We demonstrate that the differential magnetic susceptibility of a fractional quantum Hall disk, representing a Coulomb island in a Fabry--Perot interferometer, is exactly proportional to the island's conductance and its paramagnetic peaks are the equilibrium counterparts of the Coulomb blockade conductance peaks. Using as a thermodynamic potential the partition functions of the edge states' effective conformal field theory we find the positions of the Coulomb blockade peaks, when the area of the island is varied, the modulations of the distance between them as well as the thermal decay and broadening of the peaks when temperature is increased. The finite-temperature estimates of the peak's heights and widths could give important information about the experimental observability of the Coulomb blockade. In addition, the predicted peak asymmetry and displacement at finite temperature due to neutral multiplicities could serve to distinguish different fractional quantum Hall states with similar zero-temperature Coulomb blockade patterns.
We study electronic transport through an Aharonov-Bohm interferometer with single-level quantum dots embedded in the two arms. The full counting statistics in the shot-noise regime is calculated to first order in the tunnel-coupling strength. The interplay of interference and charging energy in the dots leads to a dynamical channel blockade that is tunable by the magnetic flux penetrating the Aharonov-Bohm ring. We find super-Poissonian behavior with diverging second and higher cumulants when the Aharonov-Bohm flux approaches an integer multiple of the flux quantum.
Two distinct types of magnetoresistance oscillations are observed in two electronic Fabry-Perot interferometers of different sizes in the integer quantum Hall regime. Measuring these oscillations as a function of magnetic field and gate voltages, we observe three signatures that distinguish the two types. The oscillations observed in a 2.0 square micron device are understood to arise from the Coulomb blockade mechanism, and those observed in an 18 square micron device from the Aharonov-Bohm mechanism. This work clarifies, provides ways to distinguish, and demonstrates control over, these disti…
Electron transport through two parallel quantum dots is a kind of solid-state realization of double-path interference. We demonstrate that the inter-dot Coulomb correlation and quantum coherence would result in strong current fluctuations with a divergent Fano factor at zero frequency. We also provide physical interpretation for this surprising result, which displays its generic feature and allows us to recover this phenomenon in more complicated systems.
We investigate the charge-states coherence underlying the nonequilibirum transport through a spinless double-dot Aharonov-Bohm (AB) interferometer. Both the current noise spectrum and real-time dynamics are evaluated with the well-established dissipaton-equation-of-motion method. The resulted spectrums show the characteristic peaks and dips, arising from coherent Rabi oscillation dynamics, with the environment-assisted indirect inter-dot tunnel coupling mechanism. The observed spectroscopic features are in a quantitative agreement to the real-time dynamics of the reduced density matrix off-dia…
We show how to construct the thermodynamic grand potential of a droplet of incompressible fractional quantum Hall liquid, formed inside of an electronic Fabry--Pérot interferometer, in terms of the conformal field theory disk partition function for the edge states in presence of Aharonov-Bohm flux. To this end we analyze in detail the algebraic structure of the edge states' Hilbert space and identify the effect of the variation of the flux. This allows us to compute, in the linear response approximation, all thermodynamic properties of the conductance in the regime when the Coulomb blockade is…
We study the real time dynamics of electron coherence in a double quantum dot two-terminal Aharonov-Bohm geometry, taking into account repulsion effects between the dots' electrons. The system is simulated by extending a numerically exact path integral method, suitable for treating transport and dissipation in biased impurity models [Phys. Rev. B 82, 205323 (2010)]. Numerical simulations at finite interaction strength are supported by master equation calculations in two other limits: assuming non-interacting electrons, and working in the Coulomb blockade regime. Focusing on the intrinsic coher…
We examine the relation between different electronic transport phenomena in a Fabry-Perot interferometer in the fractional quantum Hall regime. In particular, we study the way these phenomena reflect the statistics of quantum Hall quasi-particles. For two series of states we examine, one abelian and one non-abelian, we show that the information that may be obtained from measurements of the lowest order interference pattern in an open Fabry-Perot interferometer is identical to the one that may be obtained from the temperature dependence of Coulomb blockade peaks in a closed interferometer. We a…
We report on Coulomb blockade and Coulomb diamond measurements on an etched, tunable single-layer graphene quantum dot. The device consisting of a graphene island connected via two narrow graphene constrictions is fully tunable by three lateral graphene gates. Coulomb blockade resonances are observed and from Coulomb diamond measurements a charging energy of ~3.5 meV is extracted. For increasing temperatures we detect a peak broadening and a transmission increase of the nanostructured graphene barriers.
We measure the magneto-conductance through a micron-sized quantum dot hosting about 500 electrons in the quantum Hall regime. In the Coulomb blockade, when the island is weakly coupled to source and drain contacts, edge reconstruction at filling factors between one and two in the dot leads to the formation of two compressible regions tunnel coupled via an incompressible region of filling factor $ν=1$. We interpret the resulting conductance pattern in terms of a phase diagram of stable charge in the two compressible regions. Increasing the coupling of the dot to source and drain, we realize a F…
We clarify an important aspect of density functional theories, the broadening of the derivative discontinuity (DD) in a quantum system, with fluctuating particle number. Our focus is on a correlated model system, the single level quantum dot in the regime of the Coulomb blockade. We find that the DD-broadening is controlled by the small parameter $Γ/U$, where $Γ$ is the level broadening due to contacting and $U$ is a measure of the charging energy. Our analysis suggests, that Kondoesque fluctuations have a tendency to increase the DD-broadening, in our model by a factor of two.
We have fabricated and measured superconducting single-electron transistors with Al leads and Nb islands. At bias voltages below the gap of Nb we observe clear signatures of resonant tunneling of Cooper pairs, and of Coulomb blockade of the subgap currents due to linewidth broadening of the energy levels in the superconducting density of states of Nb. The experimental results are in good agreement with numerical simulations.
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 ph…
In two recent papers, O. Entin-Wohlman et al. studied the question: ``Which physical information is carried by the transmission phase through a quantum dot?'' In the present paper, this question is answered for an islolated Coulomb-blockade resonance and within a theoretical model which is more closely patterned after the geometry of the actual experiment by Schuster et al. than is the model of O. Entin-Wohlman et al. We conclude that whenever the number of leads coupled to the Aharanov-Bohm interferometer is larger than two, and the total number of channels is sufficiently large, the transmis…
We report experimental temperature dependence of the amplitude of Aharonov-Bohm oscillations in the Laughlin quasiparticle interferometer. The results fit very well the thermal dephasing dependence predicted for a g = 1/3 chiral Luttinger liquid interferometer, and are clearly distinct from the activated behavior observed in single-particle resonant tunneling and Coulomb blockade devices. The small deviation from the zero-bias theory seen below 20 mK indicates yet unrecognized source of experimental decoherence, not included in theory.
The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic electrodes via potential barriers. Based on this model, we calculate nonlinear transport characteristics (conductance-voltage and current-voltage dependences) and compare them with the results obtained within a self-consistent field approach. It is shown that the shape of transport characteristics is determined by the combined effect of the electronic structure of…
We study the role of Coulomb interaction in an electronic Fabry-Perot interferometer (FPI) realized with chiral edge states in the integer quantum Hall regime in the limit of weak backscattering. Assuming that a compressible Coulomb island in a bulk region of the FPI is formed, we develop a capacitance model which explains the plethora of experimental data on the flux and gate periodicity of conductance oscillations. It is also shown that a suppression of finite-bias visibility stems from a combination of weak Coulomb blockade and a nonequilibrium dephasing by the quantum shot noise.
Coulomb blockade (CB) in a quantum dot (QD) with one anomalously broad level is considered. In this case many consecutive pronounced CB peaks correspond to occupation of one and the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD. Single particle resonances of very different width are natural if the dot is not fully c…
Measurements of elastic and inelastic cotunneling currents are presented on a two-terminal Aharonov--Bohm interferometer with a Coulomb blockaded quantum dot embedded in each arm. Coherent current contributions, even in magnetic field, are found in the nonlinear regime of inelastic cotunneling at finite bias voltage. The phase of the Aharonov--Bohm oscillations in the current exhibits phase jumps of $π$ at the onsets of inelastic processes. We suggest that additional coherent elastic processes occur via the excited state. Our measurement technique allows the detection of such processes on a ba…
We propose the interaction of two electrons in a triple quantum dot as a minimal system to control long range superexchange transitions. These are probed by transport spectroscopy. Narrow resonances appear indicating the transfer of charge from one side of the sample to the other with the central one being occupied only virtually. We predict that two different intermediate states establish the two arms of a one dimensional interferometer. Configurations of destructive interference of the two superexchage trajectories totally block the current through the system. We emphasize the role of spin c…
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 use a Mach-Zehnder quantum Hall interferometer of a novel design to investigate the interference effects at fractional filling factors. Our device brings together the advantages of usual Mach-Zehnder and Fabry-Perot quantum Hall interferometers. It realizes the simplest-for-analysis Mach-Zehnder interference scheme, free from Coulomb blockade effects. By contrast to the standard Mach-Zehnder realization, our device does not contain an etched region inside the interference loop. For the first time for Mach-Zehnder interference scheme, the device demonstrates interference oscillations with $Φ…
We show that it is possible and rather efficient to compute at non-zero temperature the thermoelectric characteristics of Coulomb blockaded fractional quantum Hall islands, formed by two quantum point contacts inside of a Fabry-Perot interferometer, using the conformal field theory partition functions for the chiral edge excitations. The oscillations of the thermopower with the variation of the gate voltage as well as the corresponding figure-of-merit and power factors, provide finer spectroscopic tools which are sensitive to the neutral multiplicities in the partition functions and could be u…
The Fano effect, which arises from an interference between a localized state and the continuum, reveals a fundamental aspect of quantum mechanics. We have realized a tunable Fano system in a quantum dot (QD) in an Aharonov-Bohm interferometer, which is the first convincing demonstration of this effect in mesoscopic systems. With the aid of the continuum, the localized state inside the QD acquires itinerancy over the system even in the Coulomb blockade. Through tuning of the parameters, which is an advantage of the present system, unique properties of the Fano effect on the phase and coherence …
We report on the direct observation of the transmission phase shift through a Kondo correlated quantum dot by employing a new type of two-path interferometer. We observed a clear $π/2$-phase shift, which persists up to the Kondo temperature $T_{\rm K}$. Above this temperature, the phase shifts by more than $π/2$ at each Coulomb peak, approaching the behavior observed for the standard Coulomb blockade regime. These observations are in remarkable agreement with 2-level numerical renormalization group calculations. The unique combination of experimental and theoretical results presented here full…
We consider an interacting quantum dot working as a coherent source of single electrons. The dot is tunnel coupled to a reservoir and capacitively coupled to a gate terminal with an applied ac potential. At low frequencies, this is the quantum analog of the RC circuit with a purely dynamical response. We investigate the quantized dynamics as a consequence of ac pulses with large amplitude. Within a Keldysh-Green function formalism we derive the time-dependent current in the Coulomb blockade regime. Our theory thus extends previous models that considered either noninteracting electrons in nonli…
The electronic Hong-Ou-Mandel interferometer in the integer quantum Hall regime is an ideal system to probe the building up of quantum correlations between charge carriers and it has been proposed as a viable platform for quantum computing gates. Using a parallel implementation of the split-step Fourier method, we simulated the antibunching of two interacting fermionic wave packets impinging on a quantum point contact. Numerical results of the exact approach are compared with a simplified theoretical model based on one-dimensional scattering formalism. We show that, for a realistic geometry, t…
We present a microscopic picture of quantum transport in quantum antidots in the quantum Hall regime taking electron interactions into account. We discuss the edge state structure, energy level evolution, charge quantization and linear-response conductance as the magnetic field or gate voltage is varied. Particular attention is given to the conductance oscillations due to Aharonov-Bohm interference and their unexpected periodicity. To explain the latter we propose the mechanisms of scattering by point defects and Coulomb blockade tunneling. They are supported by self-consistent calculations in…
In this chapter, we present the state-of-the-art in the generation of nonclassical states of light using semiconductor cavity quantum electrodynamics (QED) platforms. Our focus is on the photon blockade effects that enable the generation of indistinguishable photon streams with high purity and efficiency. Starting with the leading platform of InGaAs quantum dots in optical nanocavities, we review the physics of a single quantum emitter strongly coupled to a cavity. Furthermore, we propose a complete model for photon blockade and tunneling in III-V quantum dot cavity QED systems. Turning toward…
We study charge transport in a single-electron transistor implemented as an interferometer such that the Coulomb blockaded middle island contains a circular chiral Majorana or Dirac edge mode. We concentrate on the regime of small conductance and provide an asymptotic solution in the limit of high transport voltage exceeding the charging energy. The solution is achieved using an instanton-like technique. The distinctions between Majorana and Dirac cases appears when the tunnel junctions are unequal. The main difference is in the offset current at high voltages which can be higher up to $50\%$ …
We study the magneto-conductance of a $1.4~\mathrm{μm}$-wide quantum dot in the fractional quantum Hall regime. For a filling factor $\approx 2/3$ and $\gtrsim 1/3$ in the quantum dot the observed Coulomb resonances show a periodic modulation in magnetic field. This indicates a non-trivial reconstruction of the 2/3 fractional quantum Hall state in the quantum dot. We present a model for the charge stability diagram of the system assuming two compressible regions separated by an incompressible stripe of filling factor $2/3$ and $1/3$, respectively. From the dependence of the magnetic field peri…
In quantum Hall systems with two narrow constrictions, tunneling between opposite edges can give rise to quantum interference and Aharonov-Bohm-like oscillations of the conductance. When there is an integer quantized Hall state within the constrictions, a region between them, with higher electron density, may form a compressible island. Electron-tunneling through this island can lead to residual transport, modulated by Coulomb-blockade type effects. We find that the coupling between the fully occupied lower Landau levels and the higher-partially occupied level gives rise to flux subperiods sma…
Coulomb diamonds are the archetypal signatures of Coulomb blockade, a well-known charging effect mainly observed in nanometer-sized "electronic islands" tunnel-coupled with charge reservoirs. Here, we identify apparent Coulomb diamond features in the scanning gate spectroscopy of a quantum point contact carved out of a semiconductor heterostructure, in the quantum Hall regime. Varying the scanning gate parameters and the magnetic field, the diamonds are found to smoothly evolve to checkerboard patterns. To explain this surprising behavior, we put forward a model which relies on the presence of…
Thermal transport through a Coulomb-blockade quantum dot (QD) coupled to two metallic leads is studied using five different approaches to the master equation in which sequential and coutuneling terms are taken into account. In the presence of intradot Coulomb interactions, a plateau in the thermo-particle, the heat, and the energy currents is seen. The current plateau diminishes at a high thermal bias between the leads. It is shown that the Pauli, the Redfield, the Lindblad-type equation with first order tunneling rates, and first-order von-Neumann master equations give very similar thermal tr…
We report experiments on temperature and Hall voltage bias dependence of the superperiodic conductance oscillations in the novel Laughlin quasiparticle interferometer, where quasiparticles of the 1/3 fractional quantum Hall fluid execute a closed path around an island of the 2/5 fluid. The amplitude of the oscillations fits well the quantum-coherent thermal dephasing dependence predicted for a two point-contact chiral edge channel interferometer in the full experimental temperature range 10.2<T<141 mK. The temperature dependence observed in the interferometer is clearly distinct from the behav…
Majorana zero modes are leading candidates for topological quantum computation due to non-local qubit encoding and non-abelian exchange statistics. Spatially separated Majorana modes are expected to allow phase-coherent single-electron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAs-Al island embedded in an Aharonov-Bohm interferometer. With increasing parallel magnetic field, a discrete sub-gap state in the island is lowered to zero energy yielding pe…
We present a new measurement-based scheme for performing braiding operations on Majorana zero modes and for detecting their non-Abelian statistics without moving or hybridizing them. In our scheme, the topological qubit encoded in any pair of well-separated Majorana zero modes in a mesoscopic superconductor island is read out from the transmission phase shift in electron teleportation through the island in the Coulomb blockade regime. We propose experimental setups to measure the teleportation phase shift via conductance in an electron interferometer or persistent current in a closed loop.
An extraordinary temperature dependence of the resonant Andreev reflection via discrete energy level in a normal-metal / quantum-dot / superconductor (N-QD-S) system is predicted theoretically by using Green function technique. The width of zero bias conductance peak in N-QD-S is about $\sqrt{Γ_L^2+Γ_R^2}$ and does not exhibit thermal broadening, where $Γ_L$ and $Γ_R$ are the coupling strength between QD and leads. Considering the intra-dot Coulomb interaction, the Coulomb blockade oscillations conducted by Andreev reflection differs dramatically from that in N-QD-N. Instead of thermal broaden…
We discuss transport experiments for various non-Abelian quantum Hall states, including the Read-Rezayi series and a paired spin singlet state. We analyze the signatures of the unique characters of these states on Coulomb blockaded transport through large quantum dots. We show that the non-Abelian nature of the states manifests itself through modulations in the spacings between Coulomb blockade peaks as a function of the area of the dot. Even though the current flows only along the edge, these modulations vary with the number of quasiholes that are localized in the bulk of the dot. We discuss …
Linear response conductance of a two terminal Aharonov-Bohm (AB) interferometer is an even function of magnetic field. This "phase symmetry" is no expected to hold beyond the linear response regime. In simple AB rings the phase of the oscillations changes smoothly (almost linearly) with voltage bias. However, in an interferometer with a quantum dot in its arm, tuned to the Coulomb blockade regime, experiments indicate that phase symmetry seems to persist even in the nonlinear regime. In this letter we discuss the processes that break AB phase symmetry. In particular we show that breaking of ph…
In the presence of Rashba spin-orbit coupling, magnetic field can drive a proximitized nanowire into a topological superconducting phase. We study transport properties of such nanowires in the Coulomb blockade regime. The associated with the topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire - a non-local signature of topological superconductivity. In this work, we focus on the case of strong hybridization of the Majorana modes with the normal leads. The induced by hybridization broadening of the Ma…
We discuss electron transport in individual nanometer-scale metallic grains at dilution refrigerator temperatures. In the weak coupling regime, the grains exhibit Coulomb blockade and discrete energy levels. Electron-electron interactions lead to clustering and broadening of quasiparticle states. Magnetic field dependences of tunneling resonances directly reveal Kramers degeneracy and Lande g-factors. In grains of Au, which have strong spin-orbit interaction, g-factors are strongly suppressed from the free electron value. We have recently studied grains in the strong coupling regime. Coulomb b…
Using the conformal field theory approach to the thermoelectric characteristics of fractional quantum Hall states, previously developed in Nucl. Phys. B 894 (2015) 284, we show that the thermoelectric power factor of Coulomb-blockaded islands, realized by point contacts in Fabry--Pérot interferometers in the $\mathbb{Z}_k$ parafermion Hall states, could give reliable signatures for distinguishing the topological orders of different quantum Hall states having identical electric properties. For example, while the conductance peak patterns in the Coulomb blockade regime for such states are practi…
Experimental study of quantum Hall corrals reveals Aharonov-Bohm-Like (ABL) oscillations. Unlike the Aharonov-Bohm effect which has a period of one flux quantum, $Φ_{0}$, the ABL oscillations possess a flux period of $Φ_{0}/f$, where $f$ is the integer number of fully filled Landau levels in the constrictions. Detection of the ABL oscillations is limited to the low magnetic field side of the $ν_{c}$ = 1, 2, 4, 6... integer quantum Hall plateaus. These oscillations can be understood within the Coulomb blockade model of quantum Hall interferometers as forward tunneling and backscattering, respec…
For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural expl…
For a variety of quantum dots, the widths of different single-particle levels may naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. We found that in this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation of the salient featur…
