Theoretical Studies of Scanning Tunneling Microscopy of

The aim of this thesis is to find a theoretical basis for describing Scanning Tunneling Mi-croscopy (STM) experiments in Bi2Sr2CaCu2O8+δ. Two different subjects have been investi-gated. Firstly, we discussed how to describe STM spectra from theoretically accessible Green’s func-tions. Using this technique, we reproduced the results of B. W. Hoogenboom et al. for the superconducting state of Bi2Sr2CaCu2O8+δ [1]. Secondly, we proposed a model to describe the electronic structure of vortices in Bi2Sr2Ca Cu2O8+δ. The basis for this model was the static stripe picture introduced by Tranquada et al. [2]. We showed that this model may be treated within a fermionic formalism and found a solution to a simplified version of the model, which considers non-interacting spinless electrons moving along two crossed stripes. This solution allows us to understand the ”checkerboard” pattern seen inside vortex cores by Hoffman et al. [3] within a stripe picture, thus establishing a universal description for different High-Tc superconductors.