Marius Eich

Localized charge carriers in graphene nanodevices

Graphene—two-dimensional carbon—is a material with unique mechanical, optical, chemical, and electronic properties. Its use in a wide range of applications was therefore suggested. From an electronic point of view, nanostructured graphene is of great interest due to the potential opening of a band gap, applications in quantum devices, and investigations of physical phenomena. Narrow graphene stripes called “nanoribbons” show clearly different electronical transport properties than micron-sized graphene devices. The conductivity is generally reduced and around the charge neutrality point, the conductance is nearly completely suppressed. While various mechanisms can lead to this observed suppression of conductance, disordered edges resulting in localized charge carriers are likely the main cause in a large number of experiments. Localized charge carriers manifest themselves in transport experiments by the appearance of Coulomb blockade diamonds. This review focuses on the mechanisms responsible for this charge localization, on interpreting the transport details, and on discussing the consequences for physics and applications. Effects such as multiple coupled sites of localized charge, cotunneling processes, and excited states are discussed. Also, different geometries of quantum devices are compared. Finally, an outlook is provided, where open questions are addressed.

Measuring the local quantum capacitance of graphene using a strongly coupled graphene nanoribbon

We present electrical transport measurements of a van-der-Waals heterostructure consisting of a graphene nanoribbon separated by a thin boron nitride layer from a micron-sized graphene sheet. The interplay between the two layers is discussed in terms of screening or, alternatively, quantum capacitance. The ribbon can be tuned into the transport gap by applying gate voltages. Multiple sites of localized charge leading to Coulomb blockade are observed, in agreement with previous experiments. Due to the strong capacitive coupling between the ribbon and the graphene top layer sheet, the evolution of the Coulomb blockade peaks in gate voltages can be used to obtain the local density of states and therefore the quantum capacitance of the graphene top layer. Spatially varying density and doping are found, which are attributed to a spatial variation of the dielectric due to fabrication imperfections.

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.

Measurement Back-Action in Stacked Graphene Quantum Dots

We present an electronic transport experiment in graphene where both classical and quantum mechanical charge detector back-action on a quantum dot are investigated. The device consists of two stacked graphene quantum dots separated by a thin layer of boron nitride. This device is fabricated by van der Waals stacking and is equipped with separate source and drain contacts to both dots. By applying a finite bias to one quantum dot, a current is induced in the other unbiased dot. We present an explanation of the observed measurement-induced current based on strong capacitive coupling and energy dependent tunneling barriers, breaking the spatial symmetry in the unbiased system. This is a special feature of graphene-based quantum devices. The experimental observation of transport in classically forbidden regimes is understood by considering higher-order quantum mechanical back-action mechanisms.

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.

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.

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.

Magnetotransport and lateral confinement in an InSe van der Waals Heterostructure

In the last six years, Indium selenide (InSe) has appeared as a new van der Waals heterostructure platform which has been extensively studied due to its unique electronic and optical properties. Such as transition metal dichalcogenides (TMDCs), the considerable bandgap and high electron mobility can provide a potential optoelectronic application. Here we present low-temperature transport measurements on a few-layer InSe van der Waals heterostructure with graphene-gated contacts. For high magnetic fields, we observe magnetoresistance minima at even filling factors related to two-fold spin degeneracy. By electrostatic gating with negatively biased split gates, a one-dimensional channel is realized. Close to pinch-off, transport through the constriction is dominated by localized states with charging energies ranging from 2 to 5 meV. This work opens new possibility to explore the low-dimensional physics including quantum point contact and quantum dot.

Edge channel confinement in a bilayer graphene n–p–n quantum dot

We combine electrostatic and magnetic confinement to define a quantum dot in bilayer graphene. The employed geometry couples

Transport Through a Network of Topological Channels in Twisted Bilayer Graphene

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