Aharonov-Bohm Interference Research Articles

Decoherence in electron transport: back-scattering, effect on interference and rectification

Decoherence is an undesirable, but ubiquitous phenomenon in quantum systems. Here, we study the effect of partial decoherence, induced via a Büttiker probe, on two-terminal electronic transport across one-dimensional quantum wires and rings, in both the linear and non-linear regimes. We find that dephasing causes backscattering when introduced locally in a ballistic channel. Further, we find that decoherence results in rectification when inversion is broken in the two-terminal transport set-up by a combination of a local dephasing centre and a static impurity. Interestingly, the rectification strength and even its direction varies strongly with the relative distance between the probe and the scatterer. We further analyze how decoherence affects characteristic quantum effects in electronic transport, such as, Fabry-Pérot oscillations in double-barrier setups, and Aharonov–Bohm interference in one-dimensional rings, and find that the amplitude of oscillations in conductance is reduced by decoherence.

Aharonov-Bohm effect mediated by massive photons

Virtual photons play an essential role in the locally realistic description of the Aharonov-Bohm interference. We show that the effect of virtual photons in the interferometer is manifested by a change in their spectrum. In particular, when a vacuum is confined between two ideal conducting plates, the photons obey the two-dimensional Proca equation, the wave equation with finite effective mass. This results in a short-range interaction between a test charge and a magnetic flux, and hence the Aharonov-Bohm effect is reduced exponentially at a large distance between the two bodies. On the other hand, a semiclassical description is also possible, and this raises the interesting question of how to prove the physical reality of virtual photons.

Temporal multilayer structures in discrete physical systems towards arbitrary-dimensional non-Abelian Aharonov-Bohm interferences

Temporal modulation recently draws great attentions in wave manipulations, with which one can introduce the concept of temporal multilayer structure, a temporal counterpart of spatially multilayer configurations. This kind of multilayer structure holds temporal interfaces in the time domain, which provides additional flexibility in temporal operations. Here we take this opportunity and propose to simulate a non-Abelian gauge field with a temporal multilayer structure in the discrete physical system. Two basic temporal operations, i.e., the folding/unfolding operation and the phase shift operation are used to design such a temporal multilayer structure, which hence can support noncommutative operations to realize the non-Abelian Aharonov-Bohm interference in the time domain. A two-/three-dimensional non-Abelian gauge field can be built, which may be further extended to higher dimensions. Our work therefore provides a unique platform enabling generalization of non-Abelian physics to arbitrary dimensions and offers a method for wave manipulations with temporal band engineering.

Aharonov-Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene.

In the fractional quantum Hall effect, quasiparticles are collective excitations that have a fractional charge and show fractional statistics as they interchange positions. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, fractional statistics is most notable through quantum interference. Here we study fractional statistics in a bilayer graphene Fabry-Pérot interferometer. We tune the interferometer from the Coulomb-dominated regime to the Aharonov-Bohm regime, both for integer and fractional quantum Hall states. Focusing on the fractional quantum Hall state with a filling factor ν = 1/3, we follow the evolution of the Aharonov-Bohm interference of quasiparticles while varying the magnetic flux through an interference loop and the charge density within the loop independently. When their combined variation is such that the Landau filling remains 1/3, the charge density in the loop varies continuously. We then observe pristine Aharonov-Bohm oscillations with a period of three flux quanta, as expected for quasiparticles of one-third of the electron charge. Yet, when the combined variation leads to discrete events of quasiparticle addition or removal, phase jumps emerge and alter the phase evolution. Notably, across all cases with discrete and continuous charge variation, the average phase consistently increases by 2π with each addition of one electron to the loop, as expected for quasiparticles, obeying fractional statistics.

Strongly coupled edge states in a graphene quantum Hall interferometer

Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a Fabry-Pérot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple integer edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting putative pairing of electrons into 2e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{2}}}{{\\boldsymbol{e}}}$$\\end{document} quasiparticles. Here, we use a highly tunable graphene-based QHE FP interferometer to observe the connection between interference phase jumps and AB frequency doubling, unveiling how strong repulsive interaction between edge channels leads to the apparent pairing phenomena. By tuning electron density in-situ from filling factor ν<2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}} \\, < \\, {{\\boldsymbol{2}}}$$\\end{document} to ν>7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}} \\, > \\, {{\\boldsymbol{7}}}$$\\end{document}, we tune the interaction strength and observe periodic interference phase jumps leading to AB frequency doubling. Our observations demonstrate that the combination of repulsive interaction between the spin-split ν=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}}={{\\boldsymbol{2}}}$$\\end{document} edge channels and charge quantization is sufficient to explain the frequency doubling, through a near-perfect charge screening between the localized and extended edge channels. Our results show that interferometers are sensitive probes of microscopic interactions and enable future experiments studying correlated electrons in 1D channels using density-tunable graphene.

Anomalous Aharonov-Bohm Interference in the Presence of Edge Reconstruction.

Interferometry is a vital tool for studying fundamental features in the quantum Hall effect. For instance, Aharonov-Bohm interference in a quantum Hall interferometer can probe the wave-particle duality of electrons and quasiparticles. Here, we report an unusual Aharonov-Bohm interference of the outermost edge mode in a quantum Hall Fabry-Pérot interferometer, whose Coulomb interactions were suppressed with a grounded drain in the interior bulk of the interferometer. In a descending bulk filling factor from ν_{b}=3 to ν_{b}≈(5/3), the magnetic field periodicity, which corresponded to a single "flux quantum," agreed accurately with the enclosed area of the interferometer. However, in the filling range, ν_{b}≈(5/3) to ν_{b}=1, the field periodicity increased markedly, apriori suggesting a drastic shrinkage of the Aharonov-Bohm area. Moreover, the modulation gate voltage periodicity decreased abruptly at this range. We attribute these unexpected observations to edge reconstruction, leading to area changing with the field and a modified modulation gate-edge capacitance. These reproducible results support future interference experiments with a quantum Hall Fabry-Pérot interferometer.

Kagome Quantum Oscillations in Graphene Superlattices.

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

Electron Pairing of Interfering Interface-Based Edge Modes.

The remarkable Cooper-like pairing phenomenon in the Aharonov-Bohm interference of a Fabry-Perot interferometer-operating in the integer quantum Hall regime-remains baffling. Here, we report the interference of paired electrons employing "interface edge modes." These modes are born at the interface between the bulk of the Fabry-Perot interferometer and an outer gated region tuned to a lower filling factor. Such a configuration allows toggling the spin and the orbital of the Landau level of the edge modes at the interface. We find that electron pairing occurs only when the two modes (the interfering outer and the first inner) belong to the same spinless Landau level.

Electronic structures and Aharonov–Bohm effect in higher-order topological Dirac Semimetal nanoribbons with strong confinements

Electronic structures and magnetotransport properties of topological Dirac semimetal (TDSM) nanoribbons are studied by adopting the tight-binding lattice model and the Landauer–Büttiker formula based on the non-equilibrium Green’s function. For concreteness, the TDSM material Cd3As2 grown along the experimentally accessible [110] crystallographic direction is taken as an example. We found that the electronic structures of the TDSM nanoribbon depend on both the strength and direction of the magnetic field (MF). The transversal local charge density (LCD) distribution of the electronic states in the TDSM nanoribbon is moved gradually from the center toward the hinge of each surface as a [010] direction MF strength is increased, forming the two-sided hinge states. However, one-sided surface states are generated in the TDSM nanoribbon when a [001] direction MF is applied. As a result, one-sided hinge states can be achieved once a tilted MF is placed to the TDSM nanoribbon. The underlying physical mechanism of the desired one-sided hinge states is attributed to both the orbital and Zeeman effects of the MF, which is given by analytical analyses. In addition, typical Aharonov–Bohm interference patterns are observed in the charge conductance of the two-terminal TDSM nanoribbon with a tilted MF. This conductance behaviour originates from the unique interfering loop shaped by the one-sided hinge states. These findings may not only further our understanding on the external-field-induced higher-order (HO) topological phases but also provide an alternative method to probe the HO boundary states.

Gate-Controlled Quantum Interference Effects in a Clean Single-Wall Carbon Nanotube p-n Junction.

The precise control and deep understanding of quantum interference in carbon nanotube (CNT) devices are particularly crucial not only for exploring quantum coherent phenomena in clean one-dimensional electronic systems, but also for developing carbon-based nanoelectronics or quantum devices. Here, we construct a double split-gate structure to explore the Aharonov-Bohm (AB) interference effect in individual single-wall CNT p-n junction devices. For the first time, we achieve the AB modulation of conductance with coaxial magnetic fields as low as 3T, where the flux through the tube is much smaller than the flux quantum. We further demonstrate direct electric-field control of the nonmonotonic magnetoconductance through a gate-tunable built-in electric field, which can be quantitatively understood in combination with the AB phase effect and Landau-Zener tunneling in a CNT p-n junction. Moreover, the nonmonotonic magnetoconductance behavior can be strongly enhanced in the presence of Fabry-Pérot resonances. Our Letter paves the way for exploring and manipulating quantum interference effects with combining magnetic and electric field controls.

Quantum anomalous Hall interferometer

Electronic interferometries in integer and fractional quantum Hall regimes have unfolded the coherence, correlation, and statistical properties of interfering constituents. This is addressed by investigating the roles played by the Aharonov–Bohm effect and Coulomb interactions on the oscillations of transmission/reflection. Here, we construct magnetic interferometers using Cr-doped (Bi,Sb)2Te3 films and demonstrate the electronic interferometry using chiral edge states in the quantum anomalous Hall regime. By controlling the extent of edge coupling and the amount of threading magnetic flux, distinct interfering patterns were observed, which highlight the interplay between the Coulomb interactions and Aharonov–Bohm interference by edge states. The observed interference is likely to exhibit a long-range coherence and robustness against thermal smearing probably owing to the long-range magnetic order. Our interferometer establishes a platform for (quasi)particle interference and topological qubits.

Altshuler-Aronov-Spivak interference of one-dimensional helical edge states in MoTe2

Recent theories predicted that $1{\mathrm{T}}^{\ensuremath{'}}\text{\ensuremath{-}}\mathrm{MoT}{\mathrm{e}}_{2}$ is a higher-order topological insulator (HOTI) exhibiting one-dimensional (1D) conducting edge states, and that ${\mathrm{T}}_{d}\text{\ensuremath{-}}\mathrm{MoT}{\mathrm{e}}_{2}$ becomes a HOTI with broken inversion symmetry under strain or lattice distortion. Here, we report the transport evidence for 1D helical edge states in ${\mathrm{MoTe}}_{2}$ thin flakes. Under an in-plane magnetic field perpendicular to the current, Altshuler-Aronov-Spivak interference of edge states is observed, in which the oscillating period corresponding to magnetic flux $h/2e$ agrees with the lateral cross-sectional area. The absence of Aharonov-Bohm interference stems from the helical nature of the edge states. Temperature evolution of the fast Fourier transform amplitude is further obtained, indicating the quasiballistic transport mode. Our work deepens the understanding of higher-order topological properties of ${\mathrm{MoTe}}_{2}$, paving the way for further topological electronics.

Topological characteristics of gap closing points in nonlinear Weyl semimetals

In this work we explore the effects of nonlinearity on three-dimensional topological phases. Of particular interest are the so-called Weyl semimetals, known for their Weyl nodes, i.e., point-like topological charges which always exist in pairs and demonstrate remarkable robustness against general perturbations. It is found that the presence of onsite nonlinearity causes each of these Weyl nodes to break down into nodal lines and nodal surfaces at two different energies while preserving its topological charge. Depending on the system considered, additional nodal lines may further emerge at high nonlinearity strength. We propose two different ways to probe the observed nodal structures. First, the use of an adiabatic pumping process allows the detection of the nodal lines and surfaces arising from the original Weyl nodes. Second, an Aharonov-Bohm interference experiment is particularly fruitful to capture additional nodal lines that emerge at high nonlinearity.

Electronic Mach-Zehnder interference in a bipolar hybrid monolayer-bilayer graphene junction

Graphene matter in a strong magnetic field, realizing one-dimensional quantum Hall channels, provides a unique platform for studying electron interference. Here, using the Landauer-Büttiker formalism along with the tight-binding model, we investigate the quantum Hall (QH) effects in unipolar and bipolar monolayer-bilayer graphene (MLG-BLG) junctions. We find that a Hall bar made of an armchair MLG-BLG junction in the bipolar regime results in valley-polarized edgechannel interferences and can operate a fully tunable Mach-Zehnder (MZ) interferometer device. Investigation of the bar-width and magnetic-field dependence of the conductance oscillations shows that the MZ interference in such structures can be drastically affected by the type of (zigzag) edge termination of the second layer in the BLG region [composed of vertical dimer or non-dimer atoms]. Our findings reveal that both interfaces exhibit a double set of Aharonov-Bohm interferences, with the one between two oppositely valley-polarized edge channels dominating and causing a large amplitude conductance oscillation ranging from 0 to 2e2/h. We explain and analyze our findings by analytically solving the Dirac-Weyl equation for a gated semi-infinite MLG-BLG junction.

Fabry-Pérot and Aharonov-Bohm interference in ideal graphene nanoribbons

Quantum-mechanical calculations of electron magneto-transport in ideal graphene nanoribbons are presented. In noninteracting theory, it is predicted that an ideal ribbon that is attached to wide leads should reveal Fabry-Perot conductance oscillations in magnetic field. In the theory with Coulomb interaction taken into account, the oscillation pattern should rather be determined by the Aharonov-Bohm interference effect. Both of these theories predict the formation of quasi-bound states, albeit of different structures, inside the ribbon because of strong electron scattering on the interfaces between the connecting ribbon and the leads. Conductance oscillations are a result of resonant backscattering via these quasi-bound states.

Transport Simulation of Graphene Devices with a Generic Potential in the Presence of an Orthogonal Magnetic Field.

The effect of an orthogonal magnetic field is introduced into a numerical simulator, based on the solution of the Dirac equation in the reciprocal space, for the study of transport in graphene devices consisting of armchair ribbons with a generic potential. Different approaches are proposed to reach this aim. Their efficiency and range of applicability are compared, with particular focus on the requirements in terms of model setup and on the possible numerical issues that may arise. Then, the extended code is successfully validated, simulating several interesting magnetic-related phenomena in graphene devices, including magnetic-field-induced energy-gap modulation, coherent electron focusing, and Aharonov–Bohm interference effects.

Electronic Mach-Zehnder Interference in a Bipolar Hybrid Monolayer-Bilayer Graphene Junction

Graphene matter in a strong magnetic field, realizing one-dimensional quantum Hall channels, provides a unique platform for studying electron interference. Here, using the Landauer-B\"uttiker formalism along with the tight-binding model, we investigate the quantum Hall (QH) effects in unipolar and bipolar monolayer-bilayer graphene (MLG-BLG) junctions. We find that a Hall bar made of an armchair MLG-BLG junction in the bipolar regime results in valley-polarized edge-channel interferences and can operate a fully tunable Mach-Zehnder (MZ) interferometer device. Investigation of the bar-width and magnetic-field dependence of the conductance oscillations shows that the MZ interference in such structures can be drastically affected by the type of (zigzag) edge termination of the second layer in the BLG region [composed of vertical dimer or non-dimer atoms]. Our findings reveal that both interfaces exhibit a double set of Aharonov-Bohm interferences, with the one between two oppositely valley-polarized edge channels dominating and causing a large-amplitude conductance oscillation ranging from 0 to $ 2 e^2 / h$. We explain and analyze our findings by analytically solving the Dirac-Weyl equation for a gated semi-infinite MLG-BLG junction.

Coherent time-dependent oscillations and temporal correlations in triangular triple quantum dots

The fluctuation behavior of triple quantum dots (TQDs) has, so far, largely focused on current cumulants in the long-time limit via full counting statistics. Given that (TQDs) are non-trivial open quantum systems with many interesting features, such as Aharonov-Bohm interference and coherent population blocking, new fluctuating-time statistics, such as the waiting time distribution (WTD), may provide more information than just the current cumulants alone. In this paper, we use a Born-Markov master equation to calculate the standard and higher-order WTDs for coherentlycoupled TQDs arrayed in triangular ring geometries for several transport regimes. In all cases we find that the WTD displays coherent oscillations that correspond directly to individual time-dependent dot occupation probabilities, a result also reported recently in Ref.[1]. Our analysis, however, goes beyond the single-occupancy and single waiting time regimes, investigating waiting time behavior for TQDs occupied by multiple electrons and with finite electron-electron interactions. We demonstrate that, in these regimes of higher occupancy, quantum coherent effects introduce correlations between successive waiting times, which we can tune via an applied magnetic field. We also show that correlations can be used to distinguish between TQD configurations that have identical FCS and that dark states can be tuned with Aharonov-Bohm interference for more complicated regimes than single-occupancy.

A tunable Fabry-Pérot quantum Hall interferometer in graphene.

Electron interferometry with quantum Hall edge channels in semiconductor heterostructures can probe and harness the exchange statistics of anyonic excitations. However, charging effects present in semiconductors often obscured the Aharonov-Bohm interference in quantum Hall interferometers and make advanced charge screening strategies necessary. Here, we show that high-mobility monolayer graphene constitutes an alternative material system, not affected by charging effects, to perform Fabry-Pérot quantum Hall interferometry in the integer quantum Hall regime. In devices equipped with gate-tunable quantum point contacts acting on the edge channels of the zeroth Landau level, we observe high-visibility Aharonov-Bohm interference widely tunable through electrostatic gating or magnetic field, in agreement with theory. A coherence length of 10 μm at a temperature of 0.02 K allows us to further achieve coherently-coupled double Fabry-Pérot interferometry. In future, quantum Hall interferometry with graphene devices may enable investigations of anyonic excitations in fractional quantum Hall states.

Aharonov-Bohm effect in graphene-based Fabry-Pérot quantum Hall interferometers.

Interferometers probe the wave-nature and exchange statistics of indistinguishable particles-for example, electrons in the chiral one-dimensional edge channels of the quantum Hall effect (QHE). Quantum point contacts can split and recombine these channels, enabling interference of charged particles. Such quantum Hall interferometers (QHIs) can unveil the exchange statistics of anyonic quasi-particles in the fractional quantum Hall effect (FQHE). Here, we present a fabrication technique for QHIs in van der Waals (vdW) materials and realize a tunable, graphene-based Fabry-Pérot (FP) QHI. The graphite-encapsulated architecture allows observation of FQHE at a magnetic field of 3T and precise partitioning of integer and fractional edge modes. We measure pure Aharonov-Bohm interference in the integer QHE, a major technical challenge in small FP interferometers, and find that edge modes exhibit high-visibility interference due to large velocities. Our results establish vdW heterostructures as a versatile alternative to GaAs-based interferometers for future experiments targeting anyonic quasi-particles.