Electron interferometry with quantum Hall edge channels holds promise for probing and harnessing exotic exchange statistics of non-Abelian anyons. In semiconductor heterostructures, however, quantum Hall interferometry has proven challenging and often obscured by charging effects. Here we show that high-mobility monolayer graphene equipped with a series of gate-tunable quantum point contacts that act as electron beam-splitters provides a model system to perform Fabry-Pérot quantum Hall interferometry. We observe high-visibility Aharonov-Bohm interference free of charging effects and widely tunable through electrostatic gating or magnetic field, in remarkable agreement with theory. A coherence length of $\mathbf{10 \,μm}$ at a temperature of $0.02$ K allows us to further achieve coherently-coupled double Fabry-Pérot interferometry. Our results open a new avenue for quantum Hall interferometry and the exploitation of topological excitations for quantum computation.
A Fabry-Perot-type interferometer is experimentally realized for electrons in a semiconductor device. A special experimental geometry creates interference conditions for co-propagating electrons in quantum Hall edge states, which results in oscillations of the current through the device. The visibility of these oscillations is found to increase at the high-field edge of the quantum Hall plateau.
We present a scheme for high sensitivity charge detection in the integer quantum Hall regime using two point contacts in a series. The setup is an electronic analog of an optical Fabry-Perot interferometer. We show that for small transmission through the point contacts the sensitivity of the interferometer is very high due to multiple reflections at the point contacts. The sensitivity can be further enhanced twice by using electrons in spin entangled state. We show that for point contacts having different reflection probabilities, the interferometer can be tuned for the quantum limited measure…
We propose an intrinsic 3D Fabry-Pérot type interferometer, coined "higher-order interferometer", that utilizes the chiral hinge states of second-order topological insulators and cannot be equivalently mapped to 2D space because of higher-order topology. Quantum interference patterns in the two-terminal conductance of this interferometer are controllable not only by tuning the strength but also, particularly, by rotating the direction of the magnetic field applied perpendicularly to the transport direction. Remarkably, the conductance exhibits a characteristic beating pattern with multiple fre…
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…
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.
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 report on shot noise measurements in carbon nanotube based Fabry-Perot electronic interferometers. As a consequence of quantum interferences, the noise power spectral density oscillates as a function of the voltage applied to the gate electrode. The quantum shot noise theory accounts for the data quantitatively. It allows to confirm the existence of two nearly degenerate orbitals. At resonance, the transmission of the nanotube approaches unity, and the nanotube becomes noiseless, as observed in quantum point contacts. In this weak backscattering regime, the dependence of the noise on the ba…
A fabrication method for electronic quantum Hall Fabry-Perot interferometers (FPI) is presented. Our method uses a combination of e-beam lithography and low-damage dry-etching to produce the FPIs and minimize the excitation of charged traps or deposition of impurities near the device. Optimization of the quantum point contacts (QPC) is achieved via systematically varying the etch depth and monitoring the device resistance between segmented etching sessions. The etching is stopped when a desired value of resistance is obtained. Finer control of interference trajectories is obtained by the gate …
Quantum interferometers are powerful tools for probing the wave-nature and exchange statistics of indistinguishable particles. Of particular interest are interferometers formed by the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) that guide electrons without dissipation. Using quantum point contacts (QPCs) as beamsplitters, these 1D channels can be split and recombined, enabling interference of charged particles. Such quantum Hall interferometers (QHIs) can be used for studying exchange statistics of anyonic quasiparticles. In this study we develop a robust QHI fa…
The charge and exchange statistics of an elementary excitation manifest in quantum coherent oscillations that can be explored in interferometry measurements. Quantum Hall interferometers are primary tools to uncover unconventional quantum statistics associated with fractional and non-Abelian anyons of a two-dimensional system, the latter being the foundation of topological quantum computing. Graphene interferometers offer new avenues to explore the physics of exotic excitations due to their relatively small charging energies and sharp confinement potentials. Bilayer graphene possesses a true b…
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…
Here we theoretically investigate the valley-dependent transmission of particles through a combined electric and magnetic barrier in the $α-T_3$ model which interpolates between the honeycomb and the dice lattices. We put forward that the combination of the Fabry-Pérot interferences and the magnetic field leads to a perfect transmission for one valley and a suppression of the transmission for the other valley. When only one of the barriers (magnetic or electric) is present, no valley polarized current can be produced. By tuning the Fermi energy, this valley-dependent peculiar behavior can be u…
We report experiments on Fabry-Perot electron interferometers in the integer quantum Hall regime. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in 2D electron layer, enclosing an approximately circular island. The interferometer is formed by counterpropagating chiral edge channels coupled by tunneling in the two constrictions. Interference fringes are observed as conductance oscillations, similar to the Aharonov-Bohm effect. Front gates deposited in etch trenches allow to fine-tune the device and to change the constriction filling f relative to t…
We report systematic quantum Hall transport experiments on Fabry-Perot electron interferometers at ultra-low-temperatures. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in 2D electron layer, enclosing an approximately circular island. Front gates deposited in etch trenches allow to fine-tune the device for symmetry and to change the constriction filling, relative to the bulk. The low-field longitudinal and Hall magnetotransport shows Shubnikov-de Haas oscillations and integer quantum Hall plateaus. A systematic variation of front-gate voltage aff…
We consider signatures of abelian and nonabelian quasiparticle statistics in quantum Hall Fabry-Perot interferometers. When quasiparticles enter and exit the interference cell, for instance due to glassy motion in the dopant layer, the anyonic phase can be observed in phase jumps. In the case of the nonabelian nu=5/2 state, if the interferometer is small, we argue that free Majorana states in the interference cell are either strongly coupled to one another or are strongly coupled to the edge. We analyze the expected phase jumps and in particular suggest that changes in the parity of the Majora…
In recent years quantum phenomena have been experimentally demonstrated on variety of optomechanical systems ranging from micro-oscillators to photonic crystals. Since single photon couplings are quite small, most experimental approaches rely on the realization of high finesse Fabry-Perot cavities in order to enhance the effective coupling. Here we show that by exploiting a, long path, low finesse fiber Fabry-Perot interferometer ground state cooling can be achieved. We model a 100 m long cavity with a finesse of 10 and analyze the impact of additional noise sources arising from the fiber. As …
We investigate a Fabry-Pérot interferometer in the integer Hall regime in which only one edge channel is transmitted and n channels are trapped into the interferometer loop. Addressing recent experimental observations, we assume that Coulomb blockade effects are completely suppressed due to screening, while keeping track of a residual strong short range electron-electron interaction between the co-propagating edge channels trapped into the interferometer loop. This kind of interaction can be completely described in the framework of the edge-magnetoplasmon scattering matrix theory allowing us t…
Design of a Fabry-Perot (double point contact) interferometer to measure fractional quantum Hall effect quasiparticle charge properties, and in particular the 5/2 excitations, poses an important trade-off: the device size should be minimized to allow two path interference, since the coherence length of the quasiparticles in the correlated states are expected be limited, yet a small device promotes the dominance of Coulomb charging effects which would overwhelm the Aharonov-Bohm interference effect. In this study a series of small but different size interferometers from the same high density he…
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…
The advent of few-layer graphenes has given rise to a new family of two-dimensional systems with emergent electronic properties governed by relativistic quantum mechanics. The multiple carbon sublattices endow the electronic wavefunctions with pseudospin, a lattice analog of the relativistic electron spin, while the multilayer structure leads to electric field effect tunable electronic bands. Here we use these properties to realize giant conductance oscillations in ballistic trilayer graphene Fabry-Perot interferometers, which result from phase coherent transport through resonant bound states …
We show that the electrical transport across a minimal model for a time-reversal symmetry(TRS) breaking Weyl semi-metal (WSM) involving two Weyl nodes can be interpreted as an interferometer in momentum space. The interference phase depends on the distance between the Weyl nodes ($\vec{δk}$) and is {\it anisotropic}. It is further shown that a minimal inversion symmetry broken model for a WSM with four Weyl nodes effectively mimics a situation corresponding to having two copies of the interferometer due to the presence of an orbital pseudo-spin domain wall in momentum space. We point out that …
In a recent paper -- F. Ciccarello \emph{et al.}, New J. Phys. \textbf{8}, 214 (2006) -- we have demonstrated that the electron transmission properties of a one-dimensional (1D) wire with two identical embedded spin-1/2 impurities can be significantly affected by entanglement between the spins of the scattering centers. Such effect is of particular interest in the control of transmission of quantum information in nanostructures and can be used as a detection scheme of maximally entangled states of two localized spins. In this letter, we relax the constraint that the two magnetic impurities are…
We analyze interference phenomena in the quantum-Hall analog of the Fabry-Perot interferometer, exploring the roles of the Aharonov-Bohm effect, Coulomb interactions, and fractional statistics on the oscillations of the resistance as one varies the magnetic field B and/or the voltage V_G applied to a side gate. Coulomb interactions couple the interfering edge mode to localized quasiparticle states in the bulk, whose occupation is quantized in integer values. For the integer quantum Hall effect, if the bulk-edge coupling is absent, the resistance exhibits an Aharonov-Bohm (AB) periodicity, wher…
We study the conductance of an electron interferometer formed in a two dimensional electron gas between a nanostructured quantum contact and the charged tip of a scanning gate microscope. Measuring the conductance as a function of the tip position, thermally induced rings may be observed in addition to Fabry-Pérot interference fringes spaced by half the Fermi wavelength. If the contact is made of a quantum dot opened in the middle of a Kondo valley, we show how the location of the rings allows to measure by electron interferometry the magnetic moment of the dot above the Kondo temperature.
We demonstrate that giant Faraday rotation in graphene in the terahertz range due to the cyclotron resonance is further increased by constructive Fabry-Perot interference in the supporting substrate. Simultaneously, an enhanced total transmission is achieved, making this effect doubly advantageous for graphene-based magneto-optical applications. As an example, we present far-infrared spectra of epitaxial multilayer graphene grown on the C-face of 6H-SiC, where the interference fringes are spectrally resolved and a Faraday rotation up to 0.15 radians (9°) is attained. Further, we discuss and co…
Interference of edge channels is expected to be a prominent tool for studying statistics of charged quasiparticles in the quantum Hall effect (QHE) [A. Stern (2008), Ann. Phys. 1:204; C. Chamon et al. (1997), Phys. Rev. B, 55:2331]. We present here a detailed study of an electronic Fabry-Perot interferometer (FPI) operating in the QHE regime [C. Chamon et al. (1997), Phys. Rev. B, 55:2331], with the phase of the interfering quasiparticles controlled by the Aharonov-Bohm (AB) effect. Our main finding is that Coulomb interactions among the electrons dominate the interference, even in a relativel…
Resistance oscillations in electronic Fabry-Perot interferometers near fractional quantum Hall (FQH) filling factors 1/3, 2/3, 4/3 and 5/3 in the constrictions are compared to corresponding oscillations near integer quantum Hall (IQH) filling factors in the constrictions, appearing in the same devices and at the same gate voltages. Two-dimensional plots of resistance versus gate voltage and magnetic field indicate that all oscillations are Coulomb dominated. Applying a Coulomb charging model yields an effective tunneling charge e* \approx e/3 for all FQH constrictions and e* \approx e for IQH …
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 consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave …
We investigate the chemical reactivity of molecular populations confined inside a nanofluidic Fabry-P{é}rot cavity. Due to strong light-matter interactions developing between a resonant electromagnetic cavity-mode and the electric dipole moment of the confined molecules, a polariton is formed. The former gets dressed by environmental vibrational and rotational degrees of freedom of the solvent. We call the resulting polariton dressed by its cloud of environmental excitation a ''reacton'', since it further undergoes chemical reactions. We characterize how the reacton formation modifies the kine…
Quantum Hall edge states offer avenues for quasiparticle interferometry, provided that the ratio between phase coherence length and quantum Hall interferometer (QHI) size is large enough. Maximizing this ratio by shrinking the QHI area favors Coulomb interactions, impairing clear interferences observation. Here, we use scanning gate spectroscopy to probe interference regime in antidots-based graphene nano-QHIs, free of localized states (LS). A simple Fabry-Perot model, without Coulomb interaction, reproduces the QHI phenomenology, even in the smallest QHI, highlighting the LS detrimental role.
We report on observation of coherent electron transport in suspended high-quality InAs nanowire-based devices. The InAs nanowires were grown by low-temperature gold-assisted vapor-liquid-solid molecular-beam-epitaxy. The high quality of the nanowires was achieved by removing the typically found stacking-faults and reducing possible Au incorporation. Minimizing substrate-induced scattering in the device was achieved by suspending the nanowires over predefined grooves. Coherent transport involving more than a single one-dimensional mode transport, was observed in the experiment, manifested by Fa…
Utilizing an electronic Fabry-Perot interferometer in which Coulomb charging effects are suppressed, we report experimental observation of anyonic braiding statistics for the $ν=1/3$ fractional quantum Hall state. Strong Aharonov-Bohm interference of the $ν=1/3$ edge mode is punctuated by discrete phase slips consistent with an anyonic phase of $θ_{anyon}=\frac{2π}{3}$. Our results are consistent with a recent theory of a Fabry-Perot interferometer operated in a regime in which device charging energy is small compared to the energy of formation of charged quasiparticles. Close correspondence b…
We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry-Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov-Bohm regime, in which effects of fractional statistics should be visible,…
Recent schemes for experimentally probing non-abelian statistics in the quantum Hall effect are based on geometries where current-carrying quasiparticles flow along edges that encircle bulk quasiparticles, which are localized. Here we consider one such scheme, the Fabry-Perot interferometer, and analyze how its interference patterns are affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, we find that at strong coupling, the bulk quasiparticle becomes essentially absorbed by …
The distribution of electron waiting times is useful to characterize quantum transport in mesoscopic structures. Here we consider a generic quantum-coherent conductor consisting of a mesoscopic scatterer in a two-terminal setup. We extend earlier results for single-channel conductors to setups with several (possibly spin-degenerate) conduction channels and we discuss the effect of a finite electronic temperature. We present detailed investigations of the electron waiting times in a quantum point contact as well as in two mesoscopic interferometers with energy-dependent transmissions: a Fabry-P…
We analyze the magnetic field and gate voltage dependence of the longitudinal resistance in an integer quantum Hall Fabry-Pérot interferometer, taking into account the interactions between an interfering edge mode, a non-interfering edge mode and the bulk. For weak bulk-edge coupling and sufficiently strong inter-edge interaction, we obtain that the interferometer operates in the Aharonov-Bohm regime with a flux periodicity halved with respect to the usual expectation. Even in the regime of strong bulk-edge coupling, this behavior can be observed as a subperiodicity of the interference signal …
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…
The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers,…
Three-dimensional topological insulator (3D TI) nanowires display various interesting magnetotransport properties that can be attributed to their spin-momentum-locked surface states such as quasiballistic transport and Aharonov-Bohm oscillations. Here, we focus on the transport properties of a 3D TI nanowire with a gated section that forms an electronic Fabry-Pérot (FP) interferometer that can be tuned to act as a surface-state filter or energy barrier. By tuning the carrier density and length of the gated section of the wire, the interference pattern can be controlled and the nanowire can bec…
The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations of the interferometer with respect to an inertial reference frame result in a shift in the interference pattern proportional to the rotation rate. Here we analyze for the first time the Sagnac effect in a mesoscopic semiconductor electron interferometer. We include in our analysis Rashba spin-orbit interactions in the ring. Our results indicate that spin-orbit interactions increase the rotation induced phase shift. We discuss the potential experimental observability of the Sagnac phase s…
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…
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…
Anyonic interferometry probes the braiding phases of excitations in topologically ordered matter. This technique is well established for charged quasiparticles in the fractional quantum Hall effect. We propose to extend it to neutral anyons, such as Ising anyons in Kitaev magnets and quasiparticles in other neutral spin liquids. We find that the thermal current through an interferometer is sensitive to the statistics of tunneling quasiparticles. We present a systematic investigation of signatures of various Abelian and non-Abelian topological orders in Fabry-Pérot and Mach-Zehnder interferomet…
Interferometry of non-Abelian edge excitations is a useful tool in topological quantum computing. In this paper we present a theory of a non-Abelian edge state interferometer in a 3D topological insulator brought in proximity to an s-wave superconductor. The non-Abelian edge excitations in this system have the same statistics as in the previously studied 5/2 fractional quantum Hall (FQH) effect and chiral p-wave superconductors. There are however crucial differences between the setup we consider and these systems, like the need for a converter between charged and neutral excitations and the ne…
We consider the scattering of particles by an obstacle which tunnels coherently between two positions. We show that the obstacle mimics two classical scatterers at fixed positions when the kinetic energy epsilon of the incident particles is smaller than the tunnel splitting Delta: If the obstacles are arranged in parallel, one observes an interference pattern as in the conventional double-slit experiment. If they are arranged in series, the observations conform with a Fabry-Perot interferometer. At larger epsilon inelastic processes result in more complex interference phenomena. Interference d…
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 bro…
