Ivan P. Levkivskyi

Dephasing in the electronic Mach-Zehnder interferometer at filling factor ν=2

We propose a simple physical model which describes dephasing in the electronic Mach-Zehnder interferometer at filling factor ν=2. This model explains very recent experimental results, such as the unusual lobe-type structure in the visibility of Aharonov-Bohm oscillations, phase rigidity, and the asymmetry of the visibility as a function of transparencies of quantum point contacts. According to our model, dephasing in the interferometer originates from strong Coulomb interaction at the edge of two-dimensional electron gas. The long-range character of the interaction leads to a separation of the spectrum of edge excitations on slow and fast mode. These modes are excited by electron tunneling and carry away the phase information. The new energy scale associated with the slow mode determines the temperature dependence of the visibility and the period of its oscillations as a function of voltage bias. Moreover, the variation of the lobe structure from one experiment to another is explained by specific charging effects, which are different in all experiments. We propose to use a strongly asymmetric Mach-Zehnder interferometer with one arm being much shorter than the other for the spectroscopy of quantum Hall edge states.

Mach-Zehnder interferometry of fractional quantum Hall edge states

We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first recall a classification of effective models based on the requirement of anomaly cancellation and illustrate the general classification with the example of a quantum Hall fluid at filling factor ν=2/3. We show that, in this example, it is impossible to describe the edge states with only one chiral channel and that there are several inequivalent models of the edge states with two fields. We focus our attention on the four simplest models of the edge states of a fluid with ν=2/3 and evaluate charges and scaling dimensions of quasiparticles. We study transport through an electronic Mach-Zehnder interferometer and show that scaling properties of the Fourier components of Aharonov-Bohm oscillations in the current provide information about the electric charges and scaling dimensions of quasiparticles. Thus, Mach-Zehnder interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor. They, therefore, can be used to test fundamental postulates underlying the low-energy effective theory of edge states. An important ingredient of our analysis is the tunneling Hamiltonian of quasiparticles, the form of which is discussed in detail.

Equilibration of quantum Hall edge states by an Ohmic contact

Ohmic contacts are crucial elements of electron optics that have not received a clear theoretical description yet. We propose a model of an Ohmic contact as a piece of metal of the finite capacitance C attached to a quantum Hall edge. It is shown that charged quantum Hall edge states may have weak coupling to neutral excitations in an Ohmic contact. Consequently, despite being a reservoir of neutral excitations, an Ohmic contact is not able to efficiently equilibrate edge states if its temperature is smaller than ℏΩc, where Ωc is the inverse RC time of the contact. This energy scale for a floating contact may become as large as the single-electron charging energy e2/C

Optimal ferromagnetically-coated carbon nanotube tips for ultra-high resolution magnetic force microscopy

Using single-walled carbon nanotubes homogeneously coated with ferromagnetic metal as ultra-high resolution magnetic force microscopy probes, we investigate the key image formation parameters and their dependence on coating thickness. The crucial step of introducing molecular beam epitaxy for deposition of the magnetic coating allows highly controlled fabrication of tips with small magnetic volume, while retaining high magnetic anisotropy and prolonged lifetime characteristics. Calculating the interaction between the tips and a magnetic sample, including hitherto neglected thermal noise effects, we show that optimal imaging is achieved for a finite, intermediate-thickness magnetic coating, in excellent agreement with experimental observations. With such optimal tips, we demonstrate outstanding resolution, revealing sub-10 nm domains in hard magnetic samples, and non-perturbative imaging of nanoscale spin structures in soft magnetic materials, all at ambient conditions with no special vacuum, temperature or humidity controls.

Theory of fractional quantum Hall interferometers

Interference of fractionally charged quasiparticles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under an adiabatic insertion of a quantum of singular flux. We resolve this seeming paradox by considering a microscopic model of electronic interferometers made from a quantum Hall liquid at filling factor 1/m with the shape of a Corbino disk. In such interferometers, the quantum Hall edge states are utilized in place of optical beams, the quantum point contacts play the role of beam splitters connecting different edge channels, and Ohmic contacts represent a source and drain of quasiparticle currents. Depending on the position of Ohmic contacts, one distinguishes interferometers of Fabry-Perot (FP) and Mach-Zehnder (MZ) type. An approximate ground state of such interferometers is described by a Laughlin-type wave function, and low-energy excitations are incompressible deformations of this state. We construct a low-energy effective theory by restricting the microscopic Hamiltonian of electrons to the space of incompressible deformations and show that the theory of the quantum Hall edge so obtained is a generalization of a chiral conformal field theory. In our theory, a quasiparticle tunneling operator is found to be a single-valued function of tunneling point coordinates, and its phase depends on the topology determined by the positions of Ohmic contacts. We describe strong coupling of the edge states to Ohmic contacts and the resulting quasiparticle current through the interferometer with the help of a master equation. We find that the coherent contribution to the average quasiparticle current through MZ interferometers does not vanish after summation over quasiparticle degrees of freedom. However, it acquires oscillations with the electronic period, in agreement with the Byers-Yang theorem. Importantly, our theory does not rely on any ad hoc constructions, such as Klein factors, etc. When the magnetic flux through an FP interferometer is varied with a modulation gate, current oscillations have the quasiparticle periodicity, thus allowing for spectroscopy of quantum Hall edge states.

Ultrahigh Currents in Dielectric-Coated Carbon Nanotube Probes

Carbon nanotubes used as conductive atomic force microscopy probes are expected to withstand extremely high currents. However, in existing prototypes, significant self-heating results in rapid degradation of the nanotube probe. Here, we investigate an alternative probe design, fabricated by dielectric encapsulation of multiwalled carbon nanotubes, which can support unexpectedly high currents with extreme stability. We show that the dielectric coating acts as a reservoir for Joule heat removal, and as a chemical barrier against thermal oxidation, greatly enhancing transport properties. In contact with Au surfaces, these probes can carry currents of 0.12 mA at a power of 1.5 mW and show no measurable change in resistance at current densities of 10(12) A/m(2) over a time scale of 10(3) s. Our observations are in good agreement with theoretical modeling and exact numerical calculations, demonstrating that the enhanced transport characteristics of such probes are governed by their more effective heat removal mechanisms.

Shot-Noise Thermometry of the Quantum Hall Edge States

We use the nonequilibrium bosonization technique to investigate the effects of the Coulomb interaction on quantum Hall edge states at a filling factor ν=2, partitioned by a quantum point contact (QPC). We find that, due to the integrability of charge dynamics, edge states evolve to a nonequilibrium stationary state with a number of specific features. In particular, the noise temperature Θ of a weak backscattering current between edge channels is linear in voltage bias applied at the QPC, independently of the interaction strength. In addition, it is a nonanalytical function of the QPC transparency T and scales as Θ proportional Tln(1/T) at T << 1. Our predictions are confirmed by exact numerical calculations.

Fermi-edge singularity in chiral one-dimensional systems far from equilibrium

In this paper we study the non-equilibrium one dimensional physics with the example of quantum Hall edge channel at integer filling factor Coulomb interacting with an artificial impurity. Electrons in an integer quantum Hall system effectively behave as free fermions, thus the interaction with a charged impurity normally leads to the orthogonality catastrophe and the Fermi edge singularity (FES). Unlike in 3D materials where the FES is commonly observed, the artificial impurity allows for a controllable interaction that can be made strong, leading to strong correlations and large scattering phases, resulting in resonant suppression of coherence on the channel, which can be detected by embedding the channel into an electronic interferometer and measuring the dip of the visibility of the interference pattern. However, in equilibrium the transition rates at the impurity satisfy the detailed balance equation and therefore the shape of the visibility dip is trivial. Thus we consider the regime where the transitions are induced by the non-equilibrium partitioning noise created in the interferometer itself by the beam splitter. The best method to describe such a system is the non-equilibrium bosonization technique which reduces the problem to the calculation of the full counting statistics of the currents after a tunneling contact. The full counting statistics is calculated analytically in the Markovian limit in the regimes of weak tunneling or weak backscattering, and supplemented by the direct numerical calculation of the electron correlation functions for intermediate transparencies. The visibility is determined by both the FES and the non-equilibrium physics via the FES exponent and the transparency of the noise emitting QPC. The non-equilibrium effects are also manifested in the asymmetry of the visibility dip and in the non-trivial dependence of the dip position on the transparency.

Thermal decay of Coulomb blockade oscillations

We study transport properties and the charge quantization phenomenon in a small metallic island connected to the leads through two quantum point contacts (QPCs). The linear conductance is calculated perturbatively with respect to weak tunneling and weak backscattering at QPCs as a function of the temperature

Universal nonequilibrium states at the fractional quantum Hall edge

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