arXiv subjects

A. Siddiki

Publications and source records attributed to A. Siddiki.

At least 19 recordsLinked to original sources

arXiv2022

The topological inequivalence of Hall bar versus Corbino geometries in real space

This work discusses the effect of topology in the frame of direct Coulomb interactions, considering two distinct geometries, namely the Hall bar and the Corbino disc. In the mainstream approaches to the quantized Hall effect, the consequences of interactions are usually underestimated. Here, we investigate the electron number density, potential and current distributions within the screening theory that considers electron-electron interactions. Inclusion of direct Coulomb interaction and realistic boundary conditions result in local metal-like compressible and (Topological) insulator-like incompressible regions. Consequently, we show that the bulk of both geometries in coordinate space is not incompressible throughout the quantized Hall plateau. Furthermore, placing two inner contacts within the Hall bar geometry shows that the quantization is unaffected by changing the genus number in real space. Finally, we propose novel experiments which will enable us to distinguish the topological properties of the two geometries in the configuration space.

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arXiv2019

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 thermal-hydrodynamical 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.

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arXiv2017

Gestalt Principles re-investigated within Heisenberg uncertainty relation

Perception, sensation and re-action are central questions both in Psychology, Arts, Neurology and Physics. Some hundred years ago, believed to start with Wertheimer, researchers and artists tried to classify our human being "understanding" of Nature, in terms of \emph{Gestalt} principles. During same period \emph{Quantum} mechanics were developed by Schroedinger, Heisenberg, Dirac, Majorana and others. In this work we briefly summarize the basic concepts of these two approaches and try to combine them at a simplistic level. We show that, perception and sensation can be handled within electrical signal processing utilizing Fourier transformation, which finds its counter-part in quantum mechanics.

physics.pop-ph↗

arXiv2016

Classical and quantum capacitances calculated locally considering a two-dimensional Hall bar

In this work we investigate the electrostatic properties of two dimensional electron system (2DES) in the integer quantum Hall regime. The alternating screening properties of compressible and incompressible strips are formed due to edge effects together with electron-electron interactions. As it is well known, the Landau quantization emanates from strong perpendicular magnetic fields. The (Landau) energy levels are broadened due to impurities, which we embedded their effects in density of states (DOS). In a basic level DOS has two different forms: the Gaussian and semi-elliptic descriptions. The second form is calculated within the self consistent Born approximation (SCBA). Having in hand the density of states, we obtain both the longitudinal and Hall (transversal) conductivities ($σ_{l}, σ_{H}$) utilizing Thomas-Fermi-Poisson approximation to calculate position dependent charge density profile and use Drude formalism to obtain transport coefficients. Since, the definition of capacitance is closely related with compressibility via DOS, (local) screening properties of 2DES is extremely important to understand local capacitances. Here we numerically simulate a translational invariant Hall bar subject to high magnetic fields which is perpendicular to the plane of the 2DES using realistic parameters extracted from the related experiments. Using the above mentioned approaches the local capacitances are calculated, numerically. Our findings are in perfect agreement with related experimental results which are based on a dynamic scanning capacitance microscopy technique.

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arXiv2016

DFT modelling of the effect of strong magnetic field on Aniline molecule

Aniline is an organic compound with the stoichiometric expression $C_{6}H_{5}NH_{2}$; consisting of a phenyl structure attached to an amino group. It is colorless, but it slowly oxidizes and resinifies in air, giving a red-brown tint to aged samples. Until now, there are only few researches on Aniline considering low magnetic fields. In this work, we study Aniline molecule under different high magnetic fields using density functional theory methods including independent particle and interacting particle approaches. We obtain charge density distrubitions, energy dispersions, dipol moments and forces as functions of position and magnetic field. Our numerical results show that magnetic field affects electron density of the considered molecule. As a result, it is observed that there are strong fluctuations in energy dispersion.

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arXiv2016

A realistic quantum capacitance model for quantum Hall edge state based Fabry-Pérot interferometers

In this work, the classical and the quantum capacitances are calculated for a Fabry-Pérot interferometer operating in the integer quantized Hall regime. We first consider a rotationally symmetric electrostatic confinement potential and obtain the widths and the spatial distribution of the insulating (incompressible) circular strips using a charge density profile stemming from self-consistent calculations. Modelling the electrical circuit of capacitors composed of metallic gates and incompressible/compressible strips, we investigate the conditions to observe Aharonov-Bohm (quantum mechanical phase dependent) and Coulomb Blockade (capacitive coupling dependent) effects reflected in conductance oscillations. In a last step, we solve the Schrödinger and the Poisson equations self-consistently in a numerical manner taking into account realistic experimental geometries. We find that, describing the conductance oscillations either by Aharanov-Bohm or Coulomb Blockade strongly depends on sample properties also other than size, therefore, determining the origin of these oscillations requires further experimental and theoretical investigation.

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arXiv2016

Formation of spin droplet at nu = 5/2 in an asymmetric quantum dot under quantum Hall conditions

In this work, a quantum dot that is defined asymmetrically by electrostatic means induced on a GaAs/AlGaAs heterostructure is investigated to unravel the effect of geometric constrains on the formation of spin droplets under quantised Hall conditions. The incompressibility of exciting nu = 5/2 state is explored by solving the Schrodinger equation within spin density functional theory, where the confinement potential is obtained self-consistently utilising the Thomas-Fermi approximation. Our numerical investigations show that the spatial distribution of the nu = 2 incompressible strips and electron occupation in the second lowest Landau level considerably differ from the results of the laterally symmetric quantum dots. Our findings yield two important consequences, first the incompressibility of the intriguing nu = 5/2 state is strongly affected by the asymmetry, and second, since the Aharonov-Bohm interference patterns depend on the velocity of the particles, asymmetry yields an additional parameter to adjust the oscillation period, which imposes a boundary condition dependency in observing quasi-particle phases.

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arXiv2015

Single-electron Transport Through Quantum Point Contact

Here, we employ a numerical approach to investigate the transport and conductance characteristics of a quantum point contact. A quantum point contact is a narrow constriction of a width comparable to the electron wavelength defined in a two-dimensional electron gas (2DEG) by means of split-gate or etching technique. Their properties have been widely investigated in the experiments. We define a quantum Hall based split-gate quantum point contact with standard gate geometry. Firstly, we obtain the spatial distribution of incompressible strips (current channels) by applying a self consistent Thomas-Fermi method to a realistic heterostructure under quantized Hall conditions. Later, time-dependent Schrodinger equation is solved for electrons injected in the current channels. The transport characteristics and time-evolutions are analyzed in the integer filling factor regime (ν = 1) with the single electron density. The results confirm that the current direction in a realistic quantum point contact can be controllable with the external interventions.

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arXiv2015

Mechanically controlled quantum switch defined on a curved 2DEG

To investigate quantum nature of two dimensional electrons subject to high perpendicular magnetic fields, usually a planar electronic Fabry-Pérot interferometer is utilized. In this work, we investigate an interferometer defined on a curved heterostructure. In the presence of a magnetic field perpendicular to the cylindrical axis, the location and the properties of the edge channels depend on the radial component of the magnetic field. Considering a curved structure, we perform numerical and semi-analytical calculations to determine widths of the incompressible edge states. We observe that the edge states form a closed loop for certain magnetic field strengths yielding observation of conductance oscillations, which can be manipulated by changing the Azimuthal angle mechanically. In addition, we investigate the effect of spin polarization on the edge state distribution considering Zeeman splitting and obtained odd integer edge states. The proposed experiment would yield a novel method to clarify the ongoing debate on the origin of conductance oscillations, namely whether they stem from Aharonov-Bohm phase or charging effects

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arXiv2014

Temperature Dependent Symmetry to Asymmetry Transition in Wide Quantum Wells

Quasi-two dimensional electron systems exhibit peculiar transport effects depending on their density profiles and temperature. A usual two dimensional electron system is assumed to have a $δ$ like density distribution along the crystal growth direction. However, once the confining quantum well is sufficiently large, this situation is changed and the density can no longer be assumed as a $δ$ function. In addition, it is known that the density profile is not a single peaked function, instead can present more than one maxima, depending on the well width. In this work, the electron density distributions in the growth direction considering a variety of wide quantum wells are investigated as function of temperature. We show that, the double peak in the density profile varies from symmetric (similar peak height) to asymmetric while changing the temperature for particular growth parameters. The alternation from symmetric to asymmetric density profiles is known to exhibit intriguing phase transitions and is decisive in defining the properties of the ground state wavefunction in the presence of an external magnetic field, i.e from insulating phases to even denominator fractional quantum Hall states. Here, by solving the temperature and material dependent Schrödinger and Poisson equations self-consistently, we found that such a phase transition may elaborated by taking into account direct Coulomb interactions together with temperature.

cond-mat.mes-hall↗

arXiv2013

The local nature of incompressibility at quantised Hall effect modified by interactions

Since the experimental realisation of the integer quantised Hall effect in a two dimensional electron system subject to strong perpendicular magnetic fields in 1980, a central question has been the interrelation between the conductance quantisation and the topological properties of the system. It is conjectured that if the electron system is described by a Bloch hamiltonian, then the system is insulating in the bulk of the sample throughout the quantised Hall plateau due to magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without the time-reversal symmetry. However, the validity of this conjecture remains unclear for finite size, non-periodically bounded real Hall bar devices. Here we show experimentally that the close relationship proposed between the quantised Hall effect and the topological bulk insulator is prone to break for specific magnetic field intervals within the plateau evidenced by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts embedded to bulk. Our data presents a similar behaviour also for fractional states, in particular for 2/3, 3/5 and 4/3.

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arXiv2013

The Dip Effect under Integer Quantized Hall Conditions

In this work we investigate an unusual transport phenomenon observed in two-dimensional electron gas under integer quantum Hall effect conditions. Our calculations are based on the screening theory, using a semi-analytical model. The transport anomalies are \emph{dip} and overshoot effects, where the Hall resistance decreases (or increases) unexpectedly at the quantized resistance plateaus intervals. We report on our numerical findings of the \emph{dip} effect in the Hall resistance, considering GaAs/AlGaAs heterostructures in which we investigated the effect under different experimental conditions. We show that, similar to overshoot, the amplitude of the dip effect is strongly influenced by the edge reconstruction due to electrostatics. It is observed that the steep potential variation close to the physical boundaries of the sample results in narrower incompressible strips, hence, the experimental observation of the dip effect is limited by the properties of these current carrying strips. By performing standard Hall resistance measurements on gate defined narrow samples, we demonstrate that the predictions of the screening theory is in well agreement with our experimental findings.

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arXiv2013

Interaction reconstructed integer quantized Hall effect topological insulator

We discuss the role of direct Coulomb interaction on the bulk insulator of the integer quantized Hall effect that bridges the topological insulators and the conductance quantization. We investigate the magneto-transport properties of a two-dimensional electron system in the bulk, numerically, utilizing the self-consistent Thomas-Fermi-Poisson screening theory. Topologically distorted Hall bars with and without potential fluctuations are considered that comprises two identical inner contacts. Although these contacts change the topology, we show that quantized Hall effect survives due to redistributed incompressible strips on account of interactions. It is shown phenomenologically that the impedance between these contacts can be obtained by a minimal transport model. An important prediction of our self-consistent approach is a finite impedance between the inner contacts even in the plateau regime, where the maximum of the impedance decreases with increasing temperature.

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arXiv2013

Anomalous resistance overshoot in the integer quantum Hall effect

In this work we report experiments on defined by shallow etching narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the integer quantized Hall effect. We observe a non-monotonic increase of Hall resistance at the low magnetic field ends of the quantized plateaus, known as the overshoot effect. Unexpectedly, for Hall bars that are defined by shallow chemical etching the overshoot effect becomes more pronounced at elevated temperatures. We observe the overshoot effect at odd and even integer plateaus, which favor a spin independent explanation, in contrast to discussion in the literature. In a second set of the experiments, we investigate the overshoot effect in gate defined Hall bar and explicitly show that the amplitude of the overshoot effect can be directly controlled by gate voltages. We offer a comprehensive explanation based on scattering between evanescent incompressible channels.

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arXiv2013

Stability of spin droplets in realistic quantum Hall devices

We study the formation and characteristics of "spin droplets",i.e., compact spin-polarized configurations in the highest occupied Landau level, in an etched quantum Hall device at filling factors $2\leqν\leq3$. The confining potential for electrons is obtained with self-consistent electrostatic calculations on a GaAs/AlGaAs heterostructure with experimental system parameters. Real-space spin-density-functional calculations for electrons confined in the obtained potential show the appearance of stable spin droplets at $ν\sim 5/2$. The qualitative features of the spin droplet are similar to those in idealized (parabolic) quantum-dot systems. The universal stability of the state against geometric deformations underline the applicability of spin droplets in, e.g., spin-transport through quantum point contacts.

cond-mat.mes-hall↗

arXiv2013

Many-electron transport in Aharonov-Bohm interferometers: Time-dependent density-functional study

We apply time-dependent density-functional theory to study many-electron transport in Aharonov-Bohm interferometers in a non-equilibrium situation. The conductance properties in the system are complex and depend on the enclosed magnetic flux in the interferometer, the number of interacting particles, and the mutual distance of the transport channels at the points of encounter. Generally, the electron-electron interactions do not suppress the visibility of Aharonov-Bohm oscillations if the interchannel distance -- determined by the positioning of the incompressible strips through the external magnetic field -- is optimized. However, the interactions also impose an interesting Aharonov-Bohm phase shift with channel distances below or above the optimal one. This effect is combined with suppressed oscillation amplitudes. We analyze these effects within different approximations for the exchange-correlation potential in time-dependent density-functional theory.

cond-mat.str-el↗

arXiv2012

Edge electrostatics revisited

In this work we investigate in detail, the different regimes of the pioneering work of Chklovskii et al. (1992), which provides an analytical description to model the electrostatics at the edges of a two-dimensional electron gas. We take into account full electrostatics and calculate the charge distribution by solving the 3D Poisson equation self-consistently. The Chklovskii formalism is reintroduced and is employed to determine the widths of the incompressible edge-states also considering the spin degree of freedom. It is shown that, the odd integer filling fractions cannot exist for large magnetic field intervals if many-body effects are neglected. We explicitly show that, the incompressible strips which are narrower than the quantum mechanical length scales vanish. We numerically and analytically show that, the non-self-consistent picture becomes inadequate considering realistic Hall bar geometries, predicting large incompressible strips. The details of this picture is investigated considering device properties together with the many-body and the disorder effects. Moreover, we provide semi-empirical formulas to estimate realistic density distributions for different physical boundary conditions.

cond-mat.mes-hall↗

arXiv2012

Time-dependent transport in Aharonov-Bohm interferometers

A numerical approach is employed to explain transport characteristics in realistic, quantum Hall based Aharonov-Bohm interferometers. First, the spatial distribution of incompressible strips, and thus the current channels, are obtained applying a self-consistent Thomas-Fermi method to a realistic heterostructure under quantized Hall conditions. Second, the time-dependent Schrödinger equation is solved for electrons injected in the current channels. Distinctive Aharonov-Bohm 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 Aharonov-Bohm interferometers as controllable current switches.

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