FeSe is the focus of intense research interest because of its unusual non-magnetic nematic state and because it forms the basis for achieving the highest critical temperatures of any iron-based superconductor. However, its Cooper pairing mechanism has not been determined because an accurate knowledge of the momentum-space structure of superconducting energy gaps ∆ i ( k) on the different electron-bands E i ( k) does not exist. Here we use Bogoliubov quasiparticle interference (BQPI) imaging to determine the coherent Fermi surface geometry of the α-and ε-bands surrounding the Γ = (0, 0) and X = (π/a Fe , 0) points of FeSe, and to measure their superconducting energy gaps ∆ α ( k) and ∆ ε ( k).We show directly that both gaps are extremely anisotropic but nodeless, and are aligned along orthogonal crystal axes. Moreover, by implementing a novel technique we demonstrate the sign change between ∆ α ( k) and ∆ ε ( k). This complex configuration of ∆ α ( k) and ∆ ε ( k), which was unanticipated within pairing theories for FeSe, reveals a unique form of superconductivity based on orbital selective Cooper pairing of electrons from the d yz orbitals of iron atoms. This new paradigm of orbital selectivity may be pivotal to understanding the microscopic interplay of quantum paramagnetism, nematicity and high temperature superconductivity. BIOGRAPHICAL SKETCHPeter Oliver Sprau was born on June 13th 1986 in the small town of Kirchheimbolanden, Germany, where he completed both his primary and secondary education. Long before he was a physicist, Peter was an active member of the track and field team in his school and a local club, even going on to compete in the dash and relay event on the state and federal youth level. Upon finishing school, he fulfilled his civic duty and carried out his alternative civilian service in the hospital in Kirchheimbolanden. While Peter's academic interests were diverse, including not just science but also Latin and history, his natural curiosity about the world finally urged him to pursue a higher education in physics. Mistakes. Make glorious, amazing mistakes. Make mistakes nobody's ever made before. Don't freeze, don't stop, don't worry that it isn't good enough, or it isn't perfect, whatever it is: art, or love, or work or family or life.Whatever it is you're scared of doing, Do it. Make your mistakes, next year and forever." I also want to acknowledge in no specific order the following people for useful discussions throughout my PhD:

We discuss the influence on spin-fluctuation pairing theory of orbital selective strong correlation effects in Fe-based superconductors, particularly Fe chalcogenide systems. We propose that a key ingredient for an improved itinerant pairing theory is orbital selectivity, i.e., incorporating the reduced coherence of quasiparticles occupying specific orbital states. This modifies the usual spinfluctuation via suppression of pair scattering processes involving those less coherent states and results in orbital selective Cooper pairing of electrons in the remaining states. We show that this paradigm yields remarkably good agreement with the experimentally observed anisotropic gap structures in both bulk and monolayer FeSe, as well as LiFeAs, indicating that orbital selective Cooper pairing plays a key role in the more strongly correlated iron-based superconductors. arXiv:1611.02643v2 [cond-mat.supr-con]

Abstract. Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, T c , ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.