Global phase diagram in the quantum Hall effect

Quantized anomalous Hall resistivity achieved in molecular beam epitaxy-grown MnBi2Te4 thin films

The intrinsic magnetic topological insulator MnBi2Te4 provides a feasible pathway to the high-temperature quantum anomalous Hall (QAH) effect as well as various novel topological quantum phases. Although quantized transport properties have been observed in exfoliated MnBi2Te4 thin flakes, it remains a big challenge to achieve molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films even close to the quantized regime. In this work, we report the realization of quantized anomalous Hall resistivity in MBE-grown MnBi2Te4 thin films with the chemical potential tuned by both controlled in situ oxygen exposure and top gating. We find that elongated post-annealing obviously elevates the temperature to achieve quantization of the Hall resistivity, but also increases the residual longitudinal resistivity, indicating a picture of high-quality QAH puddles weakly coupled by tunnel barriers. These results help to clarify the puzzles in previous experimental studies on MnBi2Te4 and to find a way out of the big difficulty in obtaining MnBi2Te4 samples showing quantized transport properties.

Continuous Phase Transitions between Fractional Quantum Hall States and Symmetry-Protected Topological States

We study quantum phase transitions in Bose-Fermi mixtures driven by interspecies interaction in the quantum Hall regime. In the absence of such an interaction, the bosons and fermions form their respective fractional quantum Hall (FQH) states at certain filling factors. A symmetry-protected topological (SPT) state is identified as the ground state for strong interspecies interaction. The phase transitions between them are proposed to be described by Chern-Simons-Higgs field theories. For a simple microscopic Hamiltonian, we present numerical evidence for the existence of the SPT state and a continuous transition to the FQH state. It is also found that the entanglement entropy between the bosons and fermions exhibits scaling behavior in the vicinity of this transition.

Zero-Field Composite Fermi Liquid in Twisted Semiconductor Bilayers

Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moiré superlattice system tMoTe_{2}. Here, we argue that a composite fermion description, already a unifying framework for the phenomenology of 2D electron gases at high magnetic fields, provides a similarly powerful perspective in this new context. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in tMoTe_{2} at fillings n=1/2 and n=3/4. We dub these non-Fermi liquid metals anomalous composite Fermi liquids (ACFLs), and we argue that they play a central organizing role in the FQAH phase diagram. We proceed to develop a long wavelength theory for this ACFL state that offers concrete experimental predictions upon doping the composite Fermi sea, including a Jain sequence of FQAH states and a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system.

Quantized resistance revealed at the criticality of the quantum anomalous Hall phase transitions

In multilayered magnetic topological insulator structures, magnetization reversal processes can drive topological phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Here we report an examination of the critical behavior of two such transitions: the quantum anomalous Hall to normal insulator (QAH-NI), and quantum anomalous Hall to axion insulator (QAH-AXI) transitions. By introducing a new analysis protocol wherein temperature dependent variations in the magnetic coercivity are accounted for, the critical behavior of the QAH-NI and QAH-AXI transitions are evaluated over a wide range of temperature and magnetic field. Despite the uniqueness of these different transitions, quantized longitudinal resistance and Hall conductance are observed at criticality in both cases. Furthermore, critical exponents were extracted for QAH-AXI transitions occurring at magnetization reversals of two different magnetic layers. The observation of consistent critical exponents and resistances in each case, independent of the magnetic layer details, demonstrates critical behaviors in quantum anomalous Hall transitions to be of electronic rather than magnetic origin. Our finding offers a new avenue for studies of phase transition and criticality in QAH insulators.

Anderson Localization in the Fractional Quantum Hall Effect

The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor ν=n/(2n+1) has a striking quantitative correspondence to the localization of a single electron in the (n+1)th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation, these results can be extended to situations where a finite density of quasiparticles is present.

Giant Magnetoresistance in a Chemical Vapor Deposition Graphene Constriction

Magnetic field-driven insulating states in graphene are associated with samples of very high quality. Here, this state is shown to exist in monolayer graphene grown by chemical vapor deposition (CVD) and wet transferred on Al₂O₃ without encapsulation with hexagonal boron nitride (h-BN) or other specialized fabrication techniques associated with superior devices. Two-terminal measurements are performed at low temperature using a GaAs-based multiplexer. During high-throughput testing, insulating properties are found in a 10 μm long graphene device which is 10 μm wide at one contact with an ≈440 nm wide constriction at the other. The low magnetic field mobility is ≈6000 cm² V^-1 s^-1. An energy gap induced by the magnetic field opens at charge neutrality, leading to diverging resistance and current switching on the order of 10⁴ with DC bias voltage at an approximate electric field strength of ≈0.04 V μm^-1 at high magnetic field. DC source-drain bias measurements show behavior associated with tunneling through a potential barrier and a transition between direct tunneling at low bias to Fowler-Nordheim tunneling at high bias from which the tunneling region is estimated to be on the order of ≈100 nm. Transport becomes activated with temperature from which the gap size is estimated to be 2.4 to 2.8 meV at B = 10 T. Results suggest that a local electronically high quality region exists within the constriction, which dominates transport at high B, causing the device to become insulating and act as a tunnel junction. The use of wet transfer fabrication techniques of CVD material without encapsulation with h-BN and the combination with multiplexing illustrates the convenience of these scalable and reasonably simple methods to find high quality devices for fundamental physics research and with functional properties.

Thickness-Driven Quantum Anomalous Hall Phase Transition in Magnetic Topological Insulator Thin Films

The quantized version of the anomalous Hall effect realized in magnetic topological insulators (MTIs) has great potential for the development of topological quantum physics and low-power electronic/spintronic applications. Here we report the thickness-tailored quantum anomalous Hall (QAH) effect in Cr-doped (Bi,Sb)₂Te₃ thin films by tuning the system across the two-dimensional (2D) limit. In addition to the Chern number-related QAH phase transition, we also demonstrate that the induced hybridization gap plays an indispensable role in determining the ground magnetic state of the MTIs; namely, the spontaneous magnetization owing to considerable Van Vleck spin susceptibility guarantees the zero-field QAH state with unitary scaling law in thick samples, while the quantization of the Hall conductance can only be achieved with the assistance of external magnetic fields in ultrathin films. The modulation of topology and magnetism through structural engineering may provide useful guidance for the pursuit of other QAH-based phase diagrams and functionalities.

Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi_{2}Te_{4}

In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators MnBi_{2}Te_{4}. Nevertheless, whether the nonzero Chern number (C≠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 et al., Science 367, 895 (2020)SCIEAS0036-807510.1126/science.aax8156]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered MnBi_{2}Te_{4}. Rather good consistency between the experimental and numerical results confirms that the bulk states are localized in the absence of a magnetic field and a QAH edge state emerges with C=1. However, under a strong magnetic field, the lowest Landau band formed with the localized bulk states, survives disorder, together with the QAH edge state, leading to a C=2 phase. Eventually, we present a phase diagram of a disordered MnBi_{2}Te_{4} which indicates more coexistence states of QAH and QH to be verified by future experiments.

Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator

The intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = -1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi2Te4.

Theory for Magnetic-Field-Driven 3D Metal-Insulator Transitions in the Quantum Limit

Metal-insulator transitions driven by magnetic fields have been extensively studied in 2D, but a 3D theory is still lacking. Motivated by recent experiments, we develop a scaling theory for the metal-insulator transitions in the strong-magnetic-field quantum limit of a 3D system. By using a renormalization-group calculation to treat electron-electron interactions, electron-phonon interactions, and disorder on the same footing, we obtain the critical exponent that characterizes the scaling relations of the resistivity to temperature and magnetic field. By comparing the critical exponent with those in a recent experiment [F. Tang et al., Nature (London) 569, 537 (2019)NATUAS0028-083610.1038/s41586-019-1180-9], we conclude that the insulating ground state was not only a charge-density wave driven by electron-phonon interactions but also coexisting with strong electron-electron interactions and backscattering disorder. We also propose a current-scaling experiment for further verification. Our theory will be helpful for exploring the emergent territory of 3D metal-insulator transitions under strong magnetic fields.

Numerical Study of a Dual Representation of the Integer Quantum Hall Transition

We study the critical properties of the noninteracting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality CF states are delocalized at all energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain ν=2.56±0.02 and η=0.51±0.01, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.

Graphene quantum Hall effect parallel resistance arrays

As first recognized in 2010, epitaxial graphene on SiC(0001) provides a platform for quantized Hall resistance (QHR) metrology unmatched by other two-dimensional structures and materials. Here we report graphene parallel QHR arrays, with metrologically precise quantization near 1000 Ω. These arrays have tunable carrier densities, due to uniform epitaxial growth and chemical functionalization, allowing quantization at the robust ν = 2 filling factor in array devices at relative precision better than 10^-8. Broad tunability of the carrier density also enables investigation of the ν = 6 plateau. Optimized networks of QHR devices described in this work suppress Ohmic contact resistance error using branched contacts and avoid crossover leakage with interconnections that are superconducting for quantizing magnetic fields up to 13.5 T. Our work enables more direct scaling of resistance for quantized values in arrays of arbitrary network geometry.

Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices

We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping-tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.

Dimensional Crossover of the Integer Quantum Hall Plateau Transition and Disordered Topological Pumping

We study the quantum Hall plateau transition on rectangular tori. As the aspect ratio of the torus is increased, the two-dimensional critical behavior, characterized by a subthermodynamic number of topological states in a vanishing energy window around a critical energy, changes drastically. In the thin-torus limit, the entire spectrum is Anderson localized; however, an extensive number of states retain a Chern number C≠0. We resolve this apparent paradox by mapping the thin-torus quantum Hall system onto a disordered Thouless pump, where the Chern number corresponds to the winding number of an electron's path in real space during a pump cycle. We then characterize quantitatively the crossover between the one- and two-dimensional regimes for finite torus thickness, where the average Thouless conductance also shows anomalous scaling.

Universal Thermodynamic Signature of Self-Dual Quantum Critical Points

Self-duality is an algebraic structure of certain critical theories, which is not encoded in the scaling dimensions and critical exponents. In this work, a universal thermodynamic signature of self-dual quantum critical points (QCPs) is proposed. It is shown that the Grüneisen ratio at a self-dual QCP remains finite as T→0, which is in sharp contrast to its universal divergence at a generic QCP without self-duality, Γ(T,g_{c})∼T^{-1/zν}. This conclusion is drawn based on the hyperscaling theory near the QCP, and has far-reaching implications for experiments and numerical simulations.

Quantum-Hall to Insulator Transition in Ultra-Low-Carrier-Density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level

A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it is challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb₂ Te₃ films, an extreme quantum limit of the topological surface state is reached and a hidden phase at the zeroth Landau level is uncovered. First, an unexpected quantum-Hall-to-insulator-transition near the zeroth Landau level is discovered. Then, through a detailed scaling analysis, it is found that this quantum-Hall-to-insulator-transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in nontopological systems.

Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene

When two sheets of graphene are stacked at a small twist angle, the resulting flat superlattice minibands are expected to strongly enhance electron-electron interactions. Here, we present evidence that near three-quarters (34) filling of the conduction miniband, these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state. In a narrow density range around an apparent insulating state at34, we observe emergent ferromagnetic hysteresis, with a giant anomalous Hall (AH) effect as large as 10.4 kilohms and indications of chiral edge states. Notably, the magnetization of the sample can be reversed by applying a small direct current. Although the AH resistance is not quantized, and dissipation is present, our measurements suggest that the system may be an incipient Chern insulator.

Current quantization and fractal hierarchy in a driven repulsive lattice gas

Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the nonequilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density.

A magnetic heterostructure of topological insulators as a candidate for an axion insulator

The axion insulator which may exhibit an exotic quantized magnetoelectric effect is one of the most interesting quantum phases predicted for the three-dimensional topological insulator (TI). The axion insulator state is expected to show up in magnetically doped TIs with magnetizations pointing inwards and outwards from the respective surfaces. Towards the realization of the axion insulator, we here engineered a TI heterostructure in which magnetic ions (Cr) are modulation-doped only in the vicinity of the top and bottom surfaces of the TI ((Bi,Sb)₂Te₃) film. A separation layer between the two magnetic layers weakens interlayer coupling between them, enabling the magnetization reversal of individual layers. We demonstrate the realization of the axion insulator by observing a zero Hall plateau (ZHP) (where both the Hall and longitudinal conductivity become zero) in the electric transport properties, excluding the other possible origins for the ZHP. The manifestation of the axion insulator can lead to a new stage of research on novel magnetoelectric responses in topological matter.

Unusual renormalization group (RG) flow and temperature-dependent phase transition in strongly-insulating monolayer epitaxial graphene

By changing the measurement temperature (T), one can vary the effective sample size so as to study the renormalization group (RG) (or T-driven) flow of a semiconductor, a topological insulator, or a graphene device in the complex conductivity plane.

Quantum-critical fluctuations in 2D metals: strange metals and superconductivity in antiferromagnets and in cuprates

The anomalous transport and thermodynamic properties in the quantum-critical region, in the cuprates, and in the quasi-two dimensional Fe-based superconductors and heavy-fermion compounds, have the same temperature dependences. This can occur only if, despite their vast microscopic differences, a common statistical mechanical model describes their phase transitions. The antiferromagnetic (AFM)-ic models for the latter two, just as the loop-current model for the cuprates, map to the dissipative XY model. The solution of this model in (2+1)D reveals that the critical fluctuations are determined by topological excitations, vortices and a variety of instantons, and not by renormalized spin-wave theories of the Landau-Ginzburg-Wilson type, adapted by Moriya, Hertz and others for quantum-criticality. The absorptive part of the fluctuations is a separable function of momentum [Formula: see text], measured from the ordering vector, and of the frequency ω and the temperature T which scale as [Formula: see text] at criticality. Direct measurements of the fluctuations by neutron scattering in the quasi-two-dimensional heavy fermion and Fe-based compounds, near their antiferromagnetic quantum critical point, are consistent with this form. Such fluctuations, together with the vertex coupling them to fermions, lead to a marginal fermi-liquid, with the imaginary part of the self-energy [Formula: see text] for all momenta, a resistivity [Formula: see text], a [Formula: see text] contribution to the specific heat, and other singular fermi-liquid properties common to these diverse compounds, as well as to d-wave superconductivity. This is explicitly verified, in the cuprates, by analysis of the pairing and the normal self-energy directly extracted from the recent high resolution angle resolved photoemission measurements. This reveals, in agreement with the theory, that the frequency dependence of the attractive irreducible particle-particle vertex in the d-wave channel is the same as the irreducible particle-hole vertex in the full symmetry of the lattice.

Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems

We theoretically investigate the localization mechanism of the quantum anomalous Hall effect (QAHE) in the presence of spin-flip disorders. We show that the QAHE stays quantized at weak disorders, then enters a Berry-curvature mediated metallic phase at moderate disorders, and finally goes into the Anderson insulating phase at strong disorders. From the phase diagram, we find that at the charge neutrality point although the QAHE is most robust against disorders, the corresponding metallic phase is much easier to be localized into the Anderson insulating phase due to the interchange of Berry curvatures carried, respectively, by the conduction and valence bands. In the end, we provide a phenomenological picture related to the topological charges to better understand the underlying physical origin of the QAHE Anderson localization.

Insulator-quantum Hall transitionin monolayer epitaxial graphene

We report on magneto-transport measurements on low-density, large-area monolayer epitaxial graphene devices grown on SiC. We observe temperature (T)-independent crossing points in the longitudinal resistivity ρxx, which are signatures of the insulator-quantum Hall (I-QH) transition, in all three devices. Upon converting the raw data into longitudinal and Hall conductivities σxx and σxy, in the most disordered device, we observed T-driven flow diagram approximated by the semi-circle law as well as the T-independent point in σxy near e2/h. We discuss our experimental results in the context of the evolution of the zero-energy Landau level at low magnetic fields B. We also compare the observed strongly insulating behaviour with metallic behaviour and the absence of the I-QH transition in graphene on SiO2 prepared by mechanical exfoliation.

Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films

We combine measurements of the longitudinal (ρxx) and Hall (ρxy) resistivities of disordered 2D amorphous indium-oxide films to study the magnetic-field tuned superconductor-to-insulator transition (H-SIT) in the T --> 0 limit. At the critical field, Hc, the full resistivity tensor is T independent with ρxx(Hc) = h/4e(2) and ρxy(Hc) = 0 within experimental uncertainty in all films (i.e., these appear to be "universal" values); this is strongly suggestive that there is a particle-vortex self-duality at H = Hc. The transition separates the (presumably) superconducting state at H < Hc from a "Hall-insulator" phase in which ρxx --> ∞ as T --> 0 whereas ρxy approaches a nonzero value smaller than its "classical value" H/nec; i.e., 0 < ρxy < H/nec. A still higher characteristic magnetic field, Hc* > Hc, at which the Hall resistance is T independent and roughly equal to its classical value, ρxy ≈ H/nec, marks an additional crossover to a high-field regime (probably to a Fermi insulator) in which ρxy > H/nec and possibly diverges as T --> 0. We also highlight a profound analogy between the H-SIT and quantum-Hall liquid-to-insulator transitions (QHIT).

Metal-to-insulator switching in quantum anomalous Hall states

After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr_0.12Bi_0.26Sb_0.62)₂Te₃ film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. In addition, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications.

The quantum anomalous Hall effect is a recently demonstrated chiral transport phenomenon arising in magnetically doped topological insulators. Here, the authors study the Hall plateau switching and universal phase diagram of the quantum anomalous Hall effect in thin films of two-dimensional Cr-doped (BiSb)₂Te₃.

Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator

We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau.

Topological quantum transitions in a two-band Chern insulator with n = 2

Based on a two-band Chern insulator with Chern number n = 2, we study the transport properties and the topological phase transition induced by either an external magnetic field or disorder. In this paper, a characteristic topological phase transition from n = 2 to n = 0, which is in sharp contrast to the plateau-plateau transition in the integer quantum Hall effect, is observed. This unique feature of the phase transition should be ascribed to the minimal two-band feature of this high Chern insulator. We prove this result by studying the transport properties of many different geometrical structures and the evolution of the Chern number in the presence of magnetic fields and strong disorder.

Localization and electron-electron interactions in few-layer epitaxial graphene

This paper presents a study of the quantum corrections caused by electron-electron interactions and localization to the conductivity in few-layer epitaxial graphene, in which the carriers responsible for transport are massive. The results demonstrate that the diffusive model, which can generally provide good insights into the magnetotransport of two-dimensional systems in conventional semiconductor structures, is applicable to few-layer epitaxial graphene when the unique properties of graphene on the substrate, such as intervalley scattering, are taken into account. It is suggested that magnetic-field-dependent electron-electron interactions and Kondo physics are required for obtaining a thorough understanding of magnetotransport in few-layer epitaxial graphene.

Dirac fermion heating, current scaling, and direct insulator-quantum Hall transition in multilayer epitaxial graphene

We have performed magnetotransport measurements on multilayer epitaxial graphene. By increasing the driving current I through our graphene devices while keeping the bath temperature fixed, we are able to study Dirac fermion heating and current scaling in such devices. Using zero-field resistivity as a self thermometer, we are able to determine the effective Dirac fermion temperature (TDF) at various driving currents. At zero field, it is found that TDF ∝ I≈1/2. Such results are consistent with electron heating in conventional two-dimensional systems in the plateau-plateau transition regime. With increasing magnetic field B, we observe an I-independent point in the measured longitudinal resistivity ρxx which is equivalent to the direct insulator-quantum Hall (I-QH) transition characterized by a temperature-independent point in ρxx. Together with recent experimental evidence for direct I-QH transition, our new data suggest that such a transition is a universal effect in graphene, albeit further studies are required to obtain a thorough understanding of such an effect.

Insulating to relativistic quantum Hall transition in disordered graphene

Quasi-particle excitations in graphene exhibit a unique behavior concerning two key phenomena of mesoscopic physics: electron localization and the quantum Hall effect. A direct transition between these two states has been found in disordered two-dimensional electron gases at low magnetic field. It has been suggested that it is a quantum phase transition, but the nature of the transition is still debated. Despite the large number of works studying either the localization or the quantum Hall regime in graphene, such a transition has not been investigated for Dirac fermions. Here we discuss measurements on low-mobility graphene where the localized state at low magnetic fields and a quantum Hall state at higher fields are observed. We find that the system undergoes a direct transition from the insulating to the Hall conductor regime. Remarkably, the transverse magneto-conductance shows a temperature independent crossing point, pointing to the existence of a genuine quantum phase transition.

Experimental evidence for direct insulator-quantum Hall transition in multi-layer graphene

We have performed magnetotransport measurements on a multi-layer graphene flake. At the crossing magnetic field Bc, an approximately temperature-independent point in the measured longitudinal resistivity ρxx, which is ascribed to the direct insulator-quantum Hall (I-QH) transition, is observed. By analyzing the amplitudes of the magnetoresistivity oscillations, we are able to measure the quantum mobility μq of our device. It is found that at the direct I-QH transition, μqBc ≈ 0.37 which is considerably smaller than 1. In contrast, at Bc, ρxx is close to the Hall resistivity ρxy, i.e., the classical mobility μBc is ≈ 1. Therefore, our results suggest that different mobilities need to be introduced for the direct I-QH transition observed in multi-layered graphene. Combined with existing experimental results obtained in various material systems, our data obtained on graphene suggest that the direct I-QH transition is a universal effect in 2D.

Insulator, semiclassical oscillations and quantum Hall liquids at low magnetic fields

Magneto-transport measurements are performed on two-dimensional GaAs electron systems to probe the quantum Hall (QH) effect at low magnetic fields. Oscillations following the Shubnikov-de Haas (SdH) formula are observed in the transition from the insulator to QH liquid when the observed almost temperature-independent Hall slope indicates insignificant interaction correction. Our study shows that the existence of SdH oscillations in such a transition can be understood based on the non-interacting model.

Probing temperature-driven flow lines in a gated two-dimensional electron gas with tunable spin-splitting

We study the temperature flow of conductivities in a gated GaAs two-dimensional electron gas (2DEG) containing self-assembled InAs dots and compare the results with recent theoretical predictions. By changing the gate voltage, we are able to tune the 2DEG density and thus vary disorder and spin-splitting. Data for both the spin-resolved and spin-degenerate phase transitions are presented, the former collapsing to the latter with decreasing gate voltage and/or decreasing spin-splitting. The experimental results support a recent theory, based on modular symmetry, which predicts how the critical Hall conductivity varies with spin-splitting.

A delta-doped quantum well system with additional modulation doping

A delta-doped quantum well with additional modulation doping may have potential applications. Utilizing such a hybrid system, it is possible to experimentally realize an extremely high two-dimensional electron gas (2DEG) density without suffering inter-electronic-subband scattering. In this article, the authors report on transport measurements on a delta-doped quantum well system with extra modulation doping. We have observed a 0-10 direct insulator-quantum Hall (I-QH) transition where the numbers 0 and 10 correspond to the insulator and Landau level filling factor ν = 10 QH state, respectively. In situ titled-magnetic field measurements reveal that the observed direct I-QH transition depends on the magnetic component perpendicular to the quantum well, and the electron system within this structure is 2D in nature. Furthermore, transport measurements on the 2DEG of this study show that carrier density, resistance and mobility are approximately temperature (T)-independent over a wide range of T. Such results could be an advantage for applications in T-insensitive devices.

On the direct insulator-quantum Hall transition in two-dimensional electron systems in the vicinity of nanoscaled scatterers

A direct insulator-quantum Hall (I-QH) transition corresponds to a crossover/transition from the insulating regime to a high Landau level filling factor ν > 2 QH state. Such a transition has been attracting a great deal of both experimental and theoretical interests. In this study, we present three different two-dimensional electron systems (2DESs) which are in the vicinity of nanoscaled scatterers. All these three devices exhibit a direct I-QH transition, and the transport properties under different nanaoscaled scatterers are discussed.

Metal to insulator transition on the N=0 Landau level in graphene

The magnetotransport in single layer graphene has been experimentally investigated in magnetic fields up to 18 T as a function of temperature. A pronounced T dependence is observed for T≲50  K, which is either metallic, or insulating, depending on the filling factor ν. The metal-insulator transition (MIT) occurs at |ν{c}|∼0.65 and in the regime of the dissipative transport, where the longitudinal resistance Rxx>1/2R{K}. The critical resistivity (Rxx per square) is ρ{xx}(ν{c})≈1/2R{K} and is correlated with the appearance of zero plateau in Hall conductivity σ{xy}(ν) and peaks in σ{xx}(ν). This leads us to construct a universal low-T (n, B) phase diagram of this quantum phase transition.

Microscopic description of a quantum Hall transition without landau levels

By restricting the motion of a high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum mechanically, the interplay of backscattering, and of the bending action of a weak magnetic field. Backscattering limits the mobility, while bending initiates quantization of the Hall conductivity. We demonstrate that, in restricted geometry, electron motion reduces to two Chalker-Coddington networks, with opposite directions of propagation along the links, which are weakly coupled by disorder. The interplay of backscattering and bending results in the quantum Hall transition in a nonquantizing magnetic field, which decreases with increasing mobility. This is in accord with the scenario of floating up delocalized states.

Influence of interlayer tunneling on the quantized Hall phases in intentionally disordered multilayer structures

Stability of the quantized Hall phases is studied in weakly coupled multilayers as a function of the interlayer correlations controlled by the interlayer tunneling and by the random variation of the well thicknesses. A strong enough interlayer disorder destroys the symmetry responsible for the quantization of the Hall conductivity, resulting in the breakdown of the quantum Hall effect. A clear difference between the dimensionalities of the metallic and insulating quantum Hall phases is demonstrated. The sharpness of the quantized Hall steps obtained in the coupled multilayers with different degrees of randomization was found consistent with the calculated interlayer tunneling energies. The observed width of the transition between the quantized Hall states in random multilayers is explained in terms of the local fluctuations of the electron density.

Microscopic theory of the quantum Hall hierarchy

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.

Low-field phase diagram of the spin Hall effect in the mesoscopic regime

When a mesoscopic two dimensional four-terminal Hall cross bar with spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field B, both integer quantum Hall effect (IQHE) and mesoscopic spin Hall effect (MSHE) may exist when disorder strength W in the sample is weak. We have calculated the low field "phase diagram" of MSHE in the (B,W) plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance G(sH) and its fluctuations rms(G(sH)) vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values G(sH)=1/2 and rms(G(sH))=0 on those odd numbered plateaus induced by Zeeman energy. At larger disorders, the system crosses over into a regime where both G(sH) and rms(G(sH)) are finite, a chaotic regime, and finally a localized regime.

Redistributing Chern numbers of Landau subbands: tight-binding electrons under staggered modulated magnetic fields

We investigate the magnetotransport properties of electrons on a square lattice under a magnetic field with the alternate flux strength phi+/-Deltaphi in neighboring plaquettes. A new peculiar behavior of the Hall conductance has been found and is robust against weak disorder: if phi=(p/2N)2pi (p and 2N are coprime integers) is fixed, the Chern numbers of Landau subbands will be redistributed between neighboring pairs and hence the total quantized Hall conductance exhibits a direct transition by +/-Ne2/h at critical fillings when Deltaphi is increased from 0 up to a critical value Deltaphi_{c}. This effect can be an experimental probe of the staggered-flux phase.

Numerical analysis of the Anderson localization

The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems. These systems undergo the metal insulator transition when either Fermi energy crosses the mobility edge or the strength of the disorder increases over critical value. We study how disorder affects the energy spectrum and spatial distribution of electronic eigenstates in the diffusive and insulating regime, as well as in the critical region of the metal-insulator transition. Then, we introduce the transfer matrix and conductance, and we discuss how the quantum character of the electron propagation influences the transport properties of disordered samples. In the weakly disordered systems, the weak localization and anti-localization as well as the universal conductance fluctuation are numerically simulated and discussed. The localization in the one dimensional system is described and interpreted as a purely quantum effect. Statistical properties of the conductance in the critical and localized regimes are demonstrated. Special attention is given to the numerical study of the transport properties of the critical regime and to the numerical verification of the single parameter scaling theory of localization. Numerical data for the critical exponent in the orthogonal models in dimension 2 <

Possible existence of a band of extended states induced by inter-Landau-band mixing in a quantum Hall system

The mixing of states with opposite chiralities in a quantum Hall system is shown to have a delocalization effect. It is possible that extended states may form bands because of this mixing, as is shown through a numerical calculation on a two-channel network model. Based on this result, a new phase diagram with a narrow metallic phase separating two adjacent QH phases and/or separating a QH phase from the insulating phase is proposed. The data from recent non-scaling experiments are reanalysed and it is shown that they seem to be consistent with the new phase diagram. However, due to finite-size effects, further study on large system size is still needed to conclude whether there are extended state bands in the thermodynamic limit.

Universal conductance and conductivity at critical points in integer quantum Hall systems

The sample averaged longitudinal two-terminal conductance and the respective Kubo conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, and , respectively. In the second-lowest Landau band, a critical conductance is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value . We argue that this difference is due to the multifractal structure of critical wave functions, a property that should generically show up in the conductance at quantum critical points.

Fractional quantum Hall states of atoms in optical lattices

We describe a method to create fractional quantum Hall states of atoms confined in optical lattices. We show that the dynamics of the atoms in the lattice is analogous to the motion of a charged particle in a magnetic field if an oscillating quadrupole potential is applied together with a periodic modulation of the tunneling between lattice sites. In a suitable parameter regime the ground state in the lattice is of the fractional quantum Hall type, and we show how these states can be reached by melting a Mott-insulator state in a superlattice potential. Finally, we discuss techniques to observe these strongly correlated states.

Localization of fractionally charged quasi-particles

An outstanding question pertaining to the microscopic properties of the fractional quantum Hall effect is understanding the nature of the particles that participate in the localization but that do not contribute to electronic transport. By using a scanning single electron transistor, we imaged the individual localized states in the fractional quantum Hall regime and determined the charge of the localizing particles. Highlighting the symmetry between filling factors 1/3 and 2/3, our measurements show that quasi-particles with fractional charge e* = e/3 localize in space to submicrometer dimensions, where e is the electron charge.

Microwave resonance of the 2D Wigner crystal around integer Landau fillings

We have observed a resonance in the real part of the finite frequency diagonal conductivity using microwave absorption measurements in high quality 2D electron systems near integer fillings. The resonance exists in some neighborhood of filling factor around corresponding integers and is qualitatively similar to previously observed resonance of weakly pinned Wigner crystal in high B and very small filling factor regime. Data measured around both nu=1 and nu=2 are presented. We interpret the resonance as the signature of the Wigner crystal state around integer Landau levels.

Observation of a quantized hall resistivity in the presence of mesoscopic fluctuations

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 nu=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 in the quantum Hall effect to the mesoscopic regime.

Reentrant metallic behavior of graphite in the quantum limit

Magnetotransport measurements performed on several well-characterized highly oriented pyrolitic graphite and single crystalline Kish graphite samples reveal a reentrant metallic behavior in the basal-plane resistance at high magnetic fields, when only the lowest Landau levels are occupied. The results suggest that the quantum Hall effect and Landau-level-quantization-induced superconducting correlations are relevant to understand the metalliclike state(s) in graphite in the quantum limit.

Metallic phase in quantum Hall systems due to inter-Landau-band mixing

The electronic eigenstates of a quantum Hall (QH) system are chiral states. Strong inter-Landau-band mixings among these states can occur when the bandwidth is comparable to the spacing of two adjacent Landau bands. We show that mixing of localized states with opposite chirality can delocalize electronic states. Based on numerical results, we propose the existence of a metallic phase between two adjacent QH phases and between a QH phase and the insulating phase. This result is consistent with nonscaling behaviors observed in recent experiments on a quantum Hall liquid-to-insulator transition.