resistivities. In other insulators, in particular when a high magnetic field (B) is added, it is possible that while the magneto-resistance diverges, the Hall resistance remains finite, which is known as a Hall insulator. In this letter we demonstrate experimentally the existence of another, more exotic, insulator. This insulator, which terminates the quantum Hall effect series…
Recently extended from the modern theory of electric polarization, quantized multipole topological insulators (QMTIs) describe higher-order multipole moments, lying in nested Wilson loops, which are inherently quantized by lattice symmetries. Overlooked in the past, QMTIs reveal new types of gapped boundaries, which themselves represent lower-dimensional topological phases and host topologically protected zero-dimensional (0D) corner states. Inspired by these pioneering theoretical predictions, tremendous efforts have been devoted to the experimental observation of topological quantized quadru…
Recently,a half-quantized Hall conductance (HQHC) plateau is experimentally observed in a semi-magnetic topological insulator heterostructure. However,the heterostructure is metallic with a nonzero longitudinal conductance, which contradicts the common belief that quantized Hall conductance is usually observed in insulators.In this work,we systematically study the surface transport of the semi-magnetic topological insulator with both gapped and gapless Dirac surfaces in the presence of dephasing process.In particular, we reveal that the HQHC is directly related to the half-quantized chiral cur…
The quantum Hall effect in a 2D electron system expresses a topological invariant, leading to a quantized conductivity. The thermal Hall and thermoelectric Nernst conductances in two dimensions are also reported to be quantized in specific systems. However, a comprehensive study of these quantities within one formalism for quantum Hall systems is so far elusive. In this work, we investigate the Hall, thermal Hall, and Nernst effects analytically and numerically in 2D and 3D. In addition to the quantized values for the Hall and thermal Hall conductances in two dimensions, we also find quasi-qua…
We show how a dc current can be generated in a Hall bar without applying a bias voltage. The Hall resistance $R_H$ that corresponds to this pumped current is quantized, just as in the usual integer quantum Hall effect (IQHE). In contrast with the IQHE, however, the longitudinal resistance $R_{xx}$ does not vanish on the plateaus, but equals the Hall resistance. We propose an experimental geometry to measure the pumped current and verify the predicted behavior of $R_H$ and $R_{xx}$.
We discuss a model where the relation between Hall potential $A_H$ = and gate potential $A_G$, which is manifested by the stepped QHE = curve, is described by an uncertainty relation $ΔA_H . = ΔA_G =3D B(\hbar/e)$.
We present a direct numerical evidence for reflection symmetry of longitudinal resistivity $ρ_{xx}$ and quantized Hall resistivity $ρ_{xy}$ near the transition between $ν=1$ quantum Hall state and insulator, in accord with the recent experiments. Our results show that a universal scaling behavior of conductances, $σ_{xx}$ and $σ_{xy}$, in the transition regime decide the reflection symmetry of $ρ_{xx}$ and quantization of $ρ_{xy}$, independent of particle-hole symmetry. We also find that in insulating phase away from the transition region $ρ_{xy}$ deviates from the quantization and diverges wi…
We study a generic two-dimensional hopping model on a honeycomb lattice with strong spin-orbit coupling, without the requirement that the half-filled lattice be a Topological Insulator. For quarter-(or three-quarter) filling, we show that a state with a quantized Hall conductance generically arises in the presence of a Zeeman field of sufficient strength. We discuss the influence of Hubbard interactions and argue that spontaneous ferromagnetism (which breaks time-reversal) will occur, leading to a quantized anomalous Hall effect.
We study two-terminal transport through two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We focus on the Anomalous Floquet-Anderson Insulator (AFAI) phase, a topologically-nontrivial phase within this class, which hosts topologically protected chiral edge modes coexisting with its fully localized bulk. We show that the unique properties of the AFAI yield remarkable far-from-equilibrium transport signatures: for a large bias between leads, a quantized amount of charge is transported through the system each driving period. Upon increasi…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitatio…
We study theoretically the role of quenched magnetic disorder at the surface of a topological insulator by numerical simulation and scaling analysis. It is found that all the surface states are localized while the transverse conductivity is quantized to be $\pm {{e^2} \over {2 h}}$ as long as the Fermi energy is within the bulk gap. This greatly facilitates the realization of the topological magnetoelectric effect proposed by Qi {\it et al.} (Phys. Rev. B\textbf{78}, 195424 (2008)) with the surface magnetization direction being controlled by the simultaneous application of magnetic and electri…
We report a theoretical study of the quantized spin pump in a traditional two-parameter quantum pump device that is based on the helical edge states of a quantum spin Hall insulator. By introducing two time-dependent magnetizations out of phase as the pumping parameters, we found that when the Fermi energy resides in the energy gap opened by magnetization, an integer number of charges or spins can be pumped out in a pumping cycle and ascribed to the possible topological interface state born in between the two pumping potentials. The quantized pump current can be fully spin-polarized, spin-unpo…
We study the effect of disorder on the anomalous Hall effect (AHE) in two-dimensional ferromagnets. The topological nature of AHE leads to the integer quantum Hall effect from a metal, i.e., the quantization of $σ_{xy}$ induced by the localization except for the few extended states carrying Chern number. Extensive numerical study on a model reveals that Pruisken's two-parameter scaling theory holds even when the system has no gap with the overlapping multibands and without the uniform magnetic field. Therefore the condition for the quantized AHE is given only by the Hall conductivity $σ_{xy}$ …
We demonstrate that the experimentally observed conductance oscillations through a gate-controlled quantum dot under quantized Hall conditions originate from a true Aharonov-Bohm phase that is acquired by the electrons as they co-propagate coherently through incompressible strips at a particular filling factor and enclose a certain magnetic flux within the dot. The absence of oscillations at certain filling factors is explained. The self-consistent screening theory of the integer quantized hall effect reveals the range of experimental parameters under which further intriguing oscillation patte…
Topological insulators have been proposed to be best characterized as bulk magnetoelectric materials that show response functions quantized in terms of fundamental physical constants. Here we lower the chemical potential of three-dimensional (3D) Bi$_2$Se$_3$ films to $\sim$ 30 meV above the Dirac point, and probe their low-energy electrodynamic response in the presence of magnetic fields with high-precision time-domain terahertz polarimetry. For fields higher than 5 T, we observed quantized Faraday and Kerr rotations, whereas the DC transport is still semi-classical. A non-trivial Berry phase…
We uncover a new family of few-body topological phases in periodically driven fermionic systems in two dimensions. These phases, which we term correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by quantized contributions to the bulk magnetization from multi-particle correlations, and are classified by a family of integer-valued topological invariants. The CIAFI phases do not require many-body localization, but arise in the generic situation of k-particle localization, where the system is localized (due to disorder) for any finite number of particles up to a maximum nu…
We discuss the role of direct Coulomb interaction on the bulk insulator of the integer quantized Hall effect that bridges the topological insulators and the conductance quantization. We investigate the magneto-transport properties of a two-dimensional electron system in the bulk, numerically, utilizing the self-consistent Thomas-Fermi-Poisson screening theory. Topologically distorted Hall bars with and without potential fluctuations are considered that comprises two identical inner contacts. Although these contacts change the topology, we show that quantized Hall effect survives due to redistr…
We report unconventional transport properties of HgTe wells with inverted band structure: the resistance does not show insulating behavior even when it is of the order of $10^2\times h/2e^{2}$. The system is expected to be a two-dimensional topological insulator with a dominant edge state contribution. The results are inconsistent with theoretical models developed within the framework of the helical Luttinger liquid.
We show that an energy gap is induced in graphene by light-matter coupling to a circularly polarized photon mode in a cavity. Using many-body perturbation theory we compute the electronic spectra which exhibit photon-dressed sidebands akin to Floquet sidebands for laser-driven materials. In contrast with Floquet topological insulators, in which a strictly quantized Hall response is induced by light only for off-resonant driving in the high-frequency limit, the photon-dressed Dirac fermions in the cavity show a quantized Hall response characterized by an integer Chern number. Specifically for g…
We report a theoretical investigation on the conductance and its fluctuation of three-dimensional topological insulators (3D TI) in $Bi_2Se_3$ and $Sb_2Te_3$ in the presence of disorders. Extensive numerical simulations are carried out. We find that in the diffusive regime the conductance is quantized with fractional value. Importantly, the conductance fluctuation is also quantized with a universal value. For 3D TI connected by two terminals, three independent conductances $G_{zz}$, $G_{xx}$ and $G_{zx}$ are identified where z is the normal direction of quintuple layer of 3D TI (see inset of F…
We consider Bloch electrons in the electromagnetic field and argue the relation between the Berry phase and the quantized Hall conductivity in three-dimension. The Berry phase we consider here is induced by the adiabatic change of the time-dependent vector potential. The relation has been shown in two-dimensional systems, and we generalize the relation in three-dimensional systems.
We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the θ-term in the bulk and the associated surface Hall conductivities, σ_{xy}^S, are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the θ-term changes by \pm 2 πn along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum…
We report on our theoretical investigation considering the widths of quantized Hall plateaus (QHPs) depending on the density asymmetry induced by the large current within the out-of-linear response regime. We solve the Schrodinger equation within the Hartree type mean field approximation using Thomas Fermi Poisson nonlinear screening theory. We observe that the two dimensional electron system splits into compressible and incompressible regions for certain magnetic field intervals, where the Hall resistance is quantized and the longitudinal resistance vanishes, if an external current is imposed…
We study the current and charge distribution in a two dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasi-local transport model, that includes non-linear screening effects on the conductivity via the self-consistently calculated density profile. The existence of ``incompressible strips'' with integer Landau level filling factor is investigated within a Hartree-type approximation, and non-local effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the lo…
We examine the magnetic field driven insulator-quantum Hall-insulator transitions of the two dimensional hole gas in a Ge/SiGe quantum well. We observe direct transitions between low and high magnetic field insulators and the $ν=1$ quantum Hall state. With increasing magnetic field, the transitions from insulating to quantum Hall and quantum Hall to insulating are very similar with respect to their transport properties. We address the temperature dependence around the transitions and show that the characteristic energy scale for the high field transition is larger.
We study the quantized charge pumping of higher-order topological insulators (HOTIs) with edge-corner correspondences based on the combination of the rotation of in-plane magnetic field and the quantum spin Hall effect. A picture of a specific charge pumping process is uncovered with the help of the non-equilibrium Green's function method. Significantly, we demonstrate that the quantized charge pumping current is achieved without the participation of bulk states, and the charges move along the boundary of the sample. Furthermore, the effects of external parameters on the pumping current is als…
Experimental and theoretical investigations on the integer quantized Hall effect in gate defined narrow Hall bars are presented. At low electron mobility the classical (high temperature) Hall resistance line RH(B) cuts through the center of all Hall plateaus. In contrast, for our high mobility samples the intersection point, at even filling factors ν= 2; 4 ..., is clearly shifted towards larger magnetic fields B. This asymmetry is in good agreement with predictions of the screening theory, i. e. taking Coulomb interaction into account. The observed effect is directly related to the formation o…
Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is investigated. It is found that chiral surface states parallel to the magnetic field are responsible to the quantized Hall (QH) conductance $(2n+1)\frac{e^2}{h}$ multiplied by the number of Dirac cones. Due to the two-dimension (2D) nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and ev…
We report the observation of a quantum anomalous Hall effect in twisted bilayer graphene showing Hall resistance quantized to within .1\% of the von Klitzing constant $h/e^2$ at zero magnetic field.The effect is driven by intrinsic strong correlations, which polarize the electron system into a single spin and valley resolved moiré miniband with Chern number $C=1$. In contrast to extrinsic, magnetically doped systems, the measured transport energy gap $Δ/k_B\approx 27$~K is larger than the Curie temperature for magnetic ordering $T_C\approx 9$~K, and Hall quantization persists to temperatures o…
A finite-temperature effective free energy of the boundary of a quantized thermal Hall system is derived microscopically from the bulk two-dimensional Dirac fermion coupled with a gravitational field. In two spatial dimensions, the thermal Hall conductivity of fully gapped insulators and superconductors is quantized and given by the bulk Chern number, in analogy to the quantized electric Hall conductivity in quantum Hall systems. From the perspective of effective action functionals, two distinct types of the field theory have been proposed to describe the quantized thermal Hall effect. One of …
In this Letter, we study an Anderson-localization-induced quantized transport in disordered Chern insulators (CIs). By investigating the disordered CIs with a step potential, we find that the chiral interface states emerge along the interfaces of the step potential, and the energy range for such quantized transport can be manipulated through the potential strength. Furthermore, numerical simulations on cases with a multi-step potential demonstrate that such chiral state can be spatially shifted by varying the Fermi energy, and the energy window for quantized transport is greatly enlarged. Expe…
We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its $ν=1$ value, $h/e^{2}$. This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity i…
We present precision measurements of the fractional quantized Hall effect where the quantized resistance $R^{[1/3]}$ in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance $R^{[2]}$, represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of $1 - (5.3 \pm 6.3) 10^{-8}$ (95% confidence level) was obtained for the ratio $(R^{[1/3]}/6R^{[2]})$. Thi…
The frictional drag between parallel two-dimensional electron systems has been measured in a regime of strong interlayer correlations. When the bilayer system enters the excitonic quantized Hall state at total Landau level filling factor ν_T=1 the longitudinal component of the drag vanishes but a strong Hall component develops. The Hall drag resistance is observed to be accurately quantized at h/e^2.
We study the current and charge distribution of a two dimensional electron gas under strong perpendicular magnetic fields within the linear response regime. We show within a self-consistent screening theory that incompressible strips with integer values of local Landau-level filling factor exist for finite intervals of the magnetic field strength $B$. Within an essentially local conductivity model, we find that the current density in these $B$ intervals is confined to the incompressible strips of vanishing local longitudinal resistivity. This leads to vanishing longitudinal and exactly quantiz…
Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor 1/k (with k an odd integer) to the insulator have indicated a ``quantized Hall insulator'' (QHI) behavior: while the longitudinal resistivity diverges with decreasing temperature and current bias, the Hall resistivity remains quantized at the value $k h/ e^2$. We review the experimental results and the theoretical studies addressing this phenomenon. In particular, we discuss a theoretical approach which employs a model of the insulator as a random network of weakly coupled puddles of QH liquid at …
