We present an experiment where the quantum coherence in the edge states of the integer quantum Hall regime is tuned with a decoupling gate. The coherence length is determined by measuring the visibility of quantum interferences in a Mach-Zehnder interferometer as a function of temperature, in the quantum Hall regime at filling factor two. The temperature dependence of the coherence length can be varied by a factor of two. The strengthening of the phase coherence at finite temperature is shown to arise from a reduction of the coupling between co-propagating edge states. This opens the way for a strong improvement of the phase coherence of Quantum Hall systems. The decoupling gate also allows us to investigate how inter-edge state coupling influence the quantum interferences' dependence on the injection bias. We find that the finite bias visibility can be decomposed into two contributions: a Gaussian envelop which is surprisingly insensitive to the coupling, and a beating component which, on the contrary, is strongly affected by the coupling.
Kang et al. have recently observed a remarkable zero-bias anomaly in the spectrum for electron tunneling between two 2D electron gases separated laterally by a narrow but high barrier in the presence of a perpendicular quantising magnetic field. We argue that this is a result of interedge phase coherence analogous to the interlayer phase coherence in quantum Hall (QHE) bilayer systems. The disruption of the QHE by the barrier is 'healed' by strong coulomb exchange enhancement of the weak tunneling through the barrier.
We have determined the finite temperature coherence length of edge states in the Integer Quantum Hall Effect (IQHE) regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at filling factor 2. The visibility shows an exponential decay with the temperature. The characteristic temperature scale is found inversely proportional to the length of the interferometer arm, allowing to define a coherence length $ł_ϕ$. The variations of $ł_ϕ$ with magnetic field are the same for all samples, with a maximum located at the upper end of the quantu…
Using three-pulse four-wave-mixing optical spectroscopy, we study the ultrafast dynamics of the quantum Hall system. We observe striking differences as compared to an undoped system, where the 2D electron gas is absent. In particular, we observe a large off-resonant signal with strong oscillations. Using a microscopic theory, we show that these are due to many-particle coherences created by interactions between photoexcited carriers and collective excitations of the 2D electron gas. We extract quantitative information about the dephasing and interference of these coherences.
The quest to realize novel phases of matter with topological order is an important pursuit with implications for strongly correlated physics and quantum information. Utilizing ideas from state-of-the-art coherent control of artificial quantum systems such as superconducting circuits, we present a proposal to realize bosonic fractional quantum Hall physics on small lattices by creating nearly flat topological bands using staggered flux patterns. Fingerprints of fractionalization through charge pumping can be observed with nearly perfect quantization using as few as 24 lattice sites (two photons…
We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $ν=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $ν=1$ and discovered at $ν=2$. In particular, three different $ν=2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.
We analyze the bilayer quantum Hall (QH) system by mapping it to the monolayer QH system with spin degrees of freedom. By this mapping the tunneling interaction term is identified with the Zeeman term. We clarify the mechanism of a spontaneous development of quantum coherence based on the Chern-Simons gauge theory with the lowest-Landau-Level projection taken into account. The symmetry group is found to be W_infty*SU(2), which says that the spin rotation affects the total electron density nearby. Using it extensively we construct the Landau-Ginzburg theory of the coherent mode. Skyrmion excita…
This tutorial paper reviews some of the physics of quantum Hall bilayers with a focus on the case where there is low or zero tunnelling between the two layers. We describe the interlayer coherent states at filling factors nu=1 and nu=2 as exciton condensates and discuss some of the theory associated with these states.
The electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling are studied by means of a pseudospin-texture effective theory and an algebraic framework of the single-mode approximation, with emphasis on clarifying the nature of the low-lying neutral collective mode responsible for interlayer tunneling phenomena. A long-wavelength effective theory, consisting of the collective mode as well as the cyclotron modes, is constructed. It is seen explicitly from the electromagnetic response that gauge invariance is kept exact, this implying, i…
We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$ν=2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.
The possibility of the existence of states with a spontaneous interlayer phase coherence in multilayer electron systems in a high perpendicular to the layers magnetic field is investigated. It is shown that phase coherence can be established in such systems only within individual pairs of adjacent layers, while such coherence does not exist between layers of different pairs. The conditions for stability of the state with interlayer phase coherence against transition to a charge-ordered state are determined. It is shown that in the system with the number of layers N\leq 10 these conditions are …
We have characterized phase coherence length, spin orbit scattering length, and the Hall factor in n-type MoS2 2D crystals via weak localization measurements and Hall-effect measurements. Weak localization measurements reveal a phase coherence length of ~50 nm at T = 400 mK for a few-layer MoS2 film, decreasing as T^-1/2 with increased temperatures. Weak localization measurements also allow us, for the first time without optical techniques, to estimate the spin orbit scattering length to be 430 nm, pointing to the potential of MoS2 for spintronics applications. Via Hall-effect measurements, we…
Recent electron quantum optics experiments performed with on-demand single electron sources call for a mixed time/frequency approach to electronic quantum coherence. Here, we present a Wigner function representation of first order electronic coherence and show that is provides a natural visualization of the excitations emitted by recently demonstrated single electron sources. It also gives a unified perspective on single particle and two particle interferometry experiments. In particular, we introduce a non-classicality criterion for single electron coherence and discuss it in the context of M…
Artificial lattices of coherently coupled macroscopic states are at the heart of applications ranging from solving hard combinatorial optimisation problems to simulating complex many-body physical systems. The size and complexity of the problems scales with the extent of coherence across the lattice. Although the fundamental limit of spatial coherence depends on the nature of the couplings and lattice parameters, it is usually engineering constrains that define the size of the system. Here, we engineer polariton condensate lattices with active control on the spatial arrangement and condensate …
We present comprehensive results on the edge-mode velocities in a quantum Hall droplet with realistic interaction and confinement at various filling fractions. We demonstrate that the charge-mode velocity scales roughly with the valence Landau level filling fraction and the Coulomb energy in the corresponding Landau level. At Landau level filling fraction nu = 5/2, the stark difference between the bosonic charge-mode velocity and the fermionic neutral-mode velocity can manifest itself in the thermal smearing of the non-Abelian quasiparticle interference. We estimate the dependence of the coher…
In superconducting circuits interrupted by Josephson junctions, the dependence of the energy spectrum on offset charges on different islands is $2e$ periodic through the Aharonov-Casher effect and resembles a crystal band structure that reflects the symmetries of the Josephson potential. We show that higher-harmonic Josephson elements described by a $\cos(2φ)$ energy-phase relation provide an increased freedom to tailor the shape of the Josephson potential and design spectra featuring multiplets of flat bands and Dirac points in the charge Brillouin zone. Flat bands provide noise-insensitive q…
We experimentally study the dynamical modes excited by spin current in Spin Hall nano-oscillators based on the Pt/[Co/Ni] multilayers with perpendicular magnetic anisotropy. Both propagating spin wave and localized solitonic modes of the oscillation are achieved and controlled by varying the applied magnetic field and current. At room temperature, the generation linewidth broadening associated with mode hopping was observed at currents close to the transition between different modes and in the mode coexistence regimes. The mode hopping was suppressed at cryogenic temperatures, confirming that …
We investigate nonlinear transport in electronic Fabry-Perot interferometers in the integer quantum Hall regime. For interferometers sufficiently large that Coulomb blockade effects are absent, a checkerboard-like pattern of conductance oscillations as a function of dc bias and perpendicular magnetic field is observed. Edge-state velocities extracted from the checkerboard data are compared to model calculations and found to be consistent with a crossover from skipping orbits at low fields to E x B drift at high fields. Suppression of visibility as a function of bias and magnetic field is accou…
We point out a practical way to induce a finite charge Hall conductivity in graphene via an off-diagonal strain. Our conclusions are based on a general analysis and supported by numerical examples. The interplay between a substrate-induced gap and the strain is discussed. We show that the substrate-induced gap itself does not break the symmetry that maps one valley onto the other, and hence does not yield a net charge Hall effect. The net charge Hall conductivity is found to be sizable and should be observable in the presence of both the gap and the strain. The sign of the Hall conductivity ca…
We investigate the AC electric field induced quantum anomalous Hall effect in honeycomb lattices and derive the full phase diagram for arbitrary field amplitude and phase polarization. We show how to induce anti-chiral edge modes as well as topological phases characterized by a Chern number larger than $1$ by means of suitable drivings. In particular, we find that the Chern number develops plateaus as a function of the frequency, providing an time-dependent analogue to the ones in the quantum Hall effect.
Quasi-particles are elementary excitations of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. Here, we consider anyons, the fractionally charged quasi-particles 20 of the Fractional Quantum Hall Effect occurring in two-dimensional electronic conductors in high magnetic fields. They obey anyonic statistics, intermediate between fermionic and bosonic. Surprisingly, anyons show large quantum coherence when transmitted through the localized states of electronic Fabry-Pérot…
We study coherence and entanglement properties of the state space of a composite bi-fermion (two electrons pierced by $λ$ magnetic flux lines) at one Landau site of a bilayer quantum Hall system. In particular, interlayer imbalance and entanglement (and its fluctuations) are analyzed for a set of $U(4)$ coherent (\emph{quasiclassical}) states generalizing the standard pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay between spin and pseudospin degrees of freedom opens new possibilities with regard to the spin-frozen case. Actually, spin degrees of freedom make interlay…
The uncontrolled interaction of a quantum system with its environment is detrimental for quantum coherence. In the context of solid-state qubits, techniques to mitigate the impact of fluctuating electric and magnetic fields from the environment are well-developed. In contrast, suppression of decoherence from thermal lattice vibrations is typically achieved only by lowering the temperature of operation. Here, we use a nano-electro-mechanical system (NEMS) to mitigate the effect of thermal phonons on a solid-state quantum emitter without changing the system temperature. We study the silicon-vaca…
Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an ``imperfect'' two-dimensional superfluidity, in which there is nearly dissipationless transport at non-vanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a {\it coherence network} induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropr…
We review recent investigations of the femtosecond non-linear optical response of the two-dimensional electron gas (2DEG) in a strong magnetic field. We probe the Quantum Hall (QH) regime for filling factors $ν\sim 1$. Our focus is on the transient coherence induced via optical excitation and on its time evolution during early femtosecond timescales. We simultaneously study the interband and intraband coherence in this system by using a nonlinear spectroscopic technique, transient three-pulse four wave mixing optical spectroscopy, and a many-body theory. We observe striking differences in the …
We report on the quantum Hall effect in two stacked graphene layers rotated by 2 degree. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a signature of Coulomb interaction induced interlayer coherence and Bose Einstein condensation of excitons that form at half filling of each layer. A density imbalance gives rise to reentrant behavior due t…
Bilayer quantum Hall systems develop strong interlayer phase-coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current-noise is that of the zero wavevector collective mode, which is sensitive to the degree of order in the system. Local elect…
The intrinsic spin Hall conductivity of a two-dimensional gas confined to SrTiO$_3$, such as occurs at an LaAlO$_3$/SrTiO$_3$ interface, is calculated from the Kubo formula. The effect of strain in the [001] (normal to the quantum well direction) and the [111] direction is incorporated into a full tight-binding Hamiltonian. We show that the spin-charge conversion ratio can be significantly altered through strain and gate voltage by tuning the chemical potential. Strain direction is also a significant factor in the spin Hall response as this direction affects the alignment of the conduction ban…
The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.
Bilayer quantum Hall systems can form collective states in which electrons exhibit spontaneous interlayer phase coherence. We discuss the possibility of using bilayer quantum dot many-electron states with this property to create two-level systems that have potential advantages as quantum bits.
Double-layer quantum Hall systems with spontaneous broken symmetry can exhibit a novel manybody quantum Hall effect due to the strong interlayer coherence. When the layer separation becomes close to the critical value, quantum fluctuations can destroy the interlayer coherence and the quantum Hall effect will disappear. We calculate the renormalized isospin stiffness $ρ_s$ due to quantum fluctuations within the Hartree-Fock-RPA formalism. The activation energy of the topological excitations thus obtained demonstrates a nice qualitative agreement with recent experiment.
Quantum Hall physics has been theoretically predicted in 4-dimensions and higher. In hypothetical 2n-dimensions, the topological characters of both the bulk and the boundary are manifested as quantized non-linear transport coefficients that connect, respectively, to the n-th Chern number of the bulk gap projection and to the n-th winding number of the Weyl spectral singularities on the (2n-1)-dimensional boundaries. Here, we introduce the concept of phason engineering in metamaterials and use it as a vehicle to access and apply the quantum Hall physics in arbitrary dimensions. Using these spec…
Proposed even-denominator fractional quantum Hall effect (FQHE) states suggest the possibility of excitations with non-Abelian braid statistics. Recent experiments on wide square quantum wells observe even-denominator FQHE even under electrostatic tilt. We theoretically analyze these structures and develop a procedure to accurately test proposed quantum Hall wavefunctions. We find that tilted wells favor partial subband polarization to yield Abelian even-denominator states. Our results show that tilting quantum wells effectively engineers different interaction potentials allowing exploration o…
We generalize the topological phase diagram of magnetic topological insulator (TI) thin films in an extended parameter space comprising out-of-plane (OP) and in-plane (IP) exchange fields in the presence of structural inversion asymmetry (SIA) while taking a generic orbital-dependent spin coupling allowed for TIs into consideration. The results show that an IP field substantially deforms phase boundaries and generically induces the quantum anomalous Hall (QAH) effect. For symmetric spin coupling, extremely weak OP and IP exchange fields create the QAH state by tuning SIA with a gate bias. For …
Motivated by the recent experimental observation [D. A. Abanin et al., Science 323, 328 (2011)] of nonlocality in magnetotransport near the Dirac point in six-terminal graphene Hall bars, for a wide range of temperatures and magnetic fields, we develop a nonequilibrium Green function (NEGF) theory of this phenomenon. In the phase-coherent regime and strong magnetic field, we find large spin Hall (SH) conductance in four-terminal bridges, where the SH current is pure only at the Dirac point (DP), as well as the nonlocal voltage at a remote location in six-terminal bars where the direct and inve…
The spontaneous interlayer phase coherent (111) state of bi-layer Quantum Hall system at filling factor $ν=1$ may be viewed as a condensate of interlayer particle-hole pairs or excitons. We show in this paper that when the layers are biased in such a way that these excitons are very dilute, they may be viewed as point-like bosons. We calculate the exciton dispersion relation, and show that the exciton-exciton interaction is dominated by the dipole moment they carry. In addition to the phase coherent state, we also find a Wigner Crystal/Glass phase in the presence/absence of disorder which is a…
Time-periodic perturbations can be used to engineer topological properties of matter by altering the Floquet band structure. This is demonstrated for a spin Hall insulator in the presence of monochromatic circularly polarized light. The inherent spin structure of the edge state is influenced by the Zeeman coupling and not by the orbital effect. The photocurrent (and the magnetization along the edge) develops a finite, helicity dependent expectation value and turns from dissipationless to dissipative with increasing radiation frequency, signalling a change in the topological properties. The con…
We demonstrate that the Magnus force acting on magnetic skyrmions can be efficiently tuned via modulation of the spin-orbit interaction strength. We show that the skyrmion Hall effect, which is a direct consequence of the non-vanishing Magnus force on the magnetic structure can be suppressed in certain limits. Our calculations show that the emergent magnetic fields in the presence of spin-orbit coupling (SOC) renormalize the Lorentz force on itinerant electrons and thus influence the topological transport. In particular, we show that for a Néel-type skyrmion and Bloch-type antiskyrmion, the sk…
The work is motivated by the puzzling results of the recent experiment [S. Tewari et al., Phys. Rev. B 93, 035420 (2016)], where a robust coherence recovery from a certain energy was detected for an electron injected into the quantum Hall edge at the filling factor 2. After passing through a quantum dot the electron then tunnels into the edge with a subsequent propagation towards a symmetric Mach-Zender interferometer, after which the visibility of Aharonov-Bohm (AB) oscillations is measured. According to conventional understanding its decay with the increasing energy of the injected electron …
We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarka…
For the realisation of scalable solid-state quantum-bit systems, spins in semiconductor quantum dots are promising candidates. A key requirement for quantum logic operations is a sufficiently long coherence time of the spin system. Recently, hole spins in III-V-based quantum dots were discussed as alternatives to electron spins, since the hole spin, in contrast to the electron spin, is not affected by contact hyperfine interaction with the nuclear spins. Here, we report a breakthrough in the spin coherence times of hole ensembles, confined in so called natural quantum dots, in narrow GaAs/AlGa…
Using exact diagonalization of bilayer quantum Hall systems at total filling factor $ν_T=1$ in the torus geometry, we show that there is a new long-range interlayer phase coherence due to spontaneous pseudospin spiral order at interlayer distances larger than the critical value at which the pseudospin ferromagnetic order is destroyed. We emphasize the distinction between the interlayer phase coherence and the pseudospin ferromagnetic order.
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 plateau disappears 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 o…
The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers,…
In this paper, we present a novel route to tunable spontaneous valley coherence in heterostructures of two dimensional valleytronic materials with other layered materials hosting anisotropic polaritonic modes. We first discuss the dependence of this coherence on the conductivity tensor of the anisotropic part of a general heterostructure and on its geometrical configuration. Subsequently, we propose two implementations - one, using anisotropic plasmons in phosphorene and another with hyperbolic phonon polaritons in MoO3. In both these systems we show for the first time electrostatic tunability…
We report on quantum interference between a pair of counterpropagating quantum Hall edge states that are separated by a high quality tunnel barrier. Observed Aharonov-Bohm oscillations are analyzed in terms of resonant tunneling between coupled Luttinger liquids that creates bound electronic states between pairs of tunnel centers that act like interference slits. We place a lower bound in the range of 20-40 $μ$m for the phase coherence length and directly confirm the extended phase coherence of quantum Hall edge states.
The bilayer systems exhibit the Bose-Einstein condensation of excitons that emerge due to Coulomb pairing of electrons belonging to one layer with the holes belonging to the other layer. Here we present the microscopic derivation of the dynamic equation for the condensate wave function at a low density of electron-hole ($e-h$) pairs in a strong magnetic field perpendicular to the layers and an electric field directed along the layers. From this equation we obtain the dispersion law for collective excitations of the condensate and calculate the electric charge of the vortex in the exciton conde…
Spin-orbit coupling fundamentally alters spin qubits, opening pathways to improve the scalability of quantum computers via long distance coupling mediated by electric fields, photons, or phonons. It also allows for new engineered hybrid and topological quantum systems. However, spin qubits with intrinsic spin-orbit coupling are not yet viable for quantum technologies due to their short ($\sim1~μ$s) coherence times $T_2$, while qubits with long $T_2$ have weak spin-orbit coupling making qubit coupling short-ranged and challenging for scale-up. Here we show that an intrinsic spin-orbit coupled "…
An interlayer phase coherence develops spontaneously in the bilayer quantum Hall system at the filling factor $ν=1$. On the other hand, the spin and pseudospin degrees of freedom are entangled coherently in the canted antiferromagnetic phase of the bilayer quantum Hall system at the filling factor $ν=2$. There emerges a complex Nambu-Goldstone mode with a linear dispersion in the zero tunneling-interaction limit for both cases. Then its phase field provokes a Josephson supercurrent in each layer, which is dissipationless as in a superconductor. We study what kind of phase coherence the Nambu-G…
Kane and Mele predicted that in presence of spin-orbit interaction graphene realizes the quantum spin Hall state. However, exceptionally weak intrinsic spin-orbit splitting in graphene ($\approx 10^{-5}$ eV) inhibits experimental observation of this topological insulating phase. To circumvent this problem, we propose a novel approach towards controlling spin-orbit interactions in graphene by means of covalent functionalization of graphene edges with functional groups containing heavy elements. Proof-of-concept first-principles calculations show that very strong spin-orbit coupling can be induc…
We investigate the effect of a high frequency electromagnetic field with both of circularly and linearly polarization, on the emergence of quantum phases on thin topological insulators. Simultaneously, the influence of the system parameters (such as magnetic impurity, thickness engineering and structural inversion asymmetry of the potential) on emergence of topological phases is studied. We take our attention to the high frequency regime in which it is possible to consider an expansion for the Floquet Hamiltonian in terms of orders of 1/Ω. The topological invariants are determined and it is de…
Material defects remain as the main bottleneck to the progress of topological insulators (TIs). In particular, efforts to achieve thin TI samples with dominant surface transport have always led to increased defects and degraded mobilities, thus making it difficult to probe the quantum regime of the topological surface states. Here, by utilizing a novel buffer layer scheme composed of an In2Se3/(Bi0.5In0.5)2Se3 heterostructure, we introduce a quantum generation of Bi2Se3 films with an order of magnitude enhanced mobilities than before. This scheme has led to the first observation of the quantum…
