Studies of Diamagnetism and Thermoelectric Transport in High Temperature Superconductors and Graphene

Abstract

Using a recently proposed Ginzburg-Landau-like free energy functional due to Banerjee et al. Phys. Rev. B 83, 024510 (2011) we calculate the fluctuation diamagnetism of high-T c superconductors as a function of doping, magnetic field, and temperature. We analyze the pairing fluctuations above the superconducting transition temperature in the cuprates, ranging from the strong phase fluctuation dominated underdoped limit to the more conventional amplitude fluctuation dominated overdoped regime. We show that a model where the pairing scale increases and the superfluid density decreases with underdoping produces features of the observed magnetization in the pseudogap region, in good qualitative and reasonable quantitative agreement with the experimental data. In particular, we explicitly show that even when the pseudogap has a pairing origin the magnetization actually tracks the superconducting dome instead of the pseudogap temperature, as seen in experiment. We discuss the doping dependence of the ‘onset’ temperature for fluctuation diamagnetism and comment on the role of vortex core-energy in our model. We also study the Nernst effect in fluctuating superconductors by calculating the transport coefficient α_xy in a phenomenological model where the relative importance of phase and amplitude fluctuations of the order parameter is tuned continuously to smoothly evolve from an effective XY model to more conventional Ginzburg-Landau description. To connect with a concrete experimental realization we choose the model parameters appropriate for cuprate superconductors and calculate α_xy and the magnetization M over the entire range of experimentally accessible values of the field, temperature, and doping. We argue that α_xy and M are both determined by the equilibrium properties of the superconducting fluctuations (and not their dynamics) despite the former being a transport quantity. Thus, the experimentally observed correlation between the Nernst signal and the magnetization arises primarily from the correlation between α_xy and M. Further, there exists a dimensionless ratio M/(T α_xy ) that quantifies this correlation. We calculate, for the first time, this ratio over the entire phase diagram of the cuprates and find it agrees with previous results obtained in specific parts of the phase diagram. We conclude that there appears to be no sharp distinction between the regimes dominated by phase fluctuations and Gaussian fluctuations for this ratio in contrast to α_xy and M individually. The utility of this ratio is that it can be used to determine the extent to which superconducting fluctuations contribute to the Nernst effect in different parts of the phase diagram given the measured values of magnetization. In the fourth chapter, we study the thermoelectric transport properties across twisted bilayer graphene. In twisted bilayer graphene, two individual graphene layers are placed within van der Waals separation with a relative twist angle between them. The charge and heat transport of such a system has been a recent focus of research from the perspective of fundamental physics and possible applications in nanoscale devices. To understand the thermoelectric transport properties of a recent experiment which measures the Seebeck effect across twisted bilayer graphene, we develop a phenomenological model based on the Landauer-Büttiker transport formalism. We analyze the measurement of the Seebeck coefficient with a calculation that takes into account the tunneling properties of Dirac electrons through a barrier as well as incorporates a disorder potential giving rise the electron-hole puddles near the charge neutral point. By performing a detailed analysis it appears that the measured thermopower is determined by the cross-plane layer-breathing mode rather than the properties of the tunnel junction.