Quantum Hall Devices Research Articles

Two-particle entanglement in capacitively coupled Mach-Zehnder interferometers

We propose and analyze a mesoscopic device producing on-demand entangled pairs of electrons. The system consists of two capacitively coupled Mach-Zehnder interferometers implemented in a quantum Hall structure. A pair of electron wave-packets is injected into the chiral edge states of two (of the four) incoming arms; scattering on the incoming interferometers splits the wave-packets into four components of which two interact. The resulting interaction phase associated with this component leads to the entanglement of the state; the latter is scattered at the outgoing beam splitter and analyzed in a Bell violation test measuring the presence of particles in the four outgoing leads. We study the two-particle case and determine the conditions to reach and observe full entanglement. We extend our two-particle analysis to include the underlying Fermi seas in the quantum Hall device; the change in shape of the wave-function, the generation of electron-hole pairs in the interaction regime, and a time delay between the pulses all reduce the degree of visible entanglement and the violation of the Bell inequality, effects which we analyze quantitatively. We determine the device settings optimizing the entanglement and the Bell test and find that violation is still possible in the presence of the Fermi seas, with a maximal Bell parameter reaching ${\cal B} = 2.18 > 2$ in our setup.

Direct imaging of topological edge states in cold-atom systems

Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes--guaranteed by the existence of nontrivial topological invariants--have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas and imaging its time evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.

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 ≤ ν ≤ 3. 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 ∼ 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 underlines the applicability of spin droplets in, for example, spin-transport through quantum point contacts.

An analogue of Hawking radiation in the quantum Hall effect

The edge of a droplet of lowest Landau-level quantum Hall fluid provides a model for a 1 + 1 dimensional chiral Dirac fermion. We use this fact to construct an analogue model for a chiral fermion in a space-time geometry possessing an event horizon. We show that the analogue horizon emits particles and holes with a thermal spectrum. Each emitted quasiparticle is correlated with an opposite-energy partner on the other side of the horizon. Once we trace out these ‘unobservable’ partners, we are left with a thermal density matrix. For typical quantum Hall device parameters, the predicted ‘Hawking’ temperature is about 2 K.

Coherent tunnelling across a quantum point contact in the quantum Hall regime

The unique properties of quantum hall devices arise from the ideal one-dimensional edge states that form in a two-dimensional electron system at high magnetic field. Tunnelling between edge states across a quantum point contact (QPC) has already revealed rich physics, like fractionally charged excitations, or chiral Luttinger liquid. Thanks to scanning gate microscopy, we show that a single QPC can turn into an interferometer for specific potential landscapes. Spectroscopy, magnetic field and temperature dependences of electron transport reveal a quantitatively consistent interferometric behavior of the studied QPC. To explain this unexpected behavior, we put forward a new model which relies on the presence of a quantum Hall island at the centre of the constriction as well as on different tunnelling paths surrounding the island, thereby creating a new type of interferometer. This work sets the ground for new device concepts based on coherent tunnelling.

Proposal on Tunneling Effect between Quantum Hall States

In the integer and fractional quantum Hall effects, the electric current flows through a thin layer under the strong magnetic field. The diagonal resistance becomes very small at integer and specific fractional filling factors where the electron scatterings are very few. Accordingly the coherent length is large and therefore a tunneling effect of electrons may be observed. We consider a new type of a quantum Hall device which has a narrow potential barrier in the thin layer. Then the electrons flow with tunneling effect through the potential barrier. When the oscillating magnetic field is applied in addition to the constant field, the voltage steps may appear in the curve of voltage V versus electric current I. If the voltage steps are found in the experiment, it is confirmed that the 2D electron system yields the same phenomenon as that of the ac-Josephson effect in a superconducting system. Furthermore the step V is related to the transfer charge Q as V = (hf)/Q where f is the frequency of the oscillating field and h is the Planck constant. Then the detection of the step V determines the transfer charge Q. The ratio Q/e (e is the elementary charge) clarifies the origin of the transfer charge. Many conditions are required for us to observe the tunneling phenomenon. The conditions are examined in details in this article.

Semiconductor Quantized Voltage Source

We realize and investigate an all-semiconductor quantized voltage source which generates quantized output voltages V(out) = f(h/e) linked only to two fundamental constants, the electron's charge e and Planck's constant h, and to an applied excitation frequency f. The device is based on an integrated quantized circuit of a single-electron pump operated at pumping frequency f and a quantum Hall device monolithically integrated in series. Robust output voltages up to several μV are generated, which are expected to be scalable by orders of magnitude using present technology. The device might open a new route towards the closure of the quantum metrology triangle.

Frequency conversion of radio-frequency edge magnetoplasmons using a quantum point contact

We report a frequency-conversion technique for edge magnetoplasmons in a quantum Hall device. The nonlinear conductance of a quantum point contact (QPC) results in the generation of high harmonics of an input microwave and the mixing of two input frequencies. We controlled the conversion efficiency by tuning the nonlinear conductance via a gate voltage. The amplitudes of the frequency-converted waves agree well with those expected from the measured dc nonlinear conductance. We demonstrate the technique up to our instrumental limit of 12 GHz and show that formation of charge-density waves does not change the nonlinear characteristics of the QPC.

Distributed electrochemical capacitance evidenced in high-frequency admittance measurements on a quantum Hall device

We describe high-frequency admittance measurements up to 3 GHz on a quantum point contact in a quantum Hall regime. When the excitation frequency is so high that the wavelength of the edge magnetoplasmons is comparable to the size of the system, the phase developing along the edge channels must be considered when analyzing electrochemical capacitance in admittance. The result cannot be accounted for by the local electrochemical capacitance near the quantum point contact but instead needs to be understood by considering the distributed capacitance within the sample as a whole. This implies that all electrons within the device are interacting because the screening in one-dimensional channels is extremely weak. A distributed-element model is essential for understanding the ac response in low-dimensional structures, which is analogous to that in high-frequency electrical circuits.

A Numerical Study of Non-local Magneto Transport Effects in Quantum Hall Device Structures

We developed a non-equilibrium network model for magneto transport in 2D electronic systems in the quantum Hall effect regime, which is able to capture the real sample geometry, including contacts, leads and in-homogeneities like introduced by gate electrodes. In this paper we investigate non-local effects in magneto transport for a number of contact configurations of a quantum Hall system, including the effect of having unused metallic contacts between the active region of classical current flow and the remote region where the non-local signals are obtained.

AFM diagnostics of graphene-based quantum Hall devices

In this paper we present the results of morphological, mechanical and electrical investigation of the properties of prepared graphene flakes and graphene-based quantum Hall devices. AFM imaging allowed us to identify the local imperfections and unintentional modifications of the graphene sheets which had caused severe deterioration of the device electrical performance. Utilizing the NanoSwing imaging method, based on the time-resolved tapping mode, we could observe non-homogeneities of the structural and mechanical properties. We also diagnosed the device under working conditions by Kelvin probe microscopy and detected its local electric field distribution.

Dynamical Resurrection of the Visibility in a Mach-Zehnder Interferometer

We study a single-electron pulse injected into the chiral edge state of a quantum Hall device and subject it to a capacitive Coulomb interaction. We find that the scattered multiparticle state remains unentangled and hence can be created itself by a suitable classical voltage pulse. The application of an appropriate inverse pulse corrects for the shakeup due to the interaction and resurrects the original injected wave packet. We suggest an experiment with an asymmetric Mach-Zehnder interferometer where the application of such pulses manifests itself in an improved visibility.

Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas

Reduced density-matrix functional theory (RDMFT) has become an appealing alternative to density-functional theory to describe electronic properties of highly-correlated systems. Here we derive exact conditions for the suitability of RDMFT to describe the two-dimensional homogeneous electron gas, which is the base system for, e.g., semiconductor quantum dots and quantum Hall devices. Following the method of Cioslowski and Pernal [J. Chem. Phys. {\bf 111}, 3396 (1999)] we focus on the properties of power functionals of the form $f(n,n')=(n n')^\alpha$ for the scaling function in the exchange-correlation energy. We show that in order to have stable and analytic solutions, and for $f$ to satisfy the homogeneous scaling constraint, the power is restricted to $1/4 \leq \alpha \leq 3/4$. Applying a reasonable ansatz for the momentum distribution and the lower bound for the exchange-correlation energy tightens the physical regime further to $0.64 \lesssim \alpha \leq 0.75$.

Josephson currents in quantum Hall devices

We consider a simple model for an SNS Josephson junction in which the "normal metal" is a section of a filling-factor $\nu=2$ integer quantum-Hall edge. We provide analytic expressions for the current/phase relations to all orders in the coupling between the superconductor and the quantum Hall edge modes, and for all temperatures. Our conclusions are consistent with the earlier perturbative study by Ma and Zyuzin [Europhysics Letters {\bf 21} 941-945 (1993)]: The Josephson current is independent of the distance between the superconducting leads, and the upper bound on the maximum Josephson current is inversely proportional to the perimeter of the Hall device.

Admittance Measurement for a Quantum Point Contact in a Multiterminal Quantum Hall Device

We present admittance measurements for a quantum point contact embedded in a multiterminal quantum Hall system, using a time-resolved technique. The real part of ac admittance agrees well with conventional dc conductance, while the imaginary part shows a crossover between inductive and capacitive admittance, as theoretically predicted in the low-frequency limit. Multiterminal measurements with different chiralities of edge channels ensure that possible extrinsic coupling is negligibly small. The characteristic capacitance in our device is estimated from dependence of the imaginary part on the frequency.

Admittance Measurement for a Quantum Point Contact in a Multiterminal Quantum Hall Device

We present admittance measurements for a quantum point contact embedded in a multiterminal quantum Hall system, using a time-resolved technique. The real part of ac admittance agrees well with conventional dc conductance, while the imaginary part shows a crossover between inductive and capacitive admittance, as theoretically predicted in the low-frequency limit. Multiterminal measurements with different chiralities of edge channels ensure that possible extrinsic coupling is negligibly small. The characteristic capacitance in our device is estimated from dependence of the imaginary part on the frequency.

The quantum Hall impedance standard

Alternating current measurements of double-shielded quantum Hall devices have revealed a fascinating property of which only a quantum effect is capable: it can detect its own frequency dependence and convert it to a current dependence which can be used to eliminate both of them. According to an experimentally verified model, the residual frequency dependence is smaller than the measuring uncertainty of 1.3 × 10−9 kHz−1. In this way, a highly precise quantum standard of impedance can be established, without having to correct for any calculated frequency dependence and without the need for any artefact with a calculated frequency dependence. Nothing else like that is known to us and we hope that our results encourage other national metrology institutes to also apply it to impedance metrology and further explore its beautiful properties.

Epitaxial graphene electronic structure and transport

Since its inception in 2001, the science and technology of epitaxial graphene on hexagonal silicon carbide has matured into a major international effort and is poised to become the first carbon electronics platform. A historical perspective is presented and the unique electronic properties of single and multilayered epitaxial graphenes on electronics grade silicon carbide are reviewed. Early results on transport and the field effect in Si-face grown graphene monolayers provided proof-of-principle demonstrations. Besides monolayer epitaxial graphene, attention is given to C-face grown multilayer graphene, which consists of electronically decoupled graphene sheets. Production, structure and electronic structure are reviewed. The electronic properties, interrogated using a wide variety of surface, electrical and optical probes, are discussed. An overview is given of recent developments of several device prototypes including resistance standards based on epitaxial graphene quantum Hall devices and new ultrahigh frequency analogue epitaxial graphene amplifiers.

Tunneling Effect in Quantum Hall Device

Tunneling Effect in Quantum Hall Device

Electron interferometry in the quantum Hall regime: Aharonov-Bohm effect of interacting electrons

An apparent $h/fe$ Aharonov-Bohm flux period, where $f$ is an integer, has been reported in coherent quantum Hall devices. Such subperiod is not expected for noninteracting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period $h/2e$ persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges (``backscattering''). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward and backscattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.