A tunable Fabry-Pérot quantum Hall interferometer in graphene

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 2 e 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 to ν > 7 , 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 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.

Electron wave and quantum optics in graphene

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states,e.g., snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.

The Roadmap of 2D Materials and Devices Toward Chips

Due to the constraints imposed by physical effects and performance degradation, silicon-based chip technology is facing certain limitations in sustaining the advancement of Moore's law. Two-dimensional (2D) materials have emerged as highly promising candidates for the post-Moore era, offering significant potential in domains such as integrated circuits and next-generation computing. Here, in this review, the progress of 2D semiconductors in process engineering and various electronic applications are summarized. A careful introduction of material synthesis, transistor engineering focused on device configuration, dielectric engineering, contact engineering, and material integration are given first. Then 2D transistors for certain electronic applications including digital and analog circuits, heterogeneous integration chips, and sensing circuits are discussed. Moreover, several promising applications (artificial intelligence chips and quantum chips) based on specific mechanism devices are introduced. Finally, the challenges for 2D materials encountered in achieving circuit-level or system-level applications are analyzed, and potential development pathways or roadmaps are further speculated and outlooked.

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, a priori 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.

Evidence for chiral supercurrent in quantum Hall Josephson junctions

Hybridizing superconductivity with the quantum Hall (QH) effect has notable potential for designing circuits capable of inducing and manipulating non-Abelian states for topological quantum computation1-3. However, despite recent experimental progress towards this hybridization4-15, concrete evidence for a chiral QH Josephson junction16-the elemental building block for coherent superconducting QH circuits-is still lacking. Its expected signature is an unusual chiral supercurrent flowing in QH edge channels, which oscillates with a specific 2ϕ0 magnetic flux periodicity16-19 (ϕ0 = h/2e is the superconducting flux quantum, where h is the Planck constant and e is the electron charge). Here we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit a chiral supercurrent, visible up to 8 T and carried by the spin-degenerate edge channel of the QH plateau of resistance h/2e2 ≈ 12.9 kΩ. We observe reproducible 2ϕ0-periodic oscillations of the supercurrent, which emerge at a constant filling factor when the area of the loop formed by the QH edge channel is constant, within a magnetic-length correction that we resolve in the data. Furthermore, by varying the junction geometry, we show that reducing the superconductor/normal interface length is crucial in obtaining a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface19-22. Our findings are important for the exploration of correlated and fractional QH-based superconducting devices that host non-Abelian Majorana and parafermion zero modes23-32.

Charge Oscillations in Bilayer Graphene Quantum Confinement Devices

Quantum confinement structures are building blocks of quantum devices in fundamental physics exploration and technological applications. In this work, we fabricate dual-gated bilayer graphene Fabry-Pérot quantum Hall interferometers employing two different gating strategies and conduct finite element simulations to understand the electrostatics of the confinement structures and to guide device design and fabrication. We observe two types of resistance oscillations arising from the charging of quantum dots formed inside the interferometers. We obtain the size, location, and charging energy of the dots by measuring the dependence of the oscillations on the magnetic field, gate voltages, and dc bias. We analyze and discuss the origin of the quantum dots and their impact on quantum Hall edge state backscattering and interference. Insights gained in these studies shed light on the construction of van der Waals quantum confinement devices.

Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact

One-dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the single-electron tunneling density of states at low voltages. The scaling exponent is predicted to be quantized when tunneling into a single isolated chiral edge state of the fractional quantum Hall effect. We report conductance measurements across a point contact linking integer and fractional quantum Hall edge states (at fillings 1 and [Formula: see text], respectively). At weak coupling, we observe the predicted universal quadratic scaling with temperature and voltage. At strong coupling, we demonstrate perfect Andreev reflection of fractionalized quasiparticles at the point contact. We use the strong coupling physics to realize a nearly dissipationless direct current voltage step-up transformer, whose gain arises directly from topological fractionalization of electrical charge.

Absence of edge reconstruction for quantum Hall edge channels in graphene devices

Quantum Hall (QH) edge channels propagating along the periphery of two-dimensional (2D) electron gases under perpendicular magnetic field are a major paradigm in physics. However, groundbreaking experiments that could use them in graphene are hampered by the conjecture that QH edge channels undergo a reconstruction with additional nontopological upstream modes. By performing scanning tunneling spectroscopy up to the edge of a graphene flake on hexagonal boron nitride, we show that QH edge channels are confined to a few magnetic lengths at the crystal edges. This implies that they are ideal 1D chiral channels defined by boundary conditions of vanishing electronic wave functions at the crystal edges, hence free of electrostatic reconstruction. We further evidence a uniform charge carrier density at the edges, incompatible with the existence of upstream modes. This work has profound implications for electron and heat transport experiments in graphene-based systems and other 2D crystalline materials.

Mechanically reconfigurable van der Waals devices via low-friction gold sliding

Interfaces of van der Waals (vdW) materials, such as graphite and hexagonal boron nitride (hBN), exhibit low-friction sliding due to their atomically flat surfaces and weak vdW bonding. We demonstrate that microfabricated gold also slides with low friction on hBN. This enables the arbitrary post-fabrication repositioning of device features both at ambient conditions and in situ to a measurement cryostat. We demonstrate mechanically reconfigurable vdW devices where device geometry and position are continuously tunable parameters. By fabricating slidable top gates on a graphene-hBN device, we produce a mechanically tunable quantum point contact where electron confinement and edge-state coupling can be continuously modified. Moreover, we combine in situ sliding with simultaneous electronic measurements to create new types of scanning probe experiments, where gate electrodes and even entire vdW heterostructure devices can be spatially scanned by sliding across a target.

Observation of electronic modes in open cavity resonator

The resemblance between electrons and optical waves has strongly driven the advancement of mesoscopic physics, evidenced by the widespread use of terms such as fermion or electron optics. However, electron waves have yet to be understood in open cavity structures which have provided contemporary optics with rich insight towards non-Hermitian systems and complex interactions between resonance modes. Here, we report the realization of an open cavity resonator in a two-dimensional electronic system. We studied the resonant electron modes within the cavity and resolved the signatures of longitudinal and transverse quantization, showing that the modes are robust despite the cavity being highly coupled to the open background continuum. The transverse modes were investigated by applying a controlled deformation to the cavity, and their spatial distributions were further analyzed using magnetoconductance measurements and numerical simulation. These results lay the groundwork to exploring matter waves in the context of modern optical frameworks.

Aharonov-Bohm Oscillations in Bilayer Graphene Quantum Hall Edge State Fabry-Pérot Interferometers

Bernal-stacked bilayer graphene exhibits a wealth of interaction-driven phenomena, including robust even-denominator fractional quantum Hall states. We construct Fabry-Pérot interferometers using a split-gate design and present measurements of the Aharonov-Bohm oscillations. The edge state velocity is found to be approximately 6 × 10⁴ m/s at filling factor ν = 2 and decreases with increasing filling factor. The dc bias and temperature dependence of the interference point to electron-electron interaction induced decoherence mechanisms. These results pave the way for the quest of fractional and non-Abelian braiding statistics in this promising device platform.

Intensity self-compensation method against multi-factors for polarization-based Fabry-Perot interrogation system

Phase interrogation methods for fiber-optic Fabry-Perot (F-P) sensors may inevitably fail in the field due to the influences of irrelevant factors on signal intensity. To address this severe problem, this Letter proposes an intensity self-compensation method (ISCM) to eliminate the consecutive signal fluctuations of a polarization-based F-P interrogation system caused by multiple factors. By providing only the initial intensities of the reference signals, this attempt realizes the real-time intensity compensation of the output signals without affecting their quadrature relationship. Consecutive intensity fluctuations caused by variation of light source power, fiber loss, and polarization state are reduced to 2%-3% by the ISCM. Furthermore, the method performs ideally under dynamic modulation of the sensor. In addition, it can be applied against the inconsistent fluctuations between signals and is suitable for F-P sensors with single or multiple cavities. Owing to the high efficiency, real-time ability, and no moving parts advantage, the proposed method provides an excellent candidate for improving the accuracy and stability of F-P interrogation systems.

Graphene-Based Quantum Hall Interferometer with Self-Aligned Side Gates

The vanishing band gap of graphene has long presented challenges for making high-quality quantum point contacts (QPCs)─the partially transparent p-n interfaces introduced by conventional split gates tend to short circuit the QPCs. This complication has hindered the fabrication of graphene quantum Hall Fabry-Pérot interferometers, until recent advances have allowed split-gate QPCs to operate utilizing the highly resistive ν = 0 state. Here, we present a simple recipe to fabricate QPCs by etching a narrow trench in the graphene sheet to separate the conducting channel from self-aligned graphene side gates. We demonstrate operation of the individual QPCs in the quantum Hall regime and further utilize these QPCs to create and study a quantum Hall interferometer.

Scaling behavior of electron decoherence in a graphene Mach-Zehnder interferometer

Over the past 20 years, many efforts have been made to understand and control decoherence in 2D electron systems. In particular, several types of electronic interferometers have been considered in GaAs heterostructures, in order to protect the interfering electrons from decoherence. Nevertheless, it is now understood that several intrinsic decoherence sources fundamentally limit more advanced quantum manipulations. Here, we show that graphene offers a unique possibility to reach a regime where the decoherence is frozen and to study unexplored regimes of electron interferometry. We probe the decoherence of electron channels in a graphene quantum Hall PN junction, forming a Mach-Zehnder interferometer1,2, and unveil a scaling behavior of decay of the interference visibility with the temperature scaled by the interferometer length. It exhibits a remarkable crossover from an exponential decay at higher temperature to an algebraic decay at lower temperature where almost no decoherence occurs, a regime previously unobserved in GaAs interferometers.

Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers

Quantum Hall interferometers have been used to probe fractional charge and statistics of quasiparticles. We present measurements of a small Fabry-Perot interferometer in which the electrostatic coupling constants which affect interferometer behavior can be determined experimentally. Near the center of the ν = 1/3 state this device exhibits Aharonov-Bohm interference interrupted by a few discrete phase jumps, and Φ0 oscillations at higher and lower magnetic fields, consistent with theoretical predictions for detection of anyonic statistics. We estimate the electrostatic parameters KI and KIL by two methods: using the ratio of oscillation periods in compressible versus incompressible regions, and from finite-bias conductance measurements. We find that the extracted KI and KIL can account for the deviation of the phase jumps from the theoretical anyonic phase θa = 2π/3. At integer states, we find that KI and KIL can account for the Aharonov-Bohm and Coulomb-dominated behavior of different edge states.

Readout of Quantum Screening Effects Using a Time-Dependent Probe

In voltage- and temperature-biased coherent conductors quantum screening effects occur if the conductor's transmission is energy dependent. Here, we show that an additional ac-driven terminal can act as a probe for a direct readout of such effects, hitherto unexplored. We find that screening of charges induced by the static biases impacts already their standard linear thermoelectric response coefficients due to nonlinear effects when accounting for the frequency of the time-dependent driving. Those effects should be observable under realistic experimental conditions and can literally be switched on and off with the ac driving.

Distinguishability and "which pathway" information in multidimensional interferometric spectroscopy with a single entangled photon-pair

Correlated photons inspire abundance of metrology-related platforms, which benefit from quantum (anti-) correlations and outperform their classical counterparts. While these mainly focus on entanglement, the role of photon exchange phase and degree of distinguishability has not been widely used in quantum applications. Using an interferometric setup, we theoretically show that, when a two-photon wave function is coupled to matter, it is encoded with “which pathway?” information even at low-degree of entanglement. An interferometric protocol, which enables phase-sensitive discrimination between microscopic interaction histories (pathways), is developed. We find that quantum light interferometry facilitates utterly different set of time delay variables, which are unbound by uncertainty to the inverse bandwidth of the wave packet. We illustrate our findings on an exciton model system and demonstrate how to probe intraband dephasing in the time domain without temporally resolved detection. The unusual scaling of multiphoton coincidence signals with the applied pump intensity is discussed.

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.