Quantum transport in encapsulated graphene "p-n" junctions

Two dimensional electron gases (2DEGs) have been an exceptional platform and a constant source of new discoveries in quantum physics during the last decades. While for a long time 2DEGs fabricated by molecular beam epitaxy have been the working-horse of quantum transport measurements, with the discovery of graphene in 2004 a new, truly two-dimensional material entered the field. Within the few years since the experimental discovery of graphene it has risen from relative obscurity to the status of an exciting and promising model for 2D solids. The great interest in graphene can be attributed to its exceptional band structure which is described at low energies by the massless Dirac Hamiltonian, where the valence- and conduction-band touch each other at a single point (Dirac point). Being a zero-gap semi-conductor separates graphene from conventional metals and semi-conductors, making it unique of its kind. The ability to combine graphene with various 2D materials in so called Van der Waals heterostructures allows to taylor its properties almost at will. The nearly defect-free grapene lattice holds the potential for ballistic transport over long distances. Futhermore, the refraction index across an n-n’ (unipolar) junction or p-n (bipolar) junction can be tuned seamlessly from positive to negative which is unique for graphene. Combining the ballistic transport with the tunability of the refraction index across an interface makes clean graphene an excellent platform for the investigation of various electron optical experiments. This Thesis focuses on quantum transport phenomena in two-terminal graphene p-n junction, as this combines two bench-mark signatures in graphene, namely the observation of massless Dirac-fermions and the ability to establish gapless p-n junction. The Thesis starts with chapter 2 where important concepts related to the unique electronic band structure of graphene are introduced. This includes the ability to establish gapless p-n junctions, approaches how to characterize clean graphene, the possibility to form superlattices with other layered materials such as hexagonal boron-nitride (hBN) or the possibility to address additional degrees of freedom such as the valley-isospin. In chapter 3 a short comparison between suspension and encapsulation of graphene is given, since these two techniques are the most common ones to fabricate ultra-clean graphene. However, the fabricational details in chapter 4 are restricted to the encapsulation. Furthermore, details on how to fabricate local top- and bottom-gates, which are needed to establish p-n junctions, are given. The currently most common method to establish electrical contact with hBN/graphene/hBN heterostructures is via so called side-contacts. In chapter 5 an alternative approach is introduced to establish inner point contacts, being compatible with the encapsulation-technique. The latter might be of special interest if an isolated electrical contact has to be established in the middle of a hBN/graphene/hBN heterostructure. With chapter 6 the experimental part of the Thesis involving quantum transport in p-n junctions starts. In this chapter Fabry-Pérot resonances in a p-n-p device in the absence and presence of a Moiré superlattice are discussed. Fabry-Pérot resonances can be used to gain information about the exact position of the p-n junction as a function of charge carrier doping and on the yet not fully known band-reconstruction due to the Moirésuperlattice. In chapter 7 we report on three types of magnetoconductance oscillations which can occur along a graphene p-n junction. While several previous studies have tried to explain the observation of individual magnetoconductance oscillations, none of them describes all at the same time. On the contrary, we present experimental results where three different kinds of oscillations are observed within the same device/measurement. The latter allows for a more direct comparison between the different types of mangetoconductance oscillations and we can rule out differences in various device architectures. Finally, we can describe the underlying physics of the different types of magnetoconductance oscillations with a consistent model. Upon further increasing the magnetic field to very high values, the transport is governed by the lowest Landau level. In combination with a p-n junction, which is located perpendicular to the transport direction, conductance oscillations resulting from valley-isospin physics are expected. In chapter 8 experimental results are presented which show signatures of this effect for the first time. By tuning the position of the p-n junction this allows to locally probe the relative edge configuration, giving rise to conductance oscillations in the order of e^2/h. In the last chapter, chapter 9, preliminary experimental results and theoretical calculations on the electrical counterpart of the Michelson Morley interferometer are presented

Fabrication of ballistic suspended graphene with local-gating

Herein we discuss the fabrication of ballistic suspended graphene nanostructures supplemented with local gating. Using in-situ current annealing, we show that exceptional high mobilities can be obtained in these devices. A detailed description is given of the fabrication of bottom and different top-gate structures, which enable the realization of complex graphene structures. We have studied the basic building block, the p-n junction in detail, where a striking oscillating pattern was observed, which can be traced back to Fabry-Perot oscillations that are localized in the electronic cavities formed by the local gates. Finally we show some examples how the method can be extended to incorporate multi-terminal junctions or shaped graphene. The structures discussed here enable the access to electron-optics experiments in ballistic graphene

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 \textit{p-n} junction perpendicular to the graphene edges can be formed, along which quantum Hall channels co-propagate. It has been predicted by Tworzid\l{}o 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 co-propagating along the \textit{p-n} interface (equilibration). Here we investigate \textit{p-n} junctions in encapsulated graphene with a movable \textit{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 \si{e^2/h} which solely depend on the \textit{p-n} junction position providing the first signature of isospin-defined conductance. Our experiments are underlined by quantum transport calculations.Comment: 5 pages, 4 figure

Point contacts in encapsulated graphene

We present a novel method to establish inner point contacts on hexagonal boron nitride (hBN) encapsulated graphene heterostructures with dimensions as small as 100 nm by pre-patterning the top-hBN in a separate step prior to dry-stacking. 2 and 4-terminal field effect measurements between different lead combinations are in qualitative agreement with an electrostatic model assuming pointlike contacts. The measured contact resistances are 0.5-1.5 k$\Omega$ per contact, which is quite low for such small contacts. By applying a perpendicular magnetic fields, an insulating behaviour in the quantum Hall regime was observed, as expected for inner contacts. The fabricated contacts are compatible with high mobility graphene structures and open up the field for the realization of several electron optical proposals

Fabry-Pérot Resonances in a Graphene/hBN Moiré Superlattice

While Fabry-Perot (FP) resonances and Moire superlattices are intensively studied in graphene on hexagonal boron nitride (hBN), the two effects have not been discussed in their coexistence. Here we investigate the FP oscillations in a ballistic pnp-junctions in the presence and absence of a Moire superlattice. First, we address the effect of the smoothness of the confining potential on the visibility of the FP resonances and carefully map the evolution of the FP cavity size as a function of densities inside and outside the cavity in the absence of a superlattice, when the cavity is bound by regular pn-junctions. Using a sample with a Moire superlattice, we next show that an FP cavity can also be formed by interfaces that mimic a pn-junction but are defined through a satellite Dirac point due to the superlattice. We carefully analyze the FP resonances, which can provide insight into the band-reconstruction due to the superlattice

Coexistence of classical snake states and Aharonov-Bohm oscillations along graphene p − n junctions

Snake states and Aharonov-Bohm interferences are examples of magnetoconductance oscillations that can be observed in a graphene p-n junction. Even though they have already been reported in suspended and encapsulated devices including different geometries, a direct comparison remains challenging as they were observed in separate measurements. Due to the similar experimental signatures of these effects a consistent assignment is difficult, leaving us with an incomplete picture. Here we present measurements on p-n junctions in encapsulated graphene revealing several sets of magnetoconductance oscillations allowing for their direct comparison. We analysed them with respect to their charge carrier density, magnetic field, temperature and bias dependence in order to assign them to either snake states or Aharonov-Bohm oscillations. Furthermore we were able to consistently assign the various Aharonov-Bohm interferences to the corresponding area which the edge states enclose. Surprisingly, we find that snake states and Aharonov-Bohm interferences can co-exist within a limited parameter range.Comment: Main article and Supporting Informatio