Integer Quantum Hall Regime Research Articles

Effects of asymmetry in Kondo channels on thermoelectric efficiency

We revisit an asymmetric two-channel charge Kondo model, which has been studied in the [Phys. Rev. B 82 (2010) 113306]. A nano-device modelling two-channel Kondo physics is a large metallic quantum dot which is embedded into a two-dimensional electron gas (2DEG) and connected strongly to two electrodes through two almost transparent single-mode quantum point contacts. The 2DEG is in the integer quantum Hall regime [Z. Iftikhar et al., Nature (London) 526 (2015) 233]. The reflection amplitudes at the quantum point contacts are asymmetric. We find that the thermopower and the figure of merit are decreased but the Kondo resonance width and Lorenz number in the vicinity of the Coulomb peak are lifted due to the effects of asymmetry in Kondo channels. We propose the method to improve the thermoelectric efficiency of the device.

Coulomb oscillations of a quantum antidot formed by an airbridged pillar gate in the integer and fractional quantum Hall regime

Abstract Quantum antidots (QAD) are attractive for manipulating quasiparticles in quantum Hall (QH) systems. Here, we form a QAD in the integer and fractional QH regimes at nominal Landau-level filling factor ν ̅ = 2, 1, and 2/3 using a submicron pillar gate with an airbridge connection. After confirming the required conditions for a fully depleted QAD, we analyze the observed Coulomb oscillations in terms of the area of the QAD and the effective charge for the oscillation period in an identical gate voltage range. The area at ν ̅ = 2/3 is significantly smaller than that at ν ̅ = 2 and 1, in qualitative agreement with the previous report. By assuming a constant gate capacitance, the effective charge at ν ̅ = 2/3 is about 2/3 of that at ν ̅ = 2 and 1. The QAD device can be used to capture and emit charges in the unit of 2e/3.

Universality of quantum phase transitions in the integer and fractional quantum Hall regimes

Fractional quantum Hall (FQH) phases emerge due to strong electronic interactions and are characterized by anyonic quasiparticles, each distinguished by unique topological parameters, fractional charge, and statistics. In contrast, the integer quantum Hall (IQH) effects can be understood from the band topology of non-interacting electrons. We report a surprising super-universality of the critical behavior across all FQH and IQH transitions. Contrary to the anticipated state-dependent critical exponents, our findings reveal the same critical scaling exponent κ = 0.41 ± 0.02 and localization length exponent γ = 2.4 ± 0.2 for fractional and integer quantum Hall transitions. From these, we extract the value of the dynamical exponent z ≈ 1. We have achieved this in ultra-high mobility trilayer graphene devices with a metallic screening layer close to the conduction channels. The observation of these global critical exponents across various quantum Hall phase transitions was masked in previous studies by significant sample-to-sample variation in the measured values of κ in conventional semiconductor heterostructures, where long-range correlated disorder dominates. We show that the robust scaling exponents are valid in the limit of short-range disorder correlations.

Signature of anyonic statistics in the integer quantum Hall regime

Anyons are exotic low-dimensional quasiparticles whose unconventional quantum statistics extend the binary particle division into fermions and bosons. The fractional quantum Hall regime provides a natural host, with the first convincing anyon signatures recently observed through interferometry and cross-correlations of colliding beams. However, the fractional regime is rife with experimental complications, such as an anomalous tunneling density of states, which impede the manipulation of anyons. Here we show experimentally that the canonical integer quantum Hall regime can provide a robust anyon platform. Exploiting the Coulomb interaction between two copropagating quantum Hall channels, an electron injected into one channel splits into two fractional charges behaving as abelian anyons. Their unconventional statistics is revealed by negative cross-correlations between dilute quasiparticle beams. Similarly to fractional quantum Hall observations, we show that the negative signal stems from a time-domain braiding process, here involving the incident fractional quasiparticles and spontaneously generated electron-hole pairs. Beyond the dilute limit, a theoretical understanding is achieved via the edge magnetoplasmon description of interacting integer quantum Hall channels. Our findings establish that, counter-intuitively, the integer quantum Hall regime provides a platform of choice for exploring and manipulating quasiparticles with fractional quantum statistics.

Numerical simulation of Rashba spin–orbit coupling effect on quantum Hall resistivity within tight-binding approximation

Numerical simulation of Rashba spin–orbit coupling effect on quantum Hall resistivity within tight-binding approximation

Topological Josephson junctions in the integer quantum Hall regime

Topological Josephson junctions in the integer quantum Hall regime

Resistance hysteresis in the integer and fractional quantum Hall regime

Resistance hysteresis in the integer and fractional quantum Hall regime

Quantum anomalous Hall interferometer

Electronic interferometries in integer and fractional quantum Hall regimes have unfolded the coherence, correlation, and statistical properties of interfering constituents. This is addressed by investigating the roles played by the Aharonov–Bohm effect and Coulomb interactions on the oscillations of transmission/reflection. Here, we construct magnetic interferometers using Cr-doped (Bi,Sb)2Te3 films and demonstrate the electronic interferometry using chiral edge states in the quantum anomalous Hall regime. By controlling the extent of edge coupling and the amount of threading magnetic flux, distinct interfering patterns were observed, which highlight the interplay between the Coulomb interactions and Aharonov–Bohm interference by edge states. The observed interference is likely to exhibit a long-range coherence and robustness against thermal smearing probably owing to the long-range magnetic order. Our interferometer establishes a platform for (quasi)particle interference and topological qubits.

Driven strongly correlated quantum circuits and Hall edge states: Unified photoassisted noise and revisited minimal excitations

We study the photo-assisted noise generated by time-dependent or random sources and transmission amplitudes. We show that it obeys a perturbative non-equilibrium fluctuation relation that fully extends the lateral-band transmission picture in terms of many-body correlated states. This relation holds in non-equilibrium strongly correlated systems such as the integer or fractional quantum Hall regime as well as in quantum circuits formed by a normal or Josephson junctions strongly coupled to an electromagnetic environment, with a possible temperature bias. We then show that the photo-assisted noise is universally super-poissonian, giving an alternative to a theorem by L. Levitov {\it et al} which states that an ac voltage increases the noise. Restricted to a linear dc current, we show that the latter does not apply to a non-linear superconducting junction. Then we characterize minimal excitations in non-linear conductors by ensuring a poissonian photo-assisted noise, and show that these can carry a non-trivial charge value in the fractional quantum Hall regime. We also propose methods for shot noise spectroscopy and for a robust determination of the fractional charge which is more advantageous than those we have proposed previously and implemented experimentally.

Multifractal Conductance Fluctuations in High-Mobility Graphene in the Integer Quantum Hall Regime.

We present the first experimental evidence for the multifractality of a transport property at a topological phase transition. In particular, we show that conductance fluctuations display multifractality at the integer quantum Hall plateau-to-plateau transitions in high-mobility mesoscopic graphene devices. The multifractality gets rapidly suppressed as the chemical potential moves away from these critical points. Our combination of experimental study and multifractal analysis provides a novel method for probing the criticality of wave functions at phase transitions in mesoscopic systems, and quantum criticality in several condensed-matter systems.

Time-dependent transport in graphene Mach-Zender interferometers

Graphene nanoribbons provide an ideal platform for electronic interferometry in the Integer Quantum Hall regime. Here, we solve the time-dependent four-component Schroedinger equation for single carriers in graphene and expose several dynamical effects of the carrier localization on their transport characteristics in pn junctions. We simulate two kinds of Mach-Zender Interferometers (MZI). The first is based on Quantum Point Contacts and is similar to traditional GaAs/AlGaAs interferometers. As expected, we observe Aharonov-Bohm oscillations and phase averaging. The second is based on Valley Beam Splitters, where we observe unexpected phenomena due to the intersection of the Edge Channels that constitute the MZI. Our results provide further insights into the behavior of graphene interferometers. Additionally, they highlight the operative regime of such nanodevices for feasible single-particle implementations.

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Double-charge quantum island in the quasiballistic regime

Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device that has been experimentally achieved quite recently, with two floating islands connected to three edge channels via quantum point contacts in the integer quantum Hall regime. At high transparency of the quantum point contacts, we establish a mapping to the boundary sine-Gordon model and thereby reveal the nature of the quantum critical point. We deduce from this mapping universal expressions for the conductance and noise, in agreement with the experimental findings, and discuss the competition between Kondo-like screening of each individual island and the cooperative transfer of electrons between them. We further predict that the device operated at finite voltage bias produces fractional charges ${e}^{*}=e/3$ and propose a generalization to $N$ islands with the fractional charge ${e}^{*}=e/(N+1)$.

Nonuniform heat redistribution among multiple channels in the integer quantum Hall regime

Heat transport in multiple quantum-Hall edge channels at Landau-level filling factor nu = 2, 4, and 8 is investigated with a quantum point contact as a heat generator and a quantum dot as a local thermometer. Heat distribution among the channels remains highly non-uniform, which can be understood with the plasmon eigenmodes of the multiple channels. The heat transport can be controlled with another quantum point contact as a quantized heat valve, as manifested by stepwise increases of heat current at the thermometer. This encourages developing integrated heat circuits with quantum-Hall edge channels.

Influence of channel mixing in fermionic Hong-Ou-Mandel experiments

We consider an electronic Hong-Ou-Mandel interferometer in the integer quantum Hall regime, where the colliding electronic states are generated by applying voltage pulses (creating for instance Levitons) to ohmic contacts. The aim of this work is to investigate possible mechanisms leading to a reduced visibility of the Pauli dip, i.e., the noise suppression expected for synchronized sources. It is known that electron-electron interactions cannot account for this effect and always lead to a full suppression of the Hong-Ou-Mandel noise. Focusing on the case of filling factor $\nu=2$, we show instead that a reduced visibility of the Pauli dip can result from mixing of the copropagating edge channels, arising from tunneling events between them.

Time-resolved investigation of plasmon mode along interface channels in integer and fractional quantum Hall regimes

The authors investigate here the fundamental charge dynamics of interface quantum Hall (QH) channels, formed at the interface of two QH regions, by using a time-resolved scheme. The measured plasmon mode is delayed and broadened due to the influence of charge puddles formed around the channel. The transport behavior can be understood with a distributed circuit model, which reveals the importance of gate-puddle capacitive coupling on plasmon dissipation. By reducing the puddle capacitance, a high-quality fractional interface channel can be realized.

The microscopic picture of the integer quantum Hall regime

Computer modeling of the integer quantum Hall effect based on self-consistent Hartree–Fock (HF) calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of up to 1 μm2 reveal self-organized clusters of locally fully filled and locally fully depleted Landau levels depending on which spin polarization is favored. The behavior results, for strong disorders, in an exchange-interaction induced g-factor enhancement and, ultimately, gives rise to narrow transport channels, including the celebrated narrow edge channels. For weak disorder, we find that bubble and stripes phases emerge with characteristics that predict experimental results very well. Hence the HF approach has become a convenient numerical basis to quantitatively study the quantum Hall effects, superseding previous more qualitative approaches.

Effects of domain walls in bilayer graphene in an external magnetic field

We investigate bilayer graphene systems with layer switching domain walls separating the two energetically equivalent Bernal stackings in the presence of an external magnetic field. To this end we calculate quantum transport and local densities of three microscopic models for a single domain wall: a hard wall, a defect due to shear, and a defect due to tension. The quantum transport calculations are performed with a recursive Green's function method. Technically, we discuss an explicit algorithm for the separation of a system into subsystems for the recursion and we present an optimization of the well known iteration scheme for lead self-energies for sparse chain couplings. We find strong physical differences for the three different types of domain walls in the integer quantum Hall regime. For a domain wall due to shearing of the upper graphene layer there is a plateau formation in the magnetoconductance for sufficiently wide defect regions. For wide domain walls due to tension in the upper graphene layer there is only an approximate plateau formation with fluctuations of the order of the elementary conuctance quantum $\sigma_0$. A direct transition between stacking regions like for the hard wall domain wall shows no plateau formation and is therefore not a good model for either of the previously mentioned extended domain walls.

Effect of magnetic field and chemical potential on the RKKY interaction in the α−T3 lattice

Using the $\alpha$-T$_3$ model, we carried out analytical and numerical calculations for the static and dynamic polarization functions in the presence of a perpendicular magnetic field. These results were employed to determine the longitudinal dielectric function and the magnetoplasmon dispersion relation. The magnetic field splits the continuous valence, conduction and flat energy subband into discrete Landau levels which present significant effects on the polarization function and magnetoplasmon dispersion. We present results for a doped layer in the integer quantum Hall regime for fixed hopping parameter $\alpha$ and various magnetic fields as well as chosen magnetic field and different $\alpha$ in the random phase approximation.

The effect of disorder on local electron temperature in quantum Hall systems

The local electron temperature distribution is calculated considering a two dimensional electron system in the integer quantum Hall regime in presence of disorder and uniform perpendicular magnetic fields. We solve thermo-hydrodynamic equations to obtain the spatial distribution of the local electron temperature in the linear-response regime. It is observed that, the variations of electron temperature exhibit an antisymmetry regarding the center of the sample in accordance with the location of incompressible strips. To understand the effect of sample mobility on the local electron temperature we impose a disorder potential calculated within the screening theory. Here, long range potential fluctuations are assumed to simulate cumulative disorder potential depending on the impurity atoms. We observe that the local electron temperature strongly depends on the number of impurities in narrow samples. The electron temperature $$T_e$$ versus position calculated for different values of the modulation potential $$V_0$$ . The calculations are done at $$T_\mathrm{L} = 0.04 \,E_F^0/k_B$$ lattice temperature considering impurity $$N_l = 6600$$ and repeated for three different values of magnetic field $$\hbar \omega _c/E_F^0 = 0.80$$ , 0.85 and 0.90. The insets show the enlarged region for the left side.