We analyze the dissipative conductance of the zero-plateau quantum Hall state appearing in undoped graphene in strong magnetic fields. Charge transport in this state is assumed to be carried by a magnetic domain wall, which forms by hybridization of two counter--propagating edge states of opposing spin due to interactions. The resulting non--chiral edge mode is a Luttinger liquid of parameter K, which enters a gapped, perfectly conducting state below a critical value K_c\approx 1/2. Backscattering in this system involves spin flip, so that interaction with localized magnetic moments generates a finite resistivity R_{xx} via a "chiral Kondo effect". At finite temperatures T, R_{xx}(T) exhibits a crossover from metallic to insulating behavior as K is tuned across a threshold K_{MI}. For T->0, R_{xx} in the intermediate regime K_{MI}<K<K_c is finite, but diverges as K approaches K_c. This model provides a natural interpretation of recent experiments.
Coexistence of insulating phases in confined fermionic chains with a Wannier-Stark potential
Centro Atómico Bariloche, Instituto Balseiro（巴里洛切原子中心，巴尔塞罗研究所）；Instituto de Nanociencia y Nanotecnología CNEA-CONICET（CNEA-CONICET纳米科学与技术研究所）；School of Physics and Astronomy, Tel Aviv University（特拉维夫大学物理与天文学学院）
We study a delocalization transition for non-interacting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realised in a dirty, gapless superconductor in which time reversal symmetry for orbital motion is broken, but spin rotation symmetry is intact. We find a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles. The energy of quasiparticles acts as a relevant, symmetry-breaking field at the critical point, which splits the direct transition into two conventiona…
Clean topological insulators exposed to a magnetic field develop Landau levels accompanied by a nonzero Hall conductivity for the infinite slab geometry. In this work we consider the case of disordered topological insulator nanowires and find, in contrast, that a zero Hall plateau emerges within a broad energy window close to the Dirac point. We numerically calculate the conductance and its distribution for a statistical ensemble of disordered nanowires, and use the conductance fluctuations to study the dependence of the insulating phase on system parameters, such as the nanowire length, disor…
The magnetization curve of the two-dimensional spin-1/2 $J_1$-$J_2$ Heisenberg model is investigated by using the Chern-Simons theory under a uniform mean-field approximation. We find that the magnetization curve is monotonically increasing for $J_2/J_1 < 0.267949$, where the system under zero external field is in the antiferromagnetic Néel phase. For larger ratios of $J_2/J_1$, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our result supports the existence of the $M/M_{\rm sat}=1/2$ plateau and predicts a new plateau at $M/M_{\rm sat}=1/3$. B…
The conductance of a two-dimensional electron gas at the transition from one quantum Hall plateau to the next has sample-specific fluctuations as a function of magnetic field and Fermi energy. Here we identify a universal feature of these mesoscopic fluctuations in a Corbino geometry: The amplitude of the magnetoconductance oscillations has an e^2/h resonance in the transition region, signaling a change in the topological quantum number of the insulating bulk. This resonance provides a signed scaling variable for the critical exponent of the phase transition (distinct from existing positive de…
We investigate the emergence of both quantum anomalous Hall and disorder-induced Anderson Chern insulating phases in two dimensional hexagonal lattices, with antiferromagnetically ordered 3Q state and in the absence of spin-orbit coupling. Using tight-binding modeling, we show that such systems display not only a spin-polarized edge-localized current, the chirality of which is energy dependent but also an impurity-induced transition from trivial metallic to topological insulating regimes, through one edge mode plateau. We compute the gaps' phase diagrams, and demonstrate the robustness of the …
We studied the unusual Quantum Hall Effect (QHE) near the charge neutrality point (CNP) in high-mobility graphene sample for magnetic fields up to 18 T. We observe breakdown of the delocalized QHE transport and strong increase in resistivities $ρ_{xx},|ρ_{xy}|$ with decreasing Landau level filling for $ν< 2$, where we identify two insulating regimes. For $1 \gtrsim |ν| \gtrsim 1/2$ we find an exponential increase of $ρ_{xx,xy} \sim e^{a(H-H_c)}$ within the range up to several resistance quanta $R_K$, while the Hall effect gradually disappears, consistent with the Hall insulator (HI) with local…
We study the nu=1/3 quantum Hall state in presence of the random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to unambiguously distinguish between insulating and current carrying states in an interacting system. The mobility gap can be determined numerically this way, which is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the mobility gap and plateau width narrow continuously and ultimately collapse leading to an insulating phase.
The effects of randomness are investigated in the fractional quantum Hall systems. Based on the Chern-Simons Ginzburg-Landou theory and considering relevant quasi-particle tunneling, the edge state network model for the hierarchical state is introduced and the plateau-plateau transition and liquid-insulator transition are discussed. This model has duality which corresponds to the relation of the quantum Hall liquid phase and the Hall insulating phase and reveals a mechanism in the weak coupling regime.
We investigate the low-temperature magneto-transport properties of monolayer epitaxial graphene films formed on the Si-face of semi-insulating 4H-SiC substrates by a high temperature sublimation process. A high-k top-gate on the epitaxial graphene is realized by inserting a fully oxidized nanometer thin aluminum film as a seeding layer, followed by an atomic layer deposition process. At low temperatures, the devices demonstrate a strong field effect by the top gate with an on/off ratio of ~7 and an electron mobility up to ~3250 cm^2/Vs. After the observation of the half-integer quantum Hall ef…
We show that H-phase transition metal dichalcogenides (TMDs) monolayers such as MoS$_2$ and WSe$_2$, are orbital Hall insulators. They present very large orbital Hall conductivity plateaus in their semiconducting gap, where the spin Hall conductivity vanishes. Our results open the possibility of using TMDs for orbital current injection and orbital torque transfers that surpass their spin-counterparts in spin-orbitronics devices. The orbital Hall effect (OHE) in TMD monolayers occurs even in the absence of spin-orbit coupling. It can be linked to exotic momentum-space Dresselhaus-like orbital t…
At a very low temperature of 9mK, electrons in the 2nd Landau level of an extremely high mobility two-dimensional electron system exhibit a very complex electronic behavior. With varying filling factor, quantum liquids of different origins compete with several insulating phases leading to an irregular pattern in the transport parameters. We observe a fully developed $ν=2+2/5$ state separated from the even-denominator $ν=2+1/2$ state by an insulating phase and a $ν=2+2/7$ and $ν=2+1/5$ state surrounded by such phases. A developing plateau at $ν=2+3/8$ points to the existence of other even-denom…
The appearance and evolution of an anomalous conductance plateau at 0.4 (in units of 2e2/h) in an In0.52Al0.48As/InAs quantum point contact (QPC), in the presence of lateral spin-orbit coupling, has been studied at T=4.2K as a function of the potential asymmetry between the in-plane gates of the QPC. The anomalous plateau, a signature of spin polarization in the channel, appears only over an intermediate range (around 3 V) of bias asymmetry. It is quite robust, being observed over a maximum range of nearly 1V of the sweep voltage common to the two in-plane gates. Our conductance measurements s…
A weak superconducting proximity effect in the vicinity of the topological transition of a quantum anomalous Hall system has been proposed as a venue to realize a topological superconductor (TSC) with chiral Majorana edge modes (CMEMs). A recent experiment [Science 357, 294 (2017)] claimed to have observed such CMEMs in the form of a half-integer quantized conductance plateau in the two-terminal transport measurement of a quantum anomalous Hall-superconductor junction. Although the presence of a superconducting proximity effect generically splits the quantum Hall transition into two phase tran…
A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer anti-ferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the spin easy plane, and simultaneously a ferromagnet order, which can further be enhanced by exchange interaction, develops in the direction of the magnetic field. The activation gap for the $ν=0$ Hall state then displays a crossover from quadratic to linear scaling with the magnetic field, as it gets stronger, and I obtain excellent agreement with a number of r…
The observation of a 0.5 conductance plateau in asymmetrically biased quantum point contacts with in-plane side gates has been attributed to the onset of spin-polarized current through these structures. For InAs quantum point contacts with the same width but longer channel length, there is roughly a fourfold increase in the range of common sweep voltage applied to the side gates over which the 0.5 conductance plateau is observed when the QPC aspect ratio (ratio of length over width of the narrow portion of the structure) is increased by a factor 3. Non-equilibrium Green s function simulations …
We numerically study the quantum Hall effect in biased bilayer graphene based on a tight-binding model in the presence of disorder. Integer quantum Hall plateaus with quantized conductivity $σ_{xy}=νe^2/h$ (where $ν$ is any integer) are observed around the band center due to the split of the valley degeneracy by an opposite voltage bias added to the two layers. The central ($n=0$) Dirac Landau level is also split, which leads to a pronounced $ν=0$ plateau. This is consistent with the opening of a sizable gap between the valence and conduction bands. The exact spectrum in an open system further…
We study one-dimensional transport in focused-ion-beam written in-plane-gate transistors on III-V heterostructures at moderately low temperatures at zero bias without any external magnetic field applied. In accordance with a recent proposal of A. Gold and L. Calmels, Valley- and spin-occupancy instability in the quasi-one-dimensional electron gas, Phil. Mag. Lett. 74, 33-42 (1996) and earlier experimental data, we observe plateaux in the source-drain conductivity considered as a function of the gate voltage, not only at multliples of 2e^2/h but also clearly at e^2/h, just before the channel cl…
In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is…
We investigate numerically the quasiparticle density of states $\varrho(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a logarithmic divergence in $\varrho(E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed o…
We report the experimental manifestation of even-odd parity effects in the transport characteristics of insulating Josephson junction chains which occur as the superconducting gap is suppressed by applied magnetic fields at millikelvin temperatures. The primary signature is a non-monotonic dependence of the critical voltage, $V_c$, for the onset of charge transport through the chain, with the parity crossover indicated by a maximum of $V_c$ at the parity field $B^*$. We also observe a distinctive change in the transport characteristics across the parity transition, indicative of Cooper-pair do…
We report complex magnetotransport patterns of the $ν=1$ integer quantum Hall state in a GaAs/AlGaAs sample from the newest generation with a record high electron mobility. The reentrant integer quantum Hall effect in the flanks of the $ν=1$ plateau indicates the formation of the integer quantum Hall Wigner solid, a collective insulator. Moreover, at a fixed filling factor, the longitudinal resistance versus temperature in the region of the integer quantum Hall Wigner solid exhibits a sharp peak. Such sharp peaks in the longitudinal resistance versus temperature so far were only detected for b…
Electrical transport in three dimensional topological insulators(TIs) occurs through spin-momentum locked topological surface states that enclose an insulating bulk. In the presence of a magnetic field, surface states get quantized into Landau levels giving rise to chiral edge states that are naturally spin-polarized due to spin momentum locking. It has been proposed that p-n junctions of TIs in the quantum Hall regime can manifest unique spin dependent effects, apart from forming basic building blocks for highly functional spintronic devices. Here, for the first time we study electrostaticall…
There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase pi, which results in a shifted positions of Hall plateaus. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and exhibit Berry's phase 2pi affecting their quantum dynamics. The L…
We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two \emph{distinct} quantum Hall effect (QHE) regimes exist in the energy band with the unconventional "half-integer" QHE appearing near the band center, consistent with the experimental observation. The latter is more robust against disorder scattering than the conventional QHE states near the band edges. The phase diagram for the unconventional QHE is obtained where the destruction of the Hall plateaus at strong disorder is throug…
The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are terminated by two distinct insulating phases, characterized by the Hall resistance with classic and quantized values, respectively, which is also in good agreement with experiments.
Recent theory predicted that the Quantum Spin Hall Effect, a fundamentally novel quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We have fabricated such sample structures with low density and high mobility in which we can tune, through an external gate voltage, the carrier conduction from n-type to the p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker q…
In the presence of a perpendicular magnetic field, ABC-stacked trilayer graphene's chiral band structure supports a 12-fold degenerate N=0 Landau level (LL). Along with the valley and spin degrees of freedom, the zeroth LL contains additional quantum numbers associated with the LL orbital index $% n=0,1,2$. Remote inter-layer hopping terms and external potential difference $Δ_{B}$ between the layers lead to LL splitting by introducing a gap $% Δ_{LL}$ between the degenerate zero-energy triplet LL orbitals. Assuming that the spin and valley degrees of freedom are frozen, we study the phase diag…
Single crystals of a honeycomb lattice antiferromagnet, Tb$_2$Ir$_3$Ga$_9$ were synthesized, and the physical properties have been studied. From magnetometry, a long-range antiferromagnetic ordering at $\approx$12.5 K with highly anisotropic magnetic behavior was found. Neutron powder diffraction confirms that the Tb spins lie along the $\va $-axis, parallel to the shortest Tb-Tb contact. Two field-induced spin-flip transitions are observed when the field is applied parallel to this axis, separated by a plateau corresponding roughly to M$\approx$M$_{\rm{s}}$/2. Transport measurements show the …
We study particle and spin transport in a single mode quantum point contact using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle…
In a multi-layer electronic system, stacking order provides a rarely-explored degree of freedom for tuning its electronic properties. Here we demonstrate the dramatically different transport properties in trilayer graphene (TLG) with different stacking orders. At the Dirac point, ABA-stacked TLG remains metallic while the ABC counterpart becomes insulating. The latter exhibits a gap-like dI/dV characteristics at low temperature and thermally activated conduction at higher temperatures, indicating an intrinsic gap ~6 meV. In magnetic fields, in addition to an insulating state at filling factor …
Recent experiments indicate that AA-stacked bilayer graphenes (BLG) could exist. Since the energy bands of the AA-stacked BLG are different from both the monolayer and AB-stacked bilayer graphenes, different integer quantum Hall effect in the AA-stacked graphene is expected. We have thus calculated the quantized Hall conductivity $σ_{xy}$ and also longitudinal conductivity $σ_{xx}$ of the AA-stacked BLG within the linear response Kubo formalism. Interestingly, we find that the AA-stacked BLG could exhibit both conventional insulating behavior (the $\barν=0$ plateau) and chirality for $|\barμ|<…
We have investigated the Hall resistance $R_H$ near the plateau-insulator transition of a two-dimensional electron gas in the quantum critical regime. High-field magnetotransport data taken on a low-mobility InGaAs/InP heterostructure with the plateau-insulator transition at a critical field $B_c$ of 17.2 T show that the Hall resistance $R_H$ is quantized at $h/e^2$ near the critical filling fraction ($ν_c$ = 0.55) when $T \to 0$. By making use of universal scaling functions extracted from the magnetotransport data we show that $R_H$ in the insulating phase in the limit $T \to 0$ is quantized …
The intrinsic spin and valley Hall conductivities of silicene, germanene and other similar two dimensional crystals are explored theoretically. Particular attention is given to the effects of the intrinsic spin-orbit coupling, electron doping and the type of insulating phase of the system (i.e., a topological insulator or a band insulator) which can be tuned by a perpendicular electric field. At finite frequency, the transverse edge to which carriers of particular spin and valley label flow can be controlled such that an accumulation of a particular combination of spin and valley index can be …
Two dimensional disordered superconductors with broken spin-rotation and time-reversal invariance, e.g. with p_x+ip_y pairing, can exhibit plateaus in the thermal Hall coefficient (the thermal quantum Hall effect). Our numerical simulations show that the Hall insulating regions of the phase diagram can support a sub-phase where the quasiparticle density of states is divergent at zero energy, ρ(E)\sim |E|^{1/z-1}, with a non-universal exponent $z>1$, due to the effects of rare configurations of disorder (``Griffiths phase'').
The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a c…
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 (TI) 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 6 quintuple-layer (Cr0.12Bi0.26Sb0.62)2Te3 film, and demonstrate the metal-to-insulator switching between two opposit…
We present magneto transport experiments of quasi 3D PbTe wide quantum wells. A plateau-like structure in the Hall resistance is observed, which corresponds to the Shubnikov de Haas oscillations in the same manner as known from the quantum Hall effect. The onsets of plateaux in Rxy do not correspond to 2D filling factors but coincide with the occupation of 3D (bulk-) Landau levels. At the same time a non-local signal is observed which corresponds to the structure in Rxx and Rxy and fulfils exactly the Onsager-Casimir relation (Rij,kl(B) = Rkl,ij(-B)). We explain the behaviour in terms of edge …
Since the experimental realisation of the integer quantised Hall effect in a two dimensional electron system subject to strong perpendicular magnetic fields in 1980, a central question has been the interrelation between the conductance quantisation and the topological properties of the system. It is conjectured that if the electron system is described by a Bloch hamiltonian, then the system is insulating in the bulk of the sample throughout the quantised Hall plateau due to magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topologi…
We demonstrate that, at the onset of conduction, an electrostatically defined quantum wire in bilayer graphene (BLG) with an interlayer asymmetry gap may act as a 1D semimetal, due to the multiple minivalley dispersion of its lowest subband. Formation of a non-monotonic subband coincides with a near-degeneracy between the bottom edges of the lowest two subbands in the wire spectrum, suggesting an $8e^2/h$ step at the conduction threshold, and the semimetallic behaviour of the lowest subband in the wire would be manifest as resonance transmission peaks on an $8e^2/h$ conductance plateau.
We present the essential findings of the screening theory of the integer quantum Hall effect (IQHE) considering a quantum point contact (QPC). Our approach is to solve the Poisson and the Schroedinger equations self-consistently, taking into account electron interactions, within a Hartree type approximation for a two dimensional electron gas (2DEG) subject to high perpendicular magnetic fields. The Coulomb interaction between the electrons separates 2DEG into two co-existing regions, namely quasi-metallic compressible and quasi-insulating incompressible regions, which exhibit peculiar screenin…
The quasi-quantized Hall effect (QQHE) is the three-dimensional (3D) counterpart of the integer quantum Hall effect (QHE),exhibited only by two-dimensional (2D) electron systems. It has recently been observed in layered materials, consisting of stacks of weakly coupled 2D platelets that are yet characterized by a 3D anisotropic Fermi surface. However, it is predicted that the quasi-quantized 3D version of the 2D QHE should occur in a much broader class of bulk materials, regardless of the underlying crystal structure. Here, we compare the observation of quasi-quantized plateau-like features in…
