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Volkov–Pankratov (VP) states are a family of sub-gap states that appear at the smooth interface/domain wall between topologically distinct gaped states. We carry out quantum transport simulations on one- and two-dimensional lattice models to demonstrate the emergence of such states in the edge spectrum of a quantum spin Hall system subjected to a smoothly varying exchange field that switches its sign at a given spatial point. We show the VP states possess non-trivial spin textures that can be characterized by a winding number in real space. It is further demonstrated that the application of an electric field along the edge provides control of this spin texture without altering the winding number. Finally, we illuminate how these spin textures can be read off via the local tunnel magnetoresistance (TMR) response of spin-polarized tunnel probes attached to the edge and the TMR can be controlled by purely electrical means akin to a Datta–Das type spin transistor. [ABSTRACT FROM AUTHOR]

An effective one-dimensional channel is formed at the periphery of a two-dimensional electron gas by electronic edge states. Robust edge states with suppressed dissipation arise from the Landau quantization in a strong magnetic field, and propagation through an edge channel formed by these states is one-way. In general, two-way edge channels rather than one-way ones have more advantages for applications and are the main topic of topological insulators. However, two-way edge channels of these are degenerate in their energies, which causes backscattering and dissipation. Here, we show that excited states in networks composed of capacitively coupled integer quantum Hall systems exhibit macroscopic two-way edge channels with different energies. Theoretical results are derived on the basis of two known effects; each system has plasmonic excitations known as edge magnetoplasmons, and the chirality of each system is diverted only locally by the capacitive interaction between nearest-neighbor systems. Because of the simplicity of the model, various extensions from regular networks to more complicated higher-dimensional networks are possible. The networks provide an ideal platform to test the functionality of plasmonic one-dimensional edge channels and suggest a dynamical model of fractional Quantum Hall systems. [ABSTRACT FROM AUTHOR]

The percolation plays an essential role in the physics of plateau transition, localization, and breakdown in quantum Hall (QH) systems. In practice, it always exists probably due to sample imperfections and has to be addressed before realizing the full potentials of topological electronics and qubits. Here, we investigate the cause, distribution, and number of the percolation in a quantum anomalous Hall (QAH) insulator of an anti-Hall bar geometry with two perimeters, which allows for probing both the inter- and intra-perimeter percolations by injecting currents into either or both perimeters. We discover the dual-QAH effect with opposite chiralities from these two perimeters, which exhibits linear modulations by the currents applied to both perimeters. By solving the formulation of such modulations with the Landauer–Büttiker formalism, the distribution and number of the inter-perimeter percolative channels could be identified. Strikingly, a dissipative constituent is detected in the transport of the QAH state, as revealed by the linear scalings in longitudinal conductivities versus the sum of currents injected to both perimeters, similar to that in the trivial-insulating state. Such a behavior unveils the quasi-2D nature of the intra-perimeter percolation, which superimposes onto and perturbs the dissipationless chiral edge transport. The formation of percolations is ascribed to the joint effect of the electric field, finite conductivity, and sample imperfections. [ABSTRACT FROM AUTHOR]

The quantum Hall effect (QHE) is a topologically protected phenomenon which has been observed in various systems. In experiments, the size of Hall bar device to realize the QHE is generally much larger than the phase coherence length, in which the quantum coherence of electrons is destroyed. Here, we theoretically study the influence of dephasing effect on the quantized Hall (QH) plateaus. We find that the QH plateaus disappear in perfectly quantum coherent systems if the coupling between leads and central region is imperfect. The Hall resistance is very large and strongly oscillates instead of presenting the QH plateaus in this case. However, by introducing the dephasing, Hall resistance decreases and the QH plateaus appear gradually. Similar results can also be observed for the quantum anomalous Hall effect. Our results propose that dephasing effect promotes the appearance of QH plateaus, which opens a new topic of the dephasing effect on topological systems. [ABSTRACT FROM AUTHOR]

Thouless pumping is the adiabatic transportation of quantized charge, which is regarded as the dynamic version of the quantum Hall effect. Here we propose the design of an acoustic system to demonstrate the topological pumping characterized by transporting acoustic energy from one side to the opposite. The system is composed of coupled acoustic waveguide arrays with modulated coupling along both cross-sections and the propagating direction. We explore multiple topological phases by introducing rich spatial frequency or enlarged range of the hopping modulation. Such distinct topological phases are evidenced by adiabatic evolution of the edge states, where the acoustic system varies continuously and slowly along the state propagating direction. The robustness behavior of the edge states transport is also verified with numerical simulations to imply their topology origin. Our work provides a route to realize topological phases and utilize the corresponding edge states in waveguide arrays that can lead to versatile acoustic wave manipulation applications. [ABSTRACT FROM AUTHOR]

An effective one-dimensional channel is formed at the periphery of a two-dimensional electron gas by electronic edge states. Robust edge states with suppressed dissipation arise from the Landau quantization in a strong magnetic field, and propagation through an edge channel formed by these states is one-way. In general, two-way edge channels rather than one-way ones have more advantages for applications and are the main topic of topological insulators. However, two-way edge channels of these are degenerate in their energies, which causes backscattering and dissipation. Here, we show that excited states in networks composed of capacitively coupled integer quantum Hall systems exhibit macroscopic two-way edge channels with different energies. Theoretical results are derived on the basis of two known effects; each system has plasmonic excitations known as edge magnetoplasmons, and the chirality of each system is diverted only locally by the capacitive interaction between nearest-neighbor systems. Because of the simplicity of the model, various extensions from regular networks to more complicated higher-dimensional networks are possible. The networks provide an ideal platform to test the functionality of plasmonic one-dimensional edge channels and suggest a dynamical model of fractional Quantum Hall systems.

Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions’ dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter–Fermi–Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor ν = 1. We reveal the nature of the low energy spin-singlet states around ν ≈ 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- $T_\mathrm{c}$ superconductivity.

The uniaxial strain is an effective way to change the symmetry of a crystal and thus tuning their electronic properties. In the present work, we elucidate the physical mechanism of the symmetry-broken-induced energy valleys drift in monolayer molybdenum disulfide. When the uniaxial strain reduces the rotational symmetry of valleys from C 3 to C 1 and an in-plane electric field breaks the balance of electron distribution of valleys, the valley dipole can survive readily and quantum nonlinear Hall effect might be realized. Our work offers key insights for understanding the uniaxial strain induced valleys drift in monolayer MoS2, which is critical to precisely control the valleytronics properties of two-dimensional materials. [ABSTRACT FROM AUTHOR]

The uniaxial strain is an effective way to change the symmetry of a crystal and thus tuning their electronic properties. In the present work, we elucidate the physical mechanism of the symmetry-broken-induced energy valleys drift in monolayer molybdenum disulfide. When the uniaxial strain reduces the rotational symmetry of valleys from C 3 to C 1 and an in-plane electric field breaks the balance of electron distribution of valleys, the valley dipole can survive readily and quantum nonlinear Hall effect might be realized. Our work offers key insights for understanding the uniaxial strain induced valleys drift in monolayer MoS2, which is critical to precisely control the valleytronics properties of two-dimensional materials. [ABSTRACT FROM AUTHOR]

Graphene is an excellent two-dimensional materials with high-mobility and relativistic electronic linear dispersion. Its rich physical properties such as half-integer quantum Hall effect and device application potential have been continuously attracting great attention. However, light carbon atoms also imply negligible intrinsic spin–orbit coupling (SOC) strength which hinders its spintronic application. To enhance the SOC effect, we introduce a special deformation vector with chiral curvature, borrowed from the Einstein theory of general relativity, to mimic space warping and twisting. The derived Rashba type pseudospin–spin coupling locks the spin orientation of an electron with respect to its pseudospin. Combined with the original Dirac type Hamiltonian specifying the pseudospin orientation of an electron with respect to its wavevector, it lifts the spin degeneracy and paves the way for graphene-based spintronic devices. An estimate suggests that a Rashba type pseudospin–spin coupling of the order of 5 meV can be achieved in tens nanometer samples. [ABSTRACT FROM AUTHOR]

Classical constraints on the reduced density matrix of quantum fluids in a single Landau level termed as local exclusion conditions (LECs) (Yang 2019 Phys. Rev. B 100 241302), have recently been shown to characterize the ground state of many fractional quantum Hall (FQH) phases. In this work, we extend the LEC construction to build the elementary excitations, namely quasiholes and quasielectrons, of these FQH phases. In particular, we elucidate the quasihole counting, categorize various types of quasielectrons, and construct their microscopic wave functions. Our extensive numerical calculations indicate that the undressed quasielectron excitations of the Laughlin state obtained from LECs are topologically equivalent to those obtained from the composite fermion theory. Intriguingly, the LEC construction unveils interesting connections between different FQH phases and offers a novel perspective on exotic states such as the Gaffnian and the Fibonacci state. [ABSTRACT FROM AUTHOR]

In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern numbers of the system bands. Here we investigate the close analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. In particular, we show that there is a one-to-one relation between the above mentioned Diophantine equation and the Bragg condition determining the far-field positions of the optical diffraction peaks. As an interesting consequence of this mapping, we discuss how the robustness of diffraction figures to structural disorder in the grating is a direct analogue of the robustness of transverse conductance in the quantum Hall effect.

Due to their high energy, hot electrons in quantum Hall edge (QHE) states can be considered as single particles that have the potential to be used for quantum optics-like experiments. Unlike photons, however, electrons typically undergo scattering processes in transport, which results in a loss of coherence and limits their ability to show quantum-coherent behaviour. Here we study theoretically the decoherence mechanisms of hot electrons in a Mach–Zehnder interferometer (MZI), and highlight the role played by both acoustic and optical phonon emission. We discuss optimal choices of experimental parameters and show that high visibilities of ≳ 85% are achievable in hot-electron devices over relatively long distances of 10 μm. We also discuss energy filtration techniques to remove decoherent electrons and show that this can increase visibilities to over 95%. This represents an improvement over Fermi-level electron quantum optics, and suggests hot-electron charge pumps as a platform for realising quantum-coherent nanoelectronic devices. [ABSTRACT FROM AUTHOR]

It is challenging to realize the quantum anomalous Hall effect (QAHE) at high operating temperatures using the two-dimensional (2D) Dirac surface states of three-dimensional (3D) topological insulators (TIs). Given the small non-trivial gap induced by adsorbing ferromagnetic (FM) CrI3 monolayer (ML) on the surface of Bi2Se3 films, we here propose another TI and FM semiconductor interfaced system to enhance the gap by inserting CrI3 ML between the first top (bottom) quintuple layers (QL) and sub-top (sub-bottom) QL of Bi2Se3 films symmetrically. The 2D non-trivial phase emerges in the Bi2Se3 films with five or more QLs and the gap is enlarged to 30 meV in 1QL-Bi2Se3/CrI3/4QL-Bi2Se3/CrI3/1QL-Bi2Se3, which can be understood by the enhanced magnetic proximity effect. The topological non-triviality is confirmed by the nonzero Chern number and the existence of chiral edge state. Our finding will provide useful guidance to optimize the Bi2Se3–CrI3 interface system for realizing QAHE at relatively high operating temperatures. [ABSTRACT FROM AUTHOR]

The topological behaviors of Sn monolayers partly passivated with H atoms are explored based on first-principles calculations. Obvious magnetism can be induced in the Sn monolayer due to the passivation. And the magnetism strength is found to be determined by the number difference of the H atoms bonding to the two sublattices of stanene. Quantum anomalous Hall (QAH) effects are found appearing easily in the systems with one of the sublattices fully passivated and the other not. The origin of the topological states can be ascribed to the coupling of the magnetism, the lattice symmetry (C3v), and the H-atom concentrations, which forms various mechanisms of the topological states. Particularly, band inversions are found playing completely different roles in forming the QAH effects for the different functionalized Sn monolayers. [ABSTRACT FROM AUTHOR]

Due to their high energy, hot electrons in quantum Hall edge (QHE) states can be considered as single particles that have the potential to be used for quantum optics-like experiments. Unlike photons, however, electrons typically undergo scattering processes in transport, which results in a loss of coherence and limits their ability to show quantum-coherent behaviour. Here we study theoretically the decoherence mechanisms of hot electrons in a Mach–Zehnder interferometer (MZI), and highlight the role played by both acoustic and optical phonon emission. We discuss optimal choices of experimental parameters and show that high visibilities of ≳ 85% are achievable in hot-electron devices over relatively long distances of 10 μ m. We also discuss energy filtration techniques to remove decoherent electrons and show that this can increase visibilities to over 95%. This represents an improvement over Fermi-level electron quantum optics, and suggests hot-electron charge pumps as a platform for realising quantum-coherent nanoelectronic devices.

After the classification of topological states of matter has been clarified for non-interacting electron systems, the theoretical connection between gapless boundary modes and nontrivial bulk topological structures, and their evolutions as a function of dimensions are now well understood. However, such dimensional hierarchy has not been well established experimentally although some indirect evidences were reported, for example, such as the half-quantized Hall conductance via quantum Hall effect and extrapolation in the quantum-oscillation measurement. In this paper, we report the appearance of the possible chiral edge mode from the surface state of topological insulators under magnetic fields, confirming the dimensional hierarchy in three-dimensional topological insulators. Applying laser pulses to the surface state of Bi1-xSbx, we find that the sign of voltage relaxation in one edge becomes opposite to that in the other edge only when magnetic fields are applied to the topological insulating phase.Weshow that this sign difference originates from the chirality of edge states, based on coupled time-dependent Poisson and Boltzmann equations. [ABSTRACT FROM AUTHOR]

After the classification of topological states of matter has been clarified for non-interacting electron systems, the theoretical connection between gapless boundary modes and nontrivial bulk topological structures, and their evolutions as a function of dimensions are now well understood. However, such dimensional hierarchy has not been well established experimentally although some indirect evidences were reported, for example, such as the half-quantized Hall conductance via quantum Hall effect and extrapolation in the quantum-oscillation measurement. In this paper, we report the appearance of the possible chiral edge mode from the surface state of topological insulators under magnetic fields, confirming the dimensional hierarchy in three-dimensional topological insulators. Applying laser pulses to the surface state of Bi1-xSbx, we find that the sign of voltage relaxation in one edge becomes opposite to that in the other edge only when magnetic fields are applied to the topological insulating phase.Weshow that this sign difference originates from the chirality of edge states, based on coupled time-dependent Poisson and Boltzmann equations. [ABSTRACT FROM AUTHOR]

Physical systems with non-trivial topological order find direct applications in metrology (Klitzing et al 1980 Phys . Rev. Lett . 45 494–7) and promise future applications in quantum computing (Freedman 2001 Found. Comput. Math. 1 183–204; Kitaev 2003 Ann. Phys. 303 2–30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system’s topology (Laughlin 1981 Phys. Rev. B 23 5632–33). At magnetic fields beyond the reach of current condensed matter experiment, around ${{\rm{10}}}^{{\rm{4}}}$ T, this conductance remains precisely quantized with values based on the topological order (Thouless et al 1982 Phys. Rev. Lett. 49 405–8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003 New J. Phys . 5 56; Miyake et al 2013 Phys. Rev. Lett. 111 185302; Aidelsburger et al 2013 Phys. Rev. Lett. 111 185301; Celi et al 2014 Phys. Rev. Lett. 112 043001; Stuhl et al 2015 Science 349 1514; Mancini et al 2015 Science 349 1510; An et al 2017 Sci. Adv. 3 ). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of ${\rm{5}} \% $ , and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.

The topological Hall effect (THE) of electrons in skyrmion crystals (SkXs) is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the SkX (THE) or of the corresponding Landau levels (QHE). Striking features in the energy dependence of the Hall conductivities are traced back to the band structure without magnetic field whose properties are dictated by the lattice geometry. Based on these findings, we derive an approximation that allows us to determine the energy dependence of the topological Hall conductivity on any two-dimensional lattice. The validity of this approximation is proven for the honeycomb lattice. We conclude that SkXs lend themselves for experiments to validate our findings for the THE and—indirectly—the QHE.

By the generalized gradient approximation in the framework of density functional theory, we find a new silicon allotrope (called dumbbell silicene) with high stability, which can turn a quantum spin Hall insulator with an inverted band gap through tuning external compression strain, just like in previous silicene. However, the obtained maximum topological nontrivial band gap about 12 meV under isotropic strain is much larger than that for previous silicene, and can be further improved to 36 meV by tuning extra anisotropic strain, which is sufficiently large to realize quantum spin Hall effect even at room-temperature, and thus is beneficial to the fabrication of high-speed spintronics devices. Furthermore, we confirm that the boron nitride sheet is an ideal substrate for the experimental realization of the dumbbell silicene under external strain, maintaining its nontrivial topology. These properties make the two-dimensional dumbbell silicene a good platform to study novel quantum states of matter, showing great potential for future applications in modern silicon-based microelectronics industry.

Spin-split heavy-hole gases in strained germanium quantum wells were characterized by polarisation-resolved terahertz time-domain spectroscopy. Effective masses, carrier densities, g-factors, transport lifetimes, mobilities and Rashba spin-splitting energies were evaluated, giving quantitative insights into the influence of strain. The Rashba coefficient was found to lower for samples with higher biaxial compressive strain, while heavy-hole mobilities were enhanced to over $1.5\times {10}^{6}$ cm ^2 V ^−1 s ^−1 at 3 K. This high mobility enabled the observation of the optical quantum Hall effect at terahertz frequencies for spin-split two-dimensional heavy-holes, evidenced as plateaux in the transverse magnetoconductivity at even and odd filling factors.

We investigate the finite frequency (FF) noise properties of edge states in the quantum Hall regime. We consider the measurement scheme of a resonant detector coupled to a quantum point contact in the weak-backscattering limit. A detailed analysis of the difference between the ‘measured’ noise, due to the presence of the resonant detector, and the symmetrized FF noise is presented. We discuss both the Laughlin and Jain sequences, studying the tunnelling excitations in these hierarchical models. We argue that the measured noise can better distinguish between the different excitations in the tunnelling process with respect to the symmetrized FF counterpart in an experimentally relevant range of parameters. Finally, we illustrate the effect of the detector temperature on the sensibility of this measure. [ABSTRACT FROM AUTHOR]

Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. We propose a way to extract edge velocities from dc transport in a point contact geometry defined by narrow gates. The width of the gates assumes two different sizes at small and large distances from the point contact. The Coulomb interaction across the gates depends on the gate width and affects the conductance of the contact. The conductance exhibits two different temperature dependencies at high and low temperatures. The transition between the two regimes is determined by the edge velocity. An interesting feature of the low-temperature I − V curve is current oscillations as a function of the voltage. The oscillations emerge due to charge reflection from the interface of the regions defined by the narrow and wide sections of the gates.

We investigate charge and energy transport in a three-terminal quantum Hall conductor. The peculiar properties of chiral propagation along the edges of the sample have important consequences on the response to thermal biases. Based on the separation of charge and heat flows, thermoelectric conversion and heat rectification can be manipulated by tuning the scattering at gate-modulated constrictions. Chiral motion in a magnetic field allows for a different behavior of left- and right-moving carriers giving rise to thermal rectification by redirecting the heat flows. We propose our system both as an efficient heat-to-work converter and as a heat diode.

We launch surface acoustic waves (SAW) along both the $\langle 110\rangle $ and the $\langle 1\bar{1}0\rangle $ directions of a Hall bar and measure the anisotropic conductivity in a high purity GaAs two-dimensional electron system in the quantum Hall regime of the stripe and the bubble phases. In the anisotropic stripe phase, SAW propagating along the ‘easy’ $\langle 110\rangle $ direction sense a compressible behavior (finite resistance) which is seen in standard transport measurement only if current flows along the ‘hard’ $\langle 1\bar{1}0\rangle $ direction. In the isotropic bubble phase, the SAW data show compressible behavior in both directions, in marked contrast to the incompressible quantum Hall behavior seen in transport measurements. These results challenge models that assume that both the stripe and the bubble phase consist of incompressible domains and raise important questions about the role of domain boundaries in SAW propagation.

We study theoretically how electrons, coherently injected at one point on the boundary of a two-dimensional electron system, are focused by a perpendicular magnetic field B onto another point on the boundary. Using the non-equilibrium Green's function approach, we calculate the generalized four-point Hall resistance Rxy as a function of B. In weak fields, Rxy shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, Rxy shows a single extended plateau reflecting the quantum Hall effect. In intermediate fields, we find superimposed upon the lower Hall plateaus anomalous oscillations, which are neither periodic in 1/B (quantum Hall effect) nor in B (classical cyclotron motion). The oscillations are explained by the interference between the occupied edge channels, which causes beatings in Rxy. In the case of two occupied edge channels, these beatings constitute a new commensurability between the magnetic flux enclosed within the edge channels and the flux quantum. Introducing decoherence and a partially specular boundary shows that this new effect is quite robust. [ABSTRACT FROM AUTHOR]

We have performed magnetotransport experiments in the high-temperature regime (up to 50 K) of the integer quantum Hall effect for two-dimensional electron gases in semiconducting heterostructures. While the magnetic field dependence of the classical Hall law presents no anomaly at high temperatures, we find a breakdown of the Drude–Lorentz law for the longitudinal conductance beyond a crossover magnetic field Bc ≃ 1 T, which turns out to be correlated with the onset of the integer quantum Hall effect at low temperatures. We show that the high magnetic field regime at B > Bc can be understood in terms of classical percolative transport in a smooth disordered potential. From the temperature dependence of the peak longitudinal conductance, we extract scaling exponents which are in good agreement with the theoretically expected values. We also prove that inelastic scattering on phonons is responsible for dissipation in a wide temperature range going from 1 to 50K at high magnetic fields. [ABSTRACT FROM AUTHOR]

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors, the topological classification is obtained systematically and non-trivial topological insulators are classified by either integer or ℤ2. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in (2 + 1) dimensions which has timereversal symmetry and a ℤ2 spin conservation symmetry. We demonstrate that the superconductors in this class are classified by ℤ8 when electron interaction is considered, while the classification is ℤ without interaction. [ABSTRACT FROM AUTHOR]

We investigate the quantum dynamics of systems involving small numbers of strongly interacting photons. Specifically, we develop an efficient method to investigate such systems when they are externally driven with a coherent field. Furthermore, we show how to quantify the many-body quantum state of light via correlation functions. Finally, we apply this method to two strongly interacting cases: the Bose-Hubbard and fractional quantum Hall models, and discuss an implementation of these ideas in atom-photon system. [ABSTRACT FROM AUTHOR]

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern-Simons electrodynamics expected of a Z2 spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step toward a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and toward a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models. [ABSTRACT FROM AUTHOR]

Nanostructures defined in high-mobility two-dimensional electron systems offer a unique way of controlling the microscopic details of the investigated device. Quantum point contacts play a key role in these investigations, since they are not only a research topic themselves, but also turn out to serve as convenient and powerful detectors for their electrostatic environment. We investigate how the sensitivity of charge detectors can be further improved by reducing screening, increasing the capacitive coupling between charge and detector and by tuning the quantum point contacts' confinement potential into the shape of a localized state. We demonstrate the benefits of utilizing a localized state by performing fast and well-resolved charge detection of a large quantum dot in the quantum Hall regime. [ABSTRACT FROM AUTHOR]

Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously probed neurons in the intact brain reveal correlations between their activity, an important measure to study information processing in the brain that also influences the macroscopic signals of neural activity, like the electroencephalogram (EEG). Networks of spiking neurons differ from most physical systems: the interaction between elements is directed, time delayed, mediated by short pulses and each neuron receives events from thousands of neurons. Even the stationary state of the network cannot be described by equilibrium statistical mechanics. Here we develop a quantitative theory of pairwise correlations in finite-sized random networks of spiking neurons. We derive explicit analytic expressions for the population-averaged cross correlation functions. Our theory explains why the intuitive mean field description fails, how the echo of single action potentials causes an apparent lag of inhibition with respect to excitation and how the size of the network can be scaled while maintaining its dynamical state. Finally, we derive a new criterion for the emergence of collective oscillations from the spectrum of the time-evolution propagator. [ABSTRACT FROM AUTHOR]

We explore transport across an ultra-small quantum Hall island (QHI) formed by closed quantum Hall edge states and connected to propagating edge channels through tunnel barriers. Scanning gate microscopy and scanning gate spectroscopy are used to first localize and then study a single QHI near a quantum point contact. The presence of Coulomb diamonds in the spectroscopy confirms that Coulomb blockade governs transport across the QHI. Varying the microscope tip bias as well as current bias across the device, we uncover the QHI discrete energy spectrum arising from electronic confinement and we extract estimates of the gradient of the confining potential and of the edge state velocity. [ABSTRACT FROM AUTHOR]

We propose a general mechanism for the renormalization of the tunnelling exponents in edge states of the fractional quantum Hall effect. Mutual effects of the coupling with out-of-equilibrium 1/ f noise and dissipation are considered for both the Laughlin sequence and the composite co- and counter-propagating edge states with Abelian or non-Abelian statistics. For states with counter-propagating modes, we demonstrate the robustness of the proposed mechanism in the so-called disorder-dominated phase. Prototypes of these states, such as v = 2/3 and v = 5/2, are discussed in detail, and the rich phenomenology induced by the presence of a noisy environment is presented. The proposed mechanism could help justify the strong renormalizations reported in many experimental observations carried out at low temperatures. We show how environmental effects could affect the relevance of the tunnelling excitations, leading to important implications, in particular for the v = 5/2 case. [ABSTRACT FROM AUTHOR]

We use dynamic scanning capacitance microscopy to image compressible and incompressible strips at the edge of a Hall bar in a twodimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives access to the complex local conductance, Gts, between a sharp metallic tip scanned across the sample surface and ground, comprising the complex sample conductance. Near integer filling factors we observe a bright stripe along the sample edge in the imaginary part of Gts. The simultaneously recorded real part exhibits a sharp peak at the boundary between the sample interior and the stripe observed in the imaginary part. The features are periodic in the inverse magnetic field and consistent with compressible and incompressible strips forming at the sample edge. For currents larger than the critical current of the QHE break-down the stripes vanish sharply and a homogeneous signal is recovered, similar to zero magnetic field. Our experiments directly illustrate the formation and a variety of properties of the conceptually important QHE edge states at the physical edge of a 2DEG. [ABSTRACT FROM AUTHOR]

We propose a topological field theory for a spinless two-dimensional (2D) chiral superconductor (SC) that contains fundamental Majorana fields. Due to a fermionic gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only at magnetic vortex cores, and on edges. We argue that these modes have the topological properties pertinent to a p-wave SC including the non-Abelian braiding statistics, and we support this claim by calculating the ground state degeneracy on a torus. We also briefly discuss the connection to the Moore-Read Pfaffian quantum Hall state and extensions to the spinfull case and to 3D topological SCs [ABSTRACT FROM AUTHOR]

We use the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms that are subjected to a geometric gauge field that was created by coupling two internal atomic states to a laser beam. On tuning the gauge field strength, the system undergoes stepwise transitions between different ground states (GSs), which we describe by using analytical trial wave functions, including the Pfaffian (Pf), the Laughlin and a Laughlin quasiparticle many-body state. Whereas for an infinitely strong laser field, the internal degree of freedom of the atoms can adiabatically follow their center-of-mass movement, a finite laser intensity gives rise to non-adiabatic transitions between the internal states, which are shown to break the cylindrical symmetry of the Hamiltonian. We study the influence of the asymmetry on the GS properties of the system. The main effect is to reduce the overlap of the numerical solutions with the analytical trial expressions by occupying states with higher angular momentum. Thus, we propose generalized wave functions arising from the Laughlin and Pf wave functions by including components where extra Jastrow factors appear while preserving important features of these states. We analyze quasihole excitations over the Laughlin and generalized Laughlin states and show that they possess effective fractional charge and obey anyonic statistics. Finally, we discuss the observability of the Laughlin state for increasing numbers of particles. [ABSTRACT FROM AUTHOR]

A numerical approach is employed to explain transport characteristics in realistic, quantum Hall-based Aharonov-Bohm (AB) interferometers. Firstly, the spatial distribution of incompressible strips, and thus the current channels, are obtained by applying a self-consistent Thomas-Fermi method to a realistic heterostructure under quantized Hall conditions. Secondly, the timedependent Schrödinger equation is solved for electrons injected in the current channels. Distinctive AB oscillations are found as a function of the magnetic flux. The oscillation amplitude strongly depends on the mutual distance between the transport channels and on their width. At an optimal distance the amplitude and thus the interchannel transport is maximized, which determines the maximum visibility condition. On the other hand, the transport is fully suppressed at magnetic fields corresponding to half-integer flux quanta. The results confirm the applicability of realistic AB interferometers as controllable current switches. [ABSTRACT FROM AUTHOR]

The k = 3 Read-Rezayi (RR) parafermion quantum Hall state hosts non-Abelian excitations which provide a platform for universal topological quantum computation. Although the RR state may be realized at the filling factor v = 12/5 in GaAs-based two-dimensional electron systems, the corresponding quantum Hall state is weak and at present nearly impossible to study experimentally. Here we argue that the RR state can alternatively be realized in a class of chiral materials with massless and massive Dirac-like band structure. This family of materials encompasses monolayer and bilayer graphene, as well as topological insulators. We show that, compared to GaAs, these systems provide several important advantages in realizing and studying the RR state. Most importantly, the effective interactions can be tuned in situ by varying the external magnetic field, and by designing the dielectric environment of the sample. This tunability enables the realization of RR state with controllable energy gaps in different Landau levels. It also allows one to probe the quantum phase transitions to other compressible and incompressible phases. [ABSTRACT FROM AUTHOR]

We present a detailed analysis of finite-frequency noise for the v = 5/2 fractional quantum Hall state in a quantum point contact geometry. The results were obtained within the Pfaffian and anti-Pfaffian models. We show that the behaviour of the coloured noise allows us to unambiguously discriminate among tunnelling excitations with different charges. Optimal values of the external bias are found in order to emphasize the visibility of the noise peak associated with the tunnelling of a 2-agglomerate, namely an excitation with charge that is double the fundamental one. These correspond to the regime in which the bias is larger than the neutral modes cut-off frequency. The dependence on temperature is also investigated to discriminate between the considered models. [ABSTRACT FROM AUTHOR]

The influence of the incompressible strips on the integer quantized Hall effect (IQHE) is investigated, considering a cleaved-edge overgrown (CEO) sample as an experimentally realizable sharp edge system. We propose a set of experiments to clarify the distinction between the large-sample limit when bulk disorder defines the IQHE plateau width and the small-sample limit smaller than the disorder correlation length, when self-consistent edge electrostatics define the IQHE plateau width. The large-sample or bulk quantized Hall (QH) regime is described by the usual localization picture, whereas the small-sample or edge regime is discussed within the compressible/incompressible strips picture, known as the screening theory of QH edges. Utilizing the unusually sharp edge profiles of the CEO samples, a Hall bar design is proposed to manipulate the edge potential profile from smooth to extremely sharp. By making use of a sidegate perpendicular to the two-dimensional electron system, it is shown that the plateau widths can be changed or even eliminated altogether. Hence, the visibility of IQHE is strongly influenced when adjusting the edge potential profile and/or changing the dc current direction under high currents in the nonlinear transport regime. As a second investigation, we consider two different types of ohmic contacts, namely highly transmitting (ideal) and highly reflecting (non-ideal) contacts. We show that if the injection contacts are non-ideal, but still ohmic, it is possible to measure directly the non-quantized transport taking place at the bulk of the CEO samples. The results of the experiments we propose will clarify the influence of the edge potential profile and the quality of the contacts, under QH conditions. [ABSTRACT FROM AUTHOR]

We report an investigation of quantum Hall induced currents by simultaneous measurements of their magnetic moment and their effect on the conductance of a quantum point contact (QPC). Correlation of features in the noise of the induced currents, caused by the breakdown of the quantum Hall effect, for the two types of measurements provides conclusive proof of the common origin of the two effects. Common features in the magnetic moment and QPC resistance at Landau-level filling factors ν = 1, 2 and 4 and their similar temperature and nonlinear sweep-rate dependences support this conclusion. In contrast, there is a distinct difference in the way the induced currents decay with time when the sweeping field halts at integer filling factor as detected by the two types of measurement. We attribute this difference to the fact that, while both effects are sensitive to the magnitude of the induced current, the QPC resistance is also sensitive to the proximity of the current to the QPC split gate, and we develop a model that describes semi-quantitatively the effects we observe. Although it is clearly demonstrated that induced currents affect the electrostatics of a QPC, the reverse effect, the QPC influencing the induced current, is not observed. [ABSTRACT FROM AUTHOR]

We investigated the non-universal part of the orbital entanglement spectrum (OES) of the ν = 1/3 fractional quantum Hall (FQH) effect ground state using Coulomb interactions. The non-universal part of the spectrum is the part that is missing in the Laughlin model state OES, whose level counting is completely determined by its topological order. We found that the OES levels of the Coulomb interaction ground state are organized in a hierarchical structure that mimics the excitation-energy structure of the model pseudopotential Hamiltonian, which has a Laughlin ground state. These structures can be accurately modeled using Jain's 'composite fermion' quasihole-quasiparticle excitation wave functions. To emphasize the connection between the entanglement spectrum and the energy spectrum, we also considered the thermodynamical OES of the model pseudopotential Hamiltonian at the finite temperature. The good match observed between the thermodynamical OES and the Coulomb OES suggests that there is a relation between the entanglement gap and the true energy gap. [ABSTRACT FROM AUTHOR]

The Système Internationale d'unités (SI) is about to undergo its biggest change in half a century by redefining the units for mass and current in terms of the fundamental constants h and e, respectively. This change crucially relies on the exactness of the relationships that link these constants to measurable quantities. Here we report the first direct comparison of the integer quantum Hall effect (QHE) in epitaxial graphene with that in GaAs/AlGaAs heterostructures. We find no difference in the quantized resistance value within the relative standard uncertainty of our measurement of 8.6×10-11, this being the most stringent test of the universality of the QHE in terms of material independence. [ABSTRACT FROM AUTHOR]

We propose a quantum tomography protocol to measure single-electron coherence in quantum Hall edge channels, and therefore access for the first time the wavefunction of single-electron excitations propagating in ballistic quantum conductors. Its implementation would open the way to quantitative studies of single-electron decoherence and would provide a quantitative tool for analyzing single- to few-electron sources. We show how this protocol could be implemented using ultrahigh-sensitivity noise measurement schemes. [ABSTRACT FROM AUTHOR]

The Abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-Abelian states emanating from the ν = 5/2 Moore-Read state in the second Landau level. Extending a recently developed formalism for hierarchical quasihole condensation, we present a theory that allows for the explicit construction of the ground state wave function, as well as its quasiparticle excitations, for any state based on the Abelian hierarchy. We relate our construction to structures in rational conformal field theory and stress the importance of using coherent state wave functions, which allows us to formulate an extension of the bulk-edge correspondence that was conjectured by Moore and Read. Finally, we study the proposed ground state wave functions in the limiting geometry of a thin torus and argue that they coincide with the known exact results. [ABSTRACT FROM AUTHOR]

We present a new approach for obtaining the scaling behavior of the entanglement entropy in fractional quantum Hall (FQH) states from finite-size wavefunctions. By employing the torus geometry and the fact that the torus aspect ratio can be readily varied, we can extract the entanglement entropy of a spatial block as a continuous function of the block boundary length. This approach allows us to extract the topological entanglement entropy with an accuracy superior to that possible for the spherical or disc geometry, where no natural continuously variable parameter is available. Other than the topological information, the study of entanglement scaling is also useful as an indicator of the difficulty posed by FQH states for various numerical techniques. [ABSTRACT FROM AUTHOR]

The ubiquitous Hofstadter butterfly describes a variety of systems characterized by incommensurable periodicities, ranging from Bloch electrons in magnetic fields and the quantum Hall effect to cold atoms in optical lattices and more. Here, we introduce nonlinearity into the underlying (Harper) model and study the nonlinear spectra and the corresponding extended eigenmodes of nonlinear quasiperiodic systems. We show that the spectra of the nonlinear eigenmodes form deformed versions of the Hofstadter butterfly and demonstrate that the modes can be classified into two families: nonlinear modes that are a 'continuation' of the linear modes of the system and new nonlinear modes that have no counterparts in the linear spectrum. Finally, we propose an optical realization of the linear and nonlinear Harper models in transversely modulated waveguide arrays, where these Hofstadter butterflies can be observed. This work is relevant to a variety of other branches of physics beyond optics, such as disorder-induced localization in ultracold bosonic gases, localization transition processes in disordered lattices, and more. [ABSTRACT FROM AUTHOR]

Low- and high-field magnetotransport measurements on two 30 nm δ-doped InSb/AlInSb quantum wells (QWs) with different doping densities are reported. The QW two-dimensional electron gas (2DEG) carrier densities and mobilities were extracted by analysis of the Hall and quantum Hall data, mobility spectra and Shubnikov-de Haas oscillations. 2DEG channel mobilities of up to 324 000 cm2 V-1 s-1 (T = 2 K) and 44 000 cm2 V-1 s-1 (T = 300 K) are extracted. Carrier densities and mobilities for transport parallel to the 2DEG layer are also deduced where observable. The importance of thermally generated carriers in the lower AlInSb barrier material and the role of transport within the δ-doping plane is considered and the total carrier population as a function of temperature of the two samples is deduced, which is in excellent agreement with experimental observation. [ABSTRACT FROM AUTHOR]