• graphene
• quantum transport
• phase coherence
• quantum interference
• defects
• field-effect transistors

The picture of charge transport in mesoscopic systems, i.e. systems whose dimensions are intermediate between atomic and macroscopic scale, must incorporate the quantum mechanical description of electrons. In the absence of phase-randomizing scattering events, transport is described in the phase coherent regime, with the conductor characterized by transmission and reflection probability amplitudes. By externally tuning the scattering properties of the conductor, as for instance with the introduction of electrostatic potential barriers, novel transfer characteristics are obtained that exploit coherent interference of scattered electron waves.
In this thesis, graphene-based devices with a periodic grating of electrostatic potential barriers are explored. Specifically, this work focuses on investigation of phase coherent phenomena in graphene Field Effect Transistors (gFETs), where the electrostatic potential landscape is modified extrinsically by means of defects-engineering, i.e. controlled introduction of defective sites via Electron Beam Irradiation (EBI). Indeed, defects offer a remarkable local control on the electronic properties of graphene, such as pinning of the Fermi energy or increase of local density of states. The use of EBI, with scanning step of 7.8 nm and beam size of 20 nm, enables straightforward and precise patterning of the sample. Therefore, exposition of graphene to EBI in a line grating introduces a periodic mismatch of Fermi energy between exposed and unexposed regions of graphene, which realizes the periodic potential modulation along the transport channel. The remarkable properties of graphene, such as its high ambipolar carrier mobilities and low electrons-phonons scattering, together with the broad knowledge on the electronic properties of defective structures, render it a suitable platform to explore coherent effects in defects-patterned devices.
The electronic transport properties of the realized patterned gFETs are probed in low-bias and low-temperature (T = 2.4 K) measurements, from which the devices' resistances are obtained as a function of the gate voltage. Cryogenic temperatures are employed to suppress sources of dynamical scattering, such as phonons, that eventually lead to phase decoherence.
All of the investigated samples have shown quantum oscillations in the channel resistances as a function of the gate voltage, induced by the periodical barriers. The gate voltage dependence of these oscillations is ascribed to the gate-tunable nature of electrons Fermi wavelength, which characterizes the length scale of the interaction between the electrons and the grating. As a result, the profile of the resistance oscillations is observed to depend on the periodic pattern pitch, with the shorter pitch p = 35 nm presenting a richer oscillations profile with respect to devices with p = 50 nm. The observed interference pattern signature in the devices’ transfer characteristics has been reproduced in different realization of defects patterned gFETs with nominally identical design parameters. Furthermore, the emergent interference pattern is explored in gFETs with N=1 to N=4 defective lines to investigate the electron dynamics in the presence of few barriers. Similarly, oscillations in the resistances as a function of the Fermi wavevector have been observed. In particular, from temperature dependent measurements, it has been observed an onset at temperatures as high as T=100 K for the emergence of the resistance oscillations.
This serves as a confirmation of the phase coherent transport regime for electrons at the core of the measured resistance oscillations. Thus, defect-engineered graphene devices can represent a viable solution to explore phase-related interference phenomena, paving the way to further interferometric geometries that can accessibly be realized with a single lithographic step.