Estados ligados e supercondutividade não convencional em sistemas com impurezas - Flávio Luis Noronha dos Santos (2021)
In this thesis we carry out a theoretical investigation on the effect of impurities in many body systems. In the first part of this work we study the behavior of a mobile impurity in a 2D topological semimetal with quadratic band touching. The impurity has a local repulsion and an anisotropic exchange interaction with the fermions in the bath. Using Wilsonian renormalization group we find regimes where the local interaction becomes effectively attractive at low energies. We calculate the spectral function of a fermion-impurity pair using the ladder approximation and verify the existence of bound states between these particles in the regimes where the interaction becomes effectively attractive. These regimes depend on the ratio between the effective masses of the majority fermions in the two bands. The number of bound states may be 0, 1 or 2 and is controlled tuning the exchange interaction. Our results suggest that this system may lead to unconventional superconductivity in the presence of a finite density of mobile impurities. In the second part of this work we study the effect of classical magnetic impurities diluted in a conventional superconductor. We use dynamical mean-field theory to solve this problem in the Bethe lattice. Electronic states localized in the impurities appear due to the magnetic interaction and their overlapping lead to the emergence of Shiba bands. We see the appearance of odd-frequency unconventional superconductivity which, similarly to the Shiba bands, is more intense in the magnetic sites than in the nonmagnetic ones. We demonstrate a way to estimate the intensity of the superconducting pairing through scanning tunneling spectroscopy measurements. We define order parameters for different superconducting pairings: even-frequency spin-singlet s-wave, odd-frequency spin-triplet s-wave and even-frequency spin-triplet odd-parity. Our results show the presence of these three pairings simultaneously in the system.