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:

The nature of the tetragonal-to-orthorhombic structural transition at Ts ≈ 90 K in single crystalline FeSe is studied using shear-modulus, heat-capacity, magnetization and NMR measurements. The transition is shown to be accompanied by a large shear-modulus softening, which is practically identical to that of underdoped Ba(Fe,Co)2As2, suggesting very similar strength of the electronlattice coupling. On the other hand, a spin-fluctuation contribution to the spin-lattice relaxation rate is only observed below Ts. This indicates that the structural, or "nematic", phase transition in FeSe is not driven by magnetic fluctuations.PACS numbers: 74.70. Xa, 74.25.Bt, 74.25.Ld, 74.25.nj One of the most intriguing questions in the study of iron-based superconductors concerns the relation between structure, magnetism and superconductivity [1][2][3][4][5][6][7][8][9][10]. Stripe-type antiferromagnetic order often occurs at the same or at a slightly lower temperature than the tetragonal-to-orthorhombic structural distortion and the two types of order are closely related by symmetry. They break the four-fold rotational symmetry of the high-temperature phase, which can be associated with a nematic degree of freedom [4,6]. Superconductivity typically is strongest around the point where the structural transition (T s ) and the antiferromagnetic transition (T N ) are suppressed by pressure or chemical substitution. Whether the magnetic or the structural instability is the primary one, is still under intense debate [10], also because of its relevance to the pairing mechanism [5,6]. Recently, scaling relations between the shear modulus related to the structural distortion, C 66 , and the spinlattice relaxation time T 1 as a measure of the strength of spin fluctuations, have been proposed [7,8] in order to address the above question. They were found to be well satisfied in the Ba(Fe,Co) 2 As 2 system [7,8], where T s and T N are in close proximity to each other, suggesting a magnetically-driven structural transition [7]. Clearly, it is of great interest to see if a relation between shear modulus and spin fluctuations is universally observed in other iron-based materials.FeSe is structurally the simplest iron-based superconductor and has attracted a lot of attention because of a nearly four-fold increase of its T c ≈ 8 K under pressure [11]. Moreover, this system is particularly interesting with respect to the relation of structure and magnetism, since it undergoes a tetragonal-to-orthorhombic structural phase transition at T s ∼ 90 K, similar to that found in the 1111-and 122-type parent compounds [2], but does not order magnetically at ambient pressure [12,13]. Spin fluctuations at low temperatures were, however, observed in nuclear magnetic resonance (NMR) measurements [14]. Surprisingly, the orthorhombic distortion of FeSe is not reduced upon entering the superconducting state [9] in strong contrast to underdoped BaFe 2 As 2 [3,15], indicating different couplings between structure and superconductivity. This strongly motivates fu...

We study superconducting FeSe (T c = 9 K) exhibiting the tetragonal-orthorhombic structural transition (T s ~ 90 K) without any antiferromagnetic ordering, by utilizing angle-resolved photoemission spectroscopy. In the detwinned orthorhombic state, the energy position of the d yz orbital band at the Brillouin zone corner is 50 meV higher than that of d xz , indicating the orbital order similar to NaFeAs and BaFe 2 As 2 families. Evidence of orbital order also appears in the hole bands at the Brillouin zone center. Precisely measured temperature dependence using strain-free samples shows that the onset of the orbital ordering (T o ) occurs very close to T s , thus suggesting that the electronic nematicity above T s is considerably weaker in FeSe compared to BaFe 2 As 2 family.

Detailed knowledge of the phase diagram and the nature of the competing magnetic and superconducting phases is imperative for a deeper understanding of the physics of iron-based superconductivity. Magnetism in the iron-based superconductors is usually a stripe-type spin-density-wave, which breaks the tetragonal symmetry of the lattice, and is known to compete strongly with superconductivity. Recently, it was found that in some systems an additional spin-density-wave transition occurs, which restores this tetragonal symmetry, however, its interaction with superconductivity remains unclear. Here, using thermodynamic measurements on Ba1−xKxFe2As2 single crystals, we show that the spin-density-wave phase of tetragonal symmetry competes much stronger with superconductivity than the stripe-type spin-density-wave phase, which results in a novel re-entrance of the latter at or slightly below the superconducting transition.

The coupling between superconductivity and othorhombic distortion is studied in vapor-grown FeSe single crystals using high-resolution thermal-expansion measurements. In contrast to the Ba122-based (Ba122) superconductors, we find that superconductivity does not reduce the orthorhombicity below Tc. Instead we find that superconductivity couples strongly to the in-plane area, which explains the large hydrostatic pressure effects. We discuss our results in light of the spinnematic scenario and argue that FeSe has many features quite different from the typical Fe-based superconductors.

We have observed Shubnikov-de Haas oscillations in FeSe. The Fermi surface deviates significantly from predictions of band-structure calculations and most likely consists of one electron and one hole thin cylinder. The carrier density is in the order of 0.01 carriers/ Fe, an order-of-magnitude smaller than predicted. Effective Fermi energies as small as 3.6 meV are estimated. These findings call for elaborate theoretical investigations incorporating both electronic correlations and orbital ordering.

Magnetism is widely considered to be a key ingredient of unconventional superconductivity.In contrast to cuprate high-temperature superconductors, antiferromagnetism in Fe-based superconductors (FeSCs) is characterized by a pair of magnetic propagation vectors 1, 2 . Consequently, three different types of magnetic order are possible. Of theses, only stripe-type spin-density wave (SSDW) and spin-charge-density wave (SCDW) orders have been observed 2-4 . A realization of the proposed spin-vortex crystal (SVC) order is noticeably absent. We report a magnetic phase consistent with the hedgehog variation of SVC order in Ni-and Co-doped CaKFe 4 As 4 based on thermodynamic, transport, structural and local magnetic probes combined with symmetry analysis. The exotic SVC phase is stabilized by the reduced symmetry of the CaKFe 4 As 4 structure.Our results suggest that the possible magnetic ground states in FeSCs have very similar energies, providing an enlarged configuration space for magnetic fluctuations to promote high-temperature superconductivity.

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