Superconductivity in strongly correlated systems: Heavy fermions, Cuprates, Infinite-layer Nickelates

Abstract

The phase diagrams of the heavy fermion, transition-metal (copper-, nickel-) oxides materials have a wide variety of different phases. It is believed that, the strong correlation among electrons governs most of the phases in these materials, and hence, they are called strongly correlated systems. The purpose of the thesis is to understand the microscopic origin of the superconductivity in the strongly correlated systems and subsequently compare/predict the experimental outcomes of the theory. It is well known that heavy fermion, transition-metal oxide systems are unconventional superconductors. However, contrary to the old results, new experiments performed on the heavy fermion systems point towards a fully gapped conventional superconductivity. Similarly, in the cuprate superconductors, the d-wave symmetry of the superconducting order parameter is well known in the copper-oxide layer. However, counter-evidence of nodeless superconductivity is observed in the underdoped region of cuprates. Recently superconductivity is observed in infinite-layer nickelates NdNiO2 and PrNiO2, a maximum Tc ~ 15 K. Based on the above-mentioned experimental motivations, we formulate a new mechanism of superconductivity in the heavy fermion system where attractive potential between impurity and conduction electrons are mediated by emergent boson fields in the slave-boson theory. We developed a self-consistent theory for the superconducting gap and found good agreement with experimental results. We found a s-wave like, fully gapped superconducting channel. For the cuprates and nickelates, we use spin-fluctuation mediated pairing potential, with multi-band random phase approximation to predict pairing symmetries of the gap function. In YBCO cuprate, we found that, if we dope the CuO chain state while keeping the CuO4 plane state’s doping fixed, the pairing symmetry change from the nodal d-wave to a nodal f-wave symmetry. We explore superconductivity in RNiO2 (R = Nd, La, Pr), based on two orbitals, Ni dx2−y2 , and R axial orbital. The axial orbital consists of Nd/La d, and Ni dz2 orbitals. We found that the superconductivity is orbital-selective in RNiO2. In this thesis, we use analytical and numerical methods to analyse the superconducting properties relevant from theoretical and experimental perspectives.