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Towards topological hybrid states in graphene

Periodic Reporting for period 1 - TopoGraph (Towards topological hybrid states in graphene)

Reporting period: 2018-09-01 to 2020-08-31

In recent years low dimensional materials got to the forefront of research for future electronic devices. These materials promise also new functionalities: examples are topological computation or electron-optics. Although many other layered materials have been discovered, graphene, a single layer of graphite, is the promising among them. Graphene is the wonder material: it has exceptional mechanical and optical properties, has high mobility and a Dirac electronics spectrum which enables the realization of “table-top high energy” experiments.
Topological insulators (TI) are novel state of matter, where symmetry protected edge modes form. Unfortunately, high quality topological insulators are still missing, due to high bulk conductivity or to the low mobility of these materials, but using graphene as a platform some of these problems can be circumvented. The combination of topological insulators with superconducting (SC) contacts can lead to the formation of novel excitations, non-abelian Majorana fermions (MFs) and parafermions (PFs). While there is extensive research both in the field of graphene and in the field of topological materials, graphene as a platform for topological superconductivity has not yet been demonstrated experimentally.
The objective of the project was to harness the exceptional electronic properties of graphene based van der Waals heterostructures, and engineer topological phases and excitations of graphene. To do so, graphene heterostructures with induced spin-orbit interaction and special quantum Hall states of twisted bilayer graphene (TBLG) have to be combined with SC contacts. On the crossroad of these different states of matter topological excitations are formed. The proposal lied on the border or several research fields: 2D materials, quantum computation, superconductivity and spintronics.
The conclusions from the project were the following: High quality Josepshon junctions have been fabricated and studied from graphene with proximity spin orbit coupling (SOC) induced by a WSe2 substrate and from TBLG (for the first time). We have measured the CPR in the double layer system (at a secondment in the nanoelectronics group in Basel), and started the measurements on the SOC system. We have demonstrated the topological nature of the double layer system via Quantum Hall measurements. We have also developed tunnel probes on graphene which we used to study the non-equilibrium distribution function in graphene. Moreover, straining and pressurizing stacks have been shown as novel and promising methods towards manipulating high quality van der Waals heterostructures.
During the period of the proposal the following work was performed
1) High quality Josepshon junctions were fabricated on hBN/Gr/hBN, WSe/Gr/hBN, and hBN/Gr/hBN/Gr/hBN systems. The last was done in collaboration with the nanoelectronics group in Basel. We have investigated the gate dependence of the supercurrent, the spatial distribution of the supercurrent and the magnetic field stability of the supercurrent. In the SOC system we have found clear signs of spin orbit, whereas in the double layer setup a quantum spin Hall state was observed in the normal state.
2) We have developed superconducting tunnel probes with hBN barriers. We have used them to study the non-equilibrium distribution function of graphene system driven out of equilibrium. For long junctions we have found dominating phonon cooling, for intermediate junctions the electron cooling was dominant. For short junctions signs of a double step distribution function were observed suggesting the absence of inelastic scatterings within our sample.
3) We have developed the structures and methodology to measure current phase relation in graphene Josephson junctions both in the SOC and double layer structures. In both cases we have found sinusoidal current-phase relation close to the CNP of graphene, whereas at high doping the relation became skewed. This we attributed to changes in the transmissions of the conductance channels of graphene. For the SOC system the presence of an in-plane magnetic field might drive the system into a Phi0 junction, however this has to be first measured.
4) The Researcher took part in the development of a straining setup with the nanoelectronics group in Basel. With this setup we have demonstrated that at low temperature we can in-situ tune the strain in encapsulated graphene devices, while doing transport measurements at the same time. We have shown, that by proper design uniaxial strains or strain gradients can be developed, which is important for the generation of pseudo magnetic fields. We have also shown that a global scalar potential is generated in strained samples which changes the work function of graphene. Finally, we have shown that we can increase the mobility of graphene samples by mechanical straining. We have attributed this to the ironing of corrugations present even in high quality samples. In another experiment we have verified the presence of these corrugations using weak-localization measurements.
5) Finally, with Researcher was part of the team who first demonstrated the existence of a super-Moiré structure. We have shown, that by aligning both the bottom and the top hBN in an hBN/Gr/hBN heterostructure, two Moiré periods form in graphene. These Moirés can together form a super-Moiré leading to band reconstructions in graphene.

Besides the work outlined here, the Researcher took part in pressure cell studies nanowire experiments. The results have been shown in several conferences of the field. The topic was also shown to the general audience during outreach activities.
The project went in several studies far beyond the state of the art, as demonstrated also by several high quality publications. The topological superconductivity in these structures is yet to be demonstrated, however all the ingredients and technical building blocks have been demonstrated by the project. The combination of the SOC proximitized Josephson junctions with in-plane magnetic fields can lead to Phi0 junctions, important building blocks for superconducting electronics. The measurement result in the double layer structure are milestones towards the topological superconductivity in this structure. Moreover this structure is one of the smallest magnetometer ever built, which can be also analysed in terms of magnetometry applications.
The super-Moiré measurements were one of the first one showing that band structure tuning of graphene can be done from both sides at the same time.
Finally, the novel and first strain tuning experiments in high quality graphene samples were laying down the field for further experiments in straintronics.