Coupled Quantum Dots in Bilayer Graphene

Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot

We predict the existence of spontaneous spin and valley symmetry-broken states of interacting massive Dirac Fermions in a gated bilayer graphene quantum dot based on the exact diagonalization of the many-body Hamiltonian. The dot is defined by a vertical electric field and lateral gates, and its single-particle (SP) energies, wave functions, and Coulomb matrix elements are computed by using the atomistic tight-binding model. The effect of the Coulomb interaction is measured by the ratio of Coulomb elements to the SP level spacing. As we increase the interaction strength, we find the electrons in a series of spin and valley symmetry-broken phases with increasing valley and spin polarizations. The phase transitions result from the competition of the SP, exchange, and correlation energy scales. A phase diagram for N = 1-6 electrons is mapped out as a function of the Coulomb interaction strength.

Polarizability characteristics of twisted bilayer graphene quantum dots in the absence of periodic moiré potential

Recent studies have documented a rich phenomenology in twisted bilayer graphene (TBG), which is significantly relevant to interlayer electronic coupling, in particular to the cases under an applied electric field. While polarizability measures the response of electrons against applied fields, this work adopts a unique strategy of decomposing global polarizability into distributional contributions to access the interlayer polarization in TBG, as a function of varying twisting angles (θ). Through the construction of a model of twisted graphene quantum dots, we assess distributional polarizability at the first-principles level. Our findings demonstrate that the polarizability perpendicular to the graphene plates can be decomposed into intralayer dipoles and interlayer charge-transfer (CT) components, the latter of which provides an explicit measurement of the interlayer coupling strength and charge transfer potential. Our analysis further reveals that interlayer polarizability dominates the polarizability variation during twisting. Intriguingly, the largest interlayer polarizability and CT driven by an external field occur in the misaligned structures with a size-dependent small angle corresponding to the first appearance of AB stacking, rather than the well-recognized Bernal structures. A derived equation is then employed to address the size dependence on the angle corresponding to the largest values in interlayer polarizability and CT. Our investigation not only characterizes the CT features in the interlayer polarizability of TBG quantum dots, but also sheds light on the existence of the strongest interlayer coupling and charge transfer at small twist angles in the presence of an external electric field, thereby providing a comprehensive understanding of the novel properties of graphene-based nanomaterials.

Dielectrics for Two-Dimensional Transition-Metal Dichalcogenide Applications

Despite over a decade of intense research efforts, the full potential of two-dimensional transition-metal dichalcogenides continues to be limited by major challenges. The lack of compatible and scalable dielectric materials and integration techniques restrict device performances and their commercial applications. Conventional dielectric integration techniques for bulk semiconductors are difficult to adapt for atomically thin two-dimensional materials. This review provides a brief introduction into various common and emerging dielectric synthesis and integration techniques and discusses their applicability for 2D transition metal dichalcogenides. Dielectric integration for various applications is reviewed in subsequent sections including nanoelectronics, optoelectronics, flexible electronics, valleytronics, biosensing, quantum information processing, and quantum sensing. For each application, we introduce basic device working principles, discuss the specific dielectric requirements, review current progress, present key challenges, and offer insights into future prospects and opportunities.

Particle-hole symmetry protects spin-valley blockade in graphene quantum dots

Particle-hole symmetry plays an important role in the characterization of topological phases in solid-state systems¹. It is found, for example, in free-fermion systems at half filling and it is closely related to the notion of antiparticles in relativistic field theories². In the low-energy limit, graphene is a prime example of a gapless particle-hole symmetric system described by an effective Dirac equation^3,4 in which topological phases can be understood by studying ways to open a gap by preserving (or breaking) symmetries^5,6. An important example is the intrinsic Kane-Mele spin-orbit gap of graphene, which leads to a lifting of the spin-valley degeneracy and renders graphene a topological insulator in a quantum spin Hall phase⁷ while preserving particle-hole symmetry. Here we show that bilayer graphene allows the realization of electron-hole double quantum dots that exhibit near-perfect particle-hole symmetry, in which transport occurs via the creation and annihilation of single electron-hole pairs with opposite quantum numbers. Moreover, we show that particle-hole symmetric spin and valley textures lead to a protected single-particle spin-valley blockade. The latter will allow robust spin-to-charge and valley-to-charge conversion, which are essential for the operation of spin and valley qubits.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Pauli Blockade of Tunable Two-Electron Spin and Valley States in Graphene Quantum Dots

Pauli blockade mechanisms-whereby carrier transport through quantum dots (QD) is blocked due to selection rules even when energetically allowed-are a direct manifestation of the Pauli exclusion principle, as well as a key mechanism for manipulating and reading out spin qubits. The Pauli spin blockade is well established for systems such as GaAs QDs, but is to be further explored for systems with additional degrees of freedom, such as the valley quantum numbers in carbon-based materials or silicon. Here we report experiments on coupled bilayer graphene double quantum dots, in which the spin and valley states are precisely controlled, enabling the observation of the two-electron combined blockade physics. We demonstrate that the doubly occupied single dot switches between two different ground states with gate and magnetic-field tuning, allowing for the switching of selection rules: with a spin-triplet-valley-singlet ground state, valley blockade is observed; and with the spin-singlet-valley-triplet ground state, robust spin blockade is shown.

Probing Two-Electron Multiplets in Bilayer Graphene Quantum Dots

We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of six orbital symmetric and ten orbital antisymmetric states. We find that orbital symmetric states are lower in energy and separated by ≈ 0.4-0.8  meV from orbital antisymmetric states. The symmetric multiplet exhibits an additional energy splitting of its six states of ≈ 0.15-0.5  meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that intervalley scattering and "current-current" interaction constants are of the same magnitude in BLG.

Site-Specific Reduction-Induced Hydrogenation of a Helical Bilayer Nanographene with K and Rb Metals: Electron Multiaddition and Selective Rb+ Complexation

The chemical reduction of π‐conjugated bilayer nanographene 1 (C₁₃₈H₁₂₀) with K and Rb in the presence of 18‐crown‐6 affords [K⁺(18‐crown‐6)(THF)₂][{K⁺(18‐crown‐6)}₂(THF)_0.5][C₁₃₈H₁₂₂³⁻] (2) and [Rb⁺(18‐crown‐6)₂][{Rb⁺(18‐crown‐6)}₂(C₁₃₈H₁₂₂³⁻)] (3). Whereas K⁺ cations are fully solvent‐separated from the trianionic core thus affording a “naked” 1^.3− anion, Rb⁺ cations are coordinated to the negatively charged layers of 1^.3−. According to DFT calculations, the localization of the first two electrons in the helicene moiety leads to an unprecedented site‐specific hydrogenation process at the carbon atoms located on the edge of the helicene backbone. This uncommon reduction‐induced site‐specific hydrogenation provokes dramatic changes in the (electronic) structure of 1 as the helicene backbone becomes more compressed and twisted upon chemical reduction, which results in a clear slippage of the bilayers.

Spin-valley coupling in single-electron bilayer graphene quantum dots

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K$$\end{document}K and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K^{\prime}$$\end{document}K′ states below 20 μeV.

Understanding the interaction between spin and valley degrees of freedom in graphene-based quantum dots underpins their applications in electronics and quantum information. Here, the authors study the low-energy spectrum and resolve the spin-valley coupling in single-electron quantum dots in bilayer graphene.

Tunable Valley Splitting and Bipolar Operation in Graphene Quantum Dots

Quantum states in graphene are 2-fold degenerate in spins, and 2-fold in valleys. Both degrees of freedom can be utilized for qubit preparations. In our bilayer graphene quantum dots, we demonstrate that the valley g-factor g_v, defined analogously to the spin g-factor g_s for valley splitting in a perpendicular magnetic field, is tunable by over a factor of 4 from 20 to 90, by gate voltage adjustments only. Larger g_v results from larger electronic dot sizes, determined from the charging energy. On our versatile device, bipolar operation, charging our quantum dot with charge carriers of the same or the opposite polarity as the leads, can be performed. Dots of both polarities are tunable to the first charge carrier, such that the transition from an electron to a hole dot by the action of the plunger gate can be observed. Addition of gates easily extends the system to host tunable double dots.

Tunnel field-effect transistors for sensitive terahertz detection

The rectification of electromagnetic waves to direct currents is a crucial process for energy harvesting, beyond-5G wireless communications, ultra-fast science, and observational astronomy. As the radiation frequency is raised to the sub-terahertz (THz) domain, ac-to-dc conversion by conventional electronics becomes challenging and requires alternative rectification protocols. Here, we address this challenge by tunnel field-effect transistors made of bilayer graphene (BLG). Taking advantage of BLG's electrically tunable band structure, we create a lateral tunnel junction and couple it to an antenna exposed to THz radiation. The incoming radiation is then down-converted by the tunnel junction nonlinearity, resulting in high responsivity (>4 kV/W) and low-noise (0.2 pW/[Formula: see text]) detection. We demonstrate how switching from intraband Ohmic to interband tunneling regime can raise detectors' responsivity by few orders of magnitude, in agreement with the developed theory. Our work demonstrates a potential application of tunnel transistors for THz detection and reveals BLG as a promising platform therefor.

Visualization and Manipulation of Bilayer Graphene Quantum Dots with Broken Rotational Symmetry and Nontrivial Topology

Electrostatically defined quantum dots (QDs) in Bernal stacked bilayer graphene (BLG) are a promising quantum information platform because of their long spin decoherence times, high sample quality, and tunability. Importantly, the shape of QD states determines the electron energy spectrum, the interactions between electrons, and the coupling of electrons to their environment, all of which are relevant for quantum information processing. Despite its importance, the shape of BLG QD states remains experimentally unexamined. Here we report direct visualization of BLG QD states by using a scanning tunneling microscope. Strikingly, we find these states exhibit a robust broken rotational symmetry. By using a numerical tight-binding model, we determine that the observed broken rotational symmetry can be attributed to low energy anisotropic bands. We then compare confined holes and electrons and demonstrate the influence of BLG's nontrivial band topology. Our study distinguishes BLG QDs from prior QD platforms with trivial band topology.

A Mechanically Tunable Quantum Dot in a Graphene Break Junction

Graphene quantum dots (QDs) are intensively studied as platforms for the next generation of quantum electronic devices. Fine tuning of the transport properties in monolayer graphene QDs, in particular with respect to the independent modulation of the tunnel barrier transparencies, remains challenging and is typically addressed using electrostatic gating. We investigate charge transport in back-gated graphene mechanical break junctions and reveal Coulomb blockade physics characteristic of a single, high-quality QD when a nanogap is opened in a graphene constriction. By mechanically controlling the distance across the newly formed graphene nanogap, we achieve reversible tunability of the tunnel coupling to the drain electrode by 5 orders of magnitude, while keeping the source-QD tunnel coupling constant. The break junction device can therefore become a powerful platform to study the physical parameters that are crucial to the development of future graphene-based devices, including energy converters and quantum calorimeters.

Unprecedented Charge State Control in Graphene Quantum Dots

High-quality double quantum dots in bilayer graphene are realized with controlled charge down to one electron. These devices provide a promising basis for spin-based qubits with long spin lifetimes.

Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic Transport

We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to 80  μeV by the displacement field. We assign this gate-tunable subband splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addition, we observe a spin polarized channel of 6e^{2}/h at high in-plane magnetic field and signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.

Theory of valley-resolved spectroscopy of a Si triple quantum dot coupled to a microwave resonator

We theoretically study a silicon triple quantum dot (TQD) system coupled to a superconducting microwave resonator. The response signal of an injected probe signal can be used to extract information about the level structure by measuring the transmission and phase shift of the output field. This information can further be used to gain knowledge about the valley splittings and valley phases in the individual dots. Since relevant valley states are typically split by several [Formula: see text], a finite temperature or an applied external bias voltage is required to populate energetically excited states. The theoretical methods in this paper include a capacitor model to fit experimental charging energies, an extended Hubbard model to describe the tunneling dynamics, a rate equation model to find the occupation probabilities, and an input-output model to determine the response signal of the resonator.

Single-Carrier Transport in Graphene/hBN Superlattices

Graphene/hexagonal boron nitride (hBN) moiré superlattices have attracted interest for use in the study of many-body effects and fractal physics in Dirac fermion systems. Many exotic transport properties have been intensively examined in such superlattices, but previous studies have not focused on single-carrier transport. The investigation of the single-carrier behavior in these superlattices would lead to an understanding of the transition of single-particle/correlated phenomena. Here, we show the single-carrier transport in a high-quality bilayer graphene/hBN superlattice-based quantum dot device. We demonstrate remarkable device controllability in the energy range near the charge neutrality point (CNP) and the hole-side satellite point. Under a perpendicular magnetic field, Coulomb oscillations disappear near the CNP, which could be a signature of the crossover between Coulomb blockade and quantum Hall regimes. Our results pave the way for exploring the relationship of single-electron transport and fractal quantum Hall effects with correlated phenomena in two-dimensional quantum materials.

Single-Electron Double Quantum Dots in Bilayer Graphene

We present transport measurements through an electrostatically defined bilayer graphene double quantum dot in the single-electron regime. With the help of a back gate, two split gates, and two finger gates, we are able to control the number of charge carriers on two gate-defined quantum dots independently between zero and five. The high tunability of the device meets requirements to make such a device a suitable building block for spin-qubits. In the single-electron regime, we determine interdot tunnel rates on the order of 2 GHz. Both, the interdot tunnel coupling as well as the capacitive interdot coupling increase with dot occupation, leading to the transition to a single quantum dot. Finite bias magneto-spectroscopy measurements allow to resolve the excited-state spectra of the first electrons in the double quantum dot and are in agreement with spin and valley conserving interdot tunneling processes.

Charge Detection in Gate-Defined Bilayer Graphene Quantum Dots

We report on charge detection in electrostatically defined quantum dot devices in bilayer graphene using an integrated charge detector. The device is fabricated without any etching and features a graphite back gate, leading to high-quality quantum dots. The charge detector is based on a second quantum dot separated from the first dot by depletion underneath a 150 nm wide gate. We show that Coulomb resonances in the sensing dot are sensitive to individual charging events on the nearby quantum dot. The potential change due to single electron charging causes a steplike change (up to 77%) in the current through the charge detector. Furthermore, the charging states of a quantum dot with tunable tunneling barriers and of coupled quantum dots can be detected.

Excited States in Bilayer Graphene Quantum Dots

We report ground- and excited-state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different from quantum dots in carbon nanotubes, where the two-particle ground state is a spin-singlet state. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35 meV and measure a valley and spin g factor of 36 and 2, respectively.

Low-Magnetic-Field Regime of a Gate-Defined Constriction in High-Mobility Graphene

We report on the evolution of the coherent electronic transport through a gate-defined constriction in a high-mobility graphene device from ballistic transport to quantum Hall regime upon increasing the magnetic field. At a low field, the conductance exhibits Fabry-Pérot resonances resulting from the npn cavities formed beneath the top-gated regions. Above a critical field B* corresponding to the cyclotron radius equal to the npn cavity length, Fabry-Pérot resonances vanish, and snake trajectories are guided through the constriction with a characteristic set of conductance oscillations. Increasing further the magnetic field allows us to probe the Landau level spectrum in the constriction and unveil distortions due to the combination of confinement and deconfinement of Landau levels in a saddle potential. These observations are confirmed by numerical calculations.

Electrically Tunable Gauge Fields in Tiny-Angle Twisted Bilayer Graphene

Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. Here we show that for very small twist angles, α≪1°, the application of a perpendicular electric field is mathematically equivalent to a new kind of artificial gauge field. This identification opens the door for the generation and detection of pseudo-Landau levels in graphene platforms within robust setups, which do not depend on strain engineering and therefore can be realistically harvested for technological applications. Furthermore, this new artificial gauge field leads to the development of highly localized modes associated with flat bands close to charge neutrality, which form an emergent kagome lattice in real space. Our findings indicate that for tiny angles biased twisted bilayer graphene is a promising platform that can realize frustrated lattices of highly localized states, opening a new direction for the investigation of strongly correlated phases of matter.