Dynamics and correlations in low-dimensional electrical systems

In this thesis, the interaction of suspended graphene and carbon nanotube mechanical resonators with superconducting microwave cavities is investigated. Due to the photon interaction between both systems, small fluctuations in the mechanical resonators translate into measurable signals in the cavity frequency domain. The experiments were carried out at low temperatures, down to 10 mK, to reduce the noise level of the measurement setup. Such clean and low noise systems are also a good platform to probe 1/f noise. In the first part, the optomechanical coupling of graphene/NbSe2/graphene and graphene/hBN mechanical resonators with a superconducting coplanar waveguide is demonstrated. High quality factors over 200000 were measured with the ring-down measurement technique in our hybrid system. Lower electrical losses of the mechanical resonator can be attributed to the additional layers of NbSe2 compared to pure graphene devices. At low temperatures, the internal quality factor is limited by two-level system dissipation, which itself relaxes over the electronic system. In the second part, we study thermal self-oscillations in a superconductor - insulator - graphene - insulator - superconductor junction formed by a suspended piece of graphene coupled to a superconducting microwave cavity. The graphene piece has a strongly non-linear temperature dependence of resistance. This leads to a switching of dissipation once the Joule heating induced by the cavity pump can't be compensated by the heat transport of the junction. A high and low quality factor state is formed, which enables a fast cycle of heating and cooling of the system. When probing the thermal sidebands with a weak probe signal, amplification of the signal by up to 20 dB with a very low noise temperature of 1.4 K was measured. In the third part, 1/f noise in suspended and hBN encapsulated graphene was studied. Because graphene is two dimensional, noise from external sources such as the substrate or surface adsorbates is particularly noticeable. We studied the influence of adsorbed neon atoms on suspended graphene. Diffusion and clustering result in a 1/fγ dependence, with γ= 1.4-1.2 for temperatures between T=4-10 K. In hBN encapsulated graphene, we investigated the critical current noise. In the superconducting state, by tuning the charge carrier density away from the Dirac point, enhanced 1/f noise is measured with a noise level SIC/IC2≈10-6. In the last part, suspended, backgated carbon nanotubes are fabricated. We measured high supercurrents of up to 53 nA. The suspended nanotube resonator was used to investigate the phases of 3He dependent on 3He coverage and temperature down to 200 μK.The nanotube resonance shifts differently depending on the distinct phases of the 3He and a 3He phase diagram could be concluded.