Scanning Nitrogen-Vacancy Magnetometry of Focused-Electron-Beam-Deposited Cobalt Nanomagnets.

Focused-electron-beam-induced deposition is a promising technique for patterning nanomagnets in a single step. We fabricate cobalt nanomagnets in such a process and characterize their content, saturation magnetization, and stray magnetic field profiles by using a combination of transmission electron microscopy and scanning nitrogen-vacancy (NV) magnetometry. We find agreement between the measured stray field profiles and saturation magnetization with micromagnetic simulations. We further characterize magnetic domains and grainy stray magnetic fields in the nanomagnets and their halo side-deposits. This work may aid in the evaluation of Co nanomagnets produced through focused electron-beam-induced deposition for applications in spin qubits, magnetic field sensing, and magnetic logic.

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.

A tunable monolithic SQUID in twisted bilayer graphene.

Magic-angle twisted bilayer graphene (MATBG) hosts a number of correlated states of matter that can be tuned by electrostatic doping1-4. Transport5,6 and scanning-probe7-9 experiments have shown evidence for band, correlated and Chern insulators along with superconductivity. This variety of in situ tunable states has allowed for the realization of tunable Josephson junctions10-12. However, although phase-coherent phenomena have been measured10-12, no control of the phase difference of the superconducting condensates has been demonstrated so far. Here we build on previous gate-defined junction realizations and form a superconducting quantum interference device13 (SQUID) in MATBG, where the superconducting phase difference is controlled through the magnetic field. We observe magneto-oscillations of the critical current, demonstrating long-range coherence of superconducting charge carriers with an effective charge of 2e. We tune to both asymmetric and symmetric SQUID configurations by electrostatically controlling the critical currents through the junctions. This tunability allows us to study the inductances in the device, finding values of up to 2 µH. Furthermore, we directly probe the current-phase relation of one of the junctions of the device. Our results show that complex devices in MATBG can be realized and used to reveal the properties of the material. We envision our findings, together with the established history of applications SQUIDs have14-16, will foster the development of a wide range of devices such as phase-slip junctions17 or high kinetic inductance detectors18.

Scattering between Minivalleys in Twisted Double Bilayer Graphene.

A unique feature of the complex band structures of moiré materials is the presence of minivalleys, their hybridization, and scattering between them. Here, we investigate magnetotransport oscillations caused by scattering between minivalleys-a phenomenon analogous to magnetointersubband oscillations-in a twisted double bilayer graphene sample with a twist angle of 1.94°. We study and discuss the potential scattering mechanisms and find an electron-phonon mechanism and valley conserving scattering to be likely. Finally, we discuss the relevance of our findings for different materials and twist angles.

Probing Magnetic Defects in Ultra-Scaled Nanowires with Optically Detected Spin Resonance in Nitrogen-Vacancy Center in Diamond.

Magnetic nanowires (NWs) are essential building blocks of spintronics devices as they offer tunable magnetic properties and anisotropy through their geometry. While the synthesis and compositional control of NWs have seen major improvements, considerable challenges remain for the characterization of local magnetic features at the nanoscale. Here, we demonstrate nonperturbative field distribution mapping in ultrascaled magnetic nanowires with diameters down to 6 nm by scanning nitrogen-vacancy magnetometry. This enables localized, minimally invasive magnetic imaging with sensitivity down to 3 µT Hz-1/2. The imaging reveals the presence of weak magnetic inhomogeneities inside in-plane magnetized nanowires that are largely undetectable with standard metrology and can be related to local fluctuations of the NWs' saturation magnetization. In addition, the strong magnetic field confinement in the nanowires allows for the study of the interaction between the stray magnetic field and the nitrogen-vacancy sensor, thus clarifying the contrasting formation mechanisms for technologically relevant magnetic nanostructures.

Tailoring the Band Structure of Twisted Double Bilayer Graphene with Pressure.

Twisted two-dimensional structures open new possibilities in band structure engineering. At magic twist angles, flat bands emerge, which gave a new drive to the field of strongly correlated physics. In twisted double bilayer graphene dual gating allows changing of the Fermi level and hence the electron density and also allows tuning of the interlayer potential, giving further control over band gaps. Here, we demonstrate that by application of hydrostatic pressure, an additional control of the band structure becomes possible due to the change of tunnel couplings between the layers. We find that the flat bands and the gaps separating them can be drastically changed by pressures up to 2 GPa, in good agreement with our theoretical simulations. Furthermore, our measurements suggest that in finite magnetic field due to pressure a topologically nontrivial band gap opens at the charge neutrality point at zero displacement field.

Correlated electron-hole state in twisted double-bilayer graphene.

When twisted to angles near 1°, graphene multilayers provide a window on electron correlation physics. Here, we report the discovery of a correlated electron-hole state in double-bilayer graphene twisted to 2.37°. At this angle, the moiré states retain much of their isolated bilayer character, allowing their bilayer projections to be separately controlled by gates. We use this property to generate an energetic overlap between narrow isolated electron and hole bands with good nesting properties. Our measurements reveal the formation of ordered states with reconstructed Fermi surfaces, consistent with a density-wave state. This state can be tuned without introducing chemical dopants, enabling studies of correlated electron-hole states and their interplay with superconductivity.

Gate-defined Josephson junctions in magic-angle twisted bilayer graphene.

In situ electrostatic control of two-dimensional superconductivity1 is commonly limited due to large charge carrier densities, and gate-defined Josephson junctions are therefore rare2,3. Magic-angle twisted bilayer graphene (MATBG)4-8 has recently emerged as a versatile platform that combines metallic, superconducting, magnetic and insulating phases in a single crystal9-14. Although MATBG appears to be an ideal two-dimensional platform for gate-tunable superconductivity9,11,13, progress towards practical implementations has been hindered by the need for well-defined gated regions. Here we use multilayer gate technology to create a device based on two distinct phases in adjustable regions of MATBG. We electrostatically define the superconducting and insulating regions of a Josephson junction and observe tunable d.c. and a.c. Josephson effects15,16. The ability to tune the superconducting state within a single material circumvents interface and fabrication challenges, which are common in multimaterial nanostructures. This work is an initial step towards devices where gate-defined correlated states are connected in single-crystal nanostructures. We envision applications in superconducting electronics17,18 and quantum information technology19,20.

Combined Minivalley and Layer Control in Twisted Double Bilayer Graphene.

Control over minivalley polarization and interlayer coupling is demonstrated in double bilayer graphene twisted with an angle of 2.37°. This intermediate angle is small enough for the minibands to form and large enough such that the charge carrier gases in the layers can be tuned independently. Using a dual-gated geometry we identify and control all possible combinations of minivalley polarization via the population of the two bilayers. An applied displacement field opens a band gap in either of the two bilayers, allowing us to even obtain full minivalley polarization. In addition, the carriers, formerly separated by their minivalley character, are mixed by tuning through a Lifshitz transition, where the Fermi surface topology changes. The high degree of control over the minivalley character of the bulk charge transport in twisted double bilayer graphene offers new opportunities for realizing valleytronics devices such as valley valves, filters, and logic gates.

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts.

In multivalley semiconductors, the valley degree of freedom can be potentially used to store, manipulate, and read quantum information, but its control remains challenging. The valleys in bilayer graphene can be addressed by a perpendicular magnetic field which couples by the valley g factor g_{v}. However, control over g_{v} has not been demonstrated yet. We experimentally determine the energy spectrum of a quantum point contact realized by a suitable gate geometry in bilayer graphene. Using finite bias spectroscopy, we measure the energy scales arising from the lateral confinement as well as the Zeeman splitting and find a spin g factor g_{s}∼2. g_{v} can be tuned by a factor of 3 using vertical electric fields, g_{v}∼40-120. The results are quantitatively explained by a calculation considering topological magnetic moment and its dependence on confinement and the vertical displacement field.

The electronic thickness of graphene.

When two dimensional crystals are atomically close, their finite thickness becomes relevant. Using transport measurements, we investigate the electrostatics of two graphene layers, twisted by θ = 22° such that the layers are decoupled by the huge momentum mismatch between the K and K' points of the two layers. We observe a splitting of the zero-density lines of the two layers with increasing interlayer energy difference. This splitting is given by the ratio of single-layer quantum capacitance over interlayer capacitance C m and is therefore suited to extract C m. We explain the large observed value of C m by considering the finite dielectric thickness d g of each graphene layer and determine d g ≈ 2.6 Å. In a second experiment, we map out the entire density range with a Fabry-Pérot resonator. We can precisely measure the Fermi wavelength λ in each layer, showing that the layers are decoupled. Our findings are reproduced using tight-binding calculations.

Gap Opening in Twisted Double Bilayer Graphene by Crystal Fields.

Crystal fields occur due to a potential difference between chemically different atomic species. In van der Waals heterostructures such fields are naturally present perpendicular to the planes. It has been realized recently that twisted graphene multilayers provide powerful playgrounds to engineer electronic properties by the number of layers, the twist angle, applied electric biases, electronic interactions, and elastic relaxations, but crystal fields have not received the attention they deserve. Here, we show that the band structure of large-angle twisted double bilayer graphene is strongly modified by crystal fields. In particular, we experimentally demonstrate that twisted double bilayer graphene, encapsulated between hBN layers, exhibits an intrinsic band gap. By the application of an external field, the gaps in the individual bilayers can be closed, allowing to determine the crystal fields. We find that crystal fields point from the outer to the inner layers with strengths in the bottom/top bilayer [Formula: see text] = 0.13 V/nm ≈ [Formula: see text] = 0.12 V/nm. We show both by means of first-principles calculations and low energy models that crystal fields open a band gap in the ground state. Our results put forward a physical scenario in which a crystal field effect in carbon substantially impacts the low energy properties of twisted double bilayer graphene, suggesting that such contributions must be taken into account in other regimes to faithfully predict the electronic properties of twisted graphene multilayers.

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.

GHz nanomechanical resonator in an ultraclean suspended graphene p-n junction.

We demonstrate high-frequency mechanical resonators in ballistic graphene p-n junctions. Fully suspended graphene devices with two bottom gates exhibit ballistic bipolar behavior after current annealing. We determine the graphene mass density and built-in tension for different current annealing steps by comparing the measured mechanical resonant response to a simplified membrane model. In a graphene membrane with high built-in tension, but still of macroscopic size with dimensions 3 × 1 µm2, a record resonance frequency of 1.17 GHz is observed after the final current annealing step. We further compare the resonance response measured in the unipolar with the one in the bipolar regime. Remarkably, the resonant signals are strongly enhanced in the bipolar regime.

Transport Through a Network of Topological Channels in Twisted Bilayer Graphene.

We explore a network of electronic quantum valley Hall states in the moiré crystal of minimally twisted bilayer graphene. In our transport measurements, we observe Fabry-Pérot and Aharanov-Bohm oscillations that are robust in magnetic fields ranging from 0 to 8 T, which is in strong contrast to more conventional two-dimensional systems where trajectories in the bulk are bent by the Lorentz force. This persistence in magnetic field and the linear spacing in density indicate that charge carriers in the bulk flow in topologically protected, one-dimensional channels. With this work, we demonstrate coherent electronic transport in a lattice of topologically protected states.

Coupled Quantum Dots in Bilayer Graphene.

Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge, or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, we form a versatile and widely tunable multiquantum dot system. We demonstrate the formation of single, double and triple quantum dots that are free of any sign of disorder. In bilayer graphene, we have the possibility to form tunnel barriers using different mechanisms. We can exploit the ambipolar nature of bilayer graphene where pn-junctions form natural tunnel barriers. Alternatively, we can use gates to form tunnel barriers, where we can vary the tunnel coupling by more than 2 orders of magnitude tuning between a deeply Coulomb blockaded system and a Fabry-Pérot-like cavity. Demonstrating such tunability is an important step toward graphene-based quantum computation.

Interactions and Magnetotransport through Spin-Valley Coupled Landau Levels in Monolayer MoS_{2}.

The strong spin-orbit coupling and the broken inversion symmetry in monolayer transition metal dichalcogenides results in spin-valley coupled band structures. Such a band structure leads to novel applications in the fields of electronics and optoelectronics. Density functional theory calculations as well as optical experiments have focused on spin-valley coupling in the valence band. Here we present magnetotransport experiments on high-quality n-type monolayer molybdenum disulphide (MoS_{2}) samples, displaying highly resolved Shubnikov-de Haas oscillations at magnetic fields as low as 2 T. We find the effective mass 0.7m_{e}, about twice as large as theoretically predicted and almost independent of magnetic field and carrier density. We further detect the occupation of the second spin-orbit split band at an energy of about 15 meV, i.e., about a factor of 5 larger than predicted. In addition, we demonstrate an intricate Landau level spectrum arising from a complex interplay between a density-dependent Zeeman splitting and spin- and valley-split Landau levels. These observations, enabled by the high electronic quality of our samples, testify to the importance of interaction effects in the conduction band of monolayer MoS_{2}.

Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts.

We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Because of the Berry curvature, states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum number with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calculations.

Electrostatically Induced Quantum Point Contacts in Bilayer Graphene.

We report the fabrication of electrostatically defined nanostructures in encapsulated bilayer graphene, with leakage resistances below depletion gates as high as R ∼ 10 GΩ. This exceeds previously reported values of R = 10-100 kΩ.1-3 We attribute this improvement to the use of a graphite back gate. We realize two split gate devices which define an electronic channel on the scale of the Fermi-wavelength. A channel gate covering the gap between the split gates varies the charge carrier density in the channel. We observe device-dependent conductance quantization of ΔG = 2e2/h and ΔG = 4e2/h. In quantizing magnetic fields normal to the sample plane, we recover the four-fold Landau level degeneracy of bilayer graphene. Unexpected mode crossings appear at the crossover between zero magnetic field and the quantum Hall regime.

Giant Valley-Isospin Conductance Oscillations in Ballistic Graphene.

At high magnetic fields the conductance of graphene is governed by the half-integer quantum Hall effect. By local electrostatic gating a p-n junction perpendicular to the graphene edges can be formed, along which quantum Hall channels copropagate. It has been predicted by Tworzidlo and co-workers that if only the lowest Landau level is filled on both sides of the junction, the conductance is determined by the valley (isospin) polarization at the edges and by the width of the flake. This effect remained hidden so far due to scattering between the channels copropagating along the p-n interface (equilibration). Here we investigate p-n junctions in encapsulated graphene with a movable p-n interface with which we are able to probe the edge-configuration of graphene flakes. We observe large quantum conductance oscillations on the order of e2/h which solely depend on the p-n junction position providing the first signature of isospin-defined conductance. Our experiments are underlined by quantum transport calculations.