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.

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.

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.

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.

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.

Gate-Defined One-Dimensional Channel and Broken Symmetry States in MoS2 van der Waals Heterostructures.

We have realized encapsulated trilayer MoS2 devices with gated graphene contacts. In the bulk, we observe an electron mobility as high as 7000 cm2/(V s) at a density of 3 × 1012 cm-2 at a temperature of 1.9 K. Shubnikov-de Haas oscillations start at magnetic fields as low as 0.9 T. The observed 3-fold Landau level degeneracy can be understood based on the valley Zeeman effect. Negatively biased split gate electrodes allow us to form a channel that can be completely pinched off for sufficiently large gate voltages. The measured conductance displays plateau-like features.

Oscillating Magnetoresistance in Graphene p-n Junctions at Intermediate Magnetic Fields.

We report on the observation of magnetoresistance oscillations in graphene p-n junctions. The oscillations have been observed for six samples, consisting of single-layer and bilayer graphene, and persist up to temperatures of 30 K, where standard Shubnikov-de Haas oscillations are no longer discernible. The oscillatory magnetoresistance can be reproduced by tight-binding simulations. We attribute this phenomenon to the modulated densities of states in the n- and p-regions.

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.