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:

Magnetoresistivity measurements with fine tuning of the field direction on high quality single crystals of the ferromagnetic superconductor UCoGe show anomalous anisotropy of the upper critical field Hc2. Hc2 for H b-axis (H b c2 ) in the orthorhombic crystal structure is strongly enhanced with decreasing temperature with an S-shape and reaches nearly 20 T at 0 K. The temperature dependence of H a c2 shows upward curvature with a low temperature value exceeding 30 T, while H c c2 at 0 K is very small (∼ 0.6 T). Contrary to conventional ferromagnets, the decrease of the Curie temperature with increasing field for H b-axis marked by an enhancement of the effective mass of the conduction electrons appears to be the origin of the S-shaped H b c2 curve. These results indicate that the field-induced ferromagnetic instability or magnetic quantum criticality reinforces superconductivity.The coexistence of superconductivity (SC) and ferromagnetism (FM) has attracted much attention, since the exotic SC state based on spin-triplet pairing mediated by longitudinal spin fluctuations is expected. 1 The first example was discovered in UGe 2 under pressure, where T sc is much lower than T Curie . 2 The SC phase exists only in the FM phase, and SC disappears in the paramagnetic (PM) phase above the critical pressure P c . Soon after that, SC was found at ambient pressure in the weak ferromagnet URhGe. 3 T sc (= 0.25 K) is much lower than T Curie (= 9.5 K). The upper critical field H c2 exceeds the Pauli paramagnetic limit, thus it is believed that the spin-triplet state with equal-spin pairing is realized. Recently, reentrant superconductivity (RSC) was found between 8 and 13 T when the field is applied along the b-axis of the orthorhombic TiNiSi-type structure (space group: Pnma). 4 With increasing field, the magnetic moment gradually tilts from the c-axis (easy-magnetization axis) to b-axis. Finally the moment is suddenly aligned to the b-axis at the spin reorientation field H R . The fieldinduced critical magnetic fluctuations induce RSC. Recently, we have observed the enhancement of effective mass in the RSC phase, and explained the emergence of RSC. 5,6 A newcomer, UCoGe, which crystallizes in the same structure as URhGe, was recently reported. 7 UCoGe is a weak ferromagnet with T Curie ∼ 3 K and the ordered moment µ 0 = 0.07 µ B /U. T sc (∼ 0.6 K) is larger than that in URhGe. Since T Curie is low, one can naively consider that UCoGe is close to the quantum critical point. Indeed, our previous measurement shows that T Curie is immediately suppressed by applying a small pressure (P c ∼ 1 GPa). 8 Contrary to the case of UGe 2 where SC exists only in the FM domain, SC survives even in the PM phase with the maximum T sc (≃ 0.75 K) around P c . A new theory * E-mail address: aokidai@gmail.com from symmetry considerations was developed in order to explain the temperature-pressure phase diagram. 9 H c2 at ambient pressure shows strong anisotropy. H c2 for H a (H a c2 ) and b-axis (H b c2 ) reveal almost the same temperature depend...

Shubnikov-de Haas measurements of high quality URu2Si2 single crystals reveal two previously unobserved Fermi surface branches in the so-called hidden order phase. Therefore about 55 % of the enhanced mass is now detected. Under pressure in the antiferromagnetic state, the Shubnikov-de Haas frequencies for magnetic fields applied along the crystalline c axis show little change compared with the zero pressure data. This implies a similar Fermi surface in both the hidden order and antiferromagnetic states, which strongly suggests that the lattice doubling in the antiferromagnetic phase due to the ordering vector QAF = (0 0 1) already occurs in the hidden order. These measurements provide a good test for existing or future theories of the hidden order parameter. PACS numbers:The electronic properties of uranium compounds are determined by the tenuous balance between the localized and itinerant character of the 5f electrons which may lead to the formation of enigmatic ground states [1]. One famous example is the heavy fermion compound URu 2 Si 2 which shows a second order phase transition to a "hidden order" (HO) state at T 0 = 17.5 K. The transition to the HO state is associated with a huge entropy loss of 0.2R ln 2 [2]. Despite intense research for 25 years, the order parameter has not yet been identified. The possible proximity to a 5f 2 configuration of the uranium atoms leads to the possibility of multipolar ordering which is highly debated in Pr 3+ systems in the 4f 2 configuration [3]. Thus the resolution of the HO parameter will have a deep impact on the understanding of heavy fermion materials. A large diversity of theoretical proposals have been given. The most recent ones include multipolar orders [4-6]), dynamical spin density wave [7] or hybridization wave [8].The Fermi surface (FS) properties are directly linked to the itineracy of the 5f electrons and to the change of the symmetry entering into the HO phase. Changes of the FS at T 0 have been observed in various experiments. Optical conductivity [9] and transport measurements [10,11] indicate a gap opening and a drop in the number of charge carriers at T 0 . Recent STM measurements show that a hybridization gap opens suddenly at T 0 [12, 13] while in ARPES measurements abrupt changes of the electronic spectrum are detected [14,15]. Here we focus on the FS determination via Shubnikov-de Haas (SdH) measurements on a new generation of high quality crystals. SdH measurements under pressure provide the great opportunity to study the difference of quantum oscillations between the low pressure HO phase and the high pressure antiferromagnetic (AF) phase with propagation vector Q AF = (0 0 1) and ordered moment m 0 = 0.3 µ B /U. A small pressure of P x ≈ 0.8 GPa is enough to switch the ground state from HO to AF [16][17][18]. The AF phase has been well characterized, notably the change from body centered tetragonal to simple tetragonal crystal structure below T 0 [7,19]. Inelastic neutron scattering experiments under pressure suggest that, due to the disappear...

Recently, another consequence of the size of the Caions has been discovered. Iyo et al. 15 have found that a family of ordered CaAFe 4 As 4 (1144) compounds can be formed for A = K, Rb, Cs where the key to the formation is the difference in ionic size between the Ca and the A ion. This family is not a (Ca 1−x A x )Fe 2 As 2 solid-solution, where the Ca and A ions randomly occupy a single crystallographic site, 16 but rather is a distinct, quaternary, line compound in which the Ca and A sites form alternating planes along the crystallographic c-axis, separated by FeAs slabs 15 . In essence, the CaAFe 4 As 4 structure is identical to the CaFe 2 As 2 structure, just with layer by layer segregation of the Ca and A ions. The 1144 structure was also found for SrAFe 4 As 4 (A = Rb, Cs). Solid-solutions of Ca (Sr) 122 structures were found for arXiv:1605.05617v2 [cond-mat.supr-con]

Precise resistivity measurements on the ferromagnetic superconductor UGe2 under pressure p and magnetic field H reveal a previously unobserved change of the anomaly at the Curie temperature. Therefore, the tricritical point (TCP) where the paramagnetic-to-ferromagnetic transition changes from a second order to a first order transition is located in the p-T phase diagram. Moreover, the evolution of the TCP can be followed under the magnetic field in the same way. It is the first report of the boundary of the first order plane which appears in the p-T-H phase diagram of weak itinerant ferromagnets. This line of critical points starts from the TCP and will terminate at a quantum critical point. These measurements provide the first estimation of the location of the quantum critical point in the p-H plane and will inspire similar studies of the other weak itinerant ferromagnets.

A hallmark of the iron-based superconductors is the strong coupling between magnetic, structural and electronic degrees of freedom. However, a universal picture of the normal state properties of these compounds has been confounded by recent investigations of FeSe where the nematic (structural) and magnetic transitions appear to be decoupled. Here, using synchrotron-based high-energy x-ray diffraction and time-domain Mössbauer spectroscopy, we show that nematicity and magnetism in FeSe under applied pressure are indeed strongly coupled. Distinct structural and magnetic transitions are observed for pressures between 1.0 and 1.7 GPa and merge into a single first-order transition for pressures ≳1.7 GPa, reminiscent of what has been found for the evolution of these transitions in the prototypical system Ba(Fe1−xCox)2As2. Our results are consistent with a spin-driven mechanism for nematic order in FeSe and provide an important step towards a universal description of the normal state properties of the iron-based superconductors.

Simultaneous neutron scattering and thermal expansion measurements on the heavy-fermion superconductor URu 2 Si 2 under hydrostatic pressure of 0.67 GPa have been performed in order to detect the successive paramagnetic, hidden order, and large moment antiferromagnetic phases on cooling. The temperature dependence of the sharp low energy excitation at the wave vector Q 0 = ͑1,0,0͒ shows clearly that this resonance is a signature of the hidden order state. In the antiferromagnetic phase, this resonance disappears. The higher energy excitation at the incommensurate wave vector Q 1 = ͑1.4,0,0͒ persists in the antiferromagnetic phase but increases in energy.The elucidation of the nature of a hidden order in exotic materials, which belong often to the rich class of strongly correlated electronic systems, is a hot subject as it can lead to the discovery of unexpected new order parameters. Debates exist on quite different proposals such as orbital hidden order in the heavy fermion system URu 2 Si 2 , 1 multipolar ordering in rare earth skutterudites 2 or "spin order accompanying loop current" in cuprate superconductors. 3 Due to the dual character of the 5f electrons in URu 2 Si 2 between localized ͑leading to the possibility of multipolar ordering͒ and itinerant ͑possibility of large Fermi surface instabilities͒, this compound has been the subject of a large variety of experiments. 4 At zero pressure, a phase transition occurs from the paramagnetic ͑PM͒ phase to a so-called hidden order ͑HO͒ phase at a temperature T 0 ϳ 17.5 K. The hidden order label reflects the fact that this order may not be of dipolar origin. The order parameter is not yet determined: spin or charge density wave, 5-7 multipolar ordering, [8][9][10][11] orbital antiferromagnetism, 1 chiral spin state, 12 and helicity order 13 have been proposed. The long standing debate on the occurrence of a tiny ordered moment M 0 ϳ 0.02 B per U atom at T → 0 K for the antiferromagnetic ͑AF͒ wave vector Q AF = ͑0,0,1͒ seems to converge now toward an extrinsic origin directly related to the high sensitivity of URu 2 Si 2 to pressure and stress ͑low critical pressure P x ϳ 0.5 GPa͒. 4,[14][15][16] Pressure studies 4,17-19 reveal an interesting phase diagram ͑Fig. 1͒. At T → 0 K, neutron scattering experiments 4 show that the hidden-order ground state switches at P x to a large moment antiferromagnetic ͑AF͒ state of sublattice magnetization M 0 near 0.3 B / U with a propagation vector Q AF . The HO-AF boundary T x ͑P͒ meets the T 0 ͑P͒ line at the tricritical point ͑T ‫ء‬ ϳ 19.3 K, P ‫ء‬ ϳ 1.36 GPa͒; 19 above P ‫ء‬ , a unique ordered phase ͑AF͒ is established below T N ͑P͒. Previous nuclear magnetic resonance ͑NMR͒ experiments, 14,20 as well as transport measurements, 5,19 indicate clearly that nesting occurs at T 0 , as well as at T N , indicating also that the Fermi surface is not deeply modified through the transition line T x .The interest in URu 2 Si 2 is reinforced by the appearance of unconventional superconductivity at T sc ϳ 1.2 K for P =0 ͑Ref. 21͒, which d...

The in-plane resistivity anisotropy is studied in strain-detwinned single crystals of FeSe. In contrast to other iron-based superconductors, FeSe does not develop long-range magnetic order below the nematic/structural transition at Ts ≈90 K. This allows for the disentanglement of the contributions to the resistivity anisotropy due to nematic and magnetic orders. Comparing direct transport and elastoresistivity measurements, we extract the intrinsic resistivity anisotropy of strainfree samples. The anisotropy peaks slightly below Ts and decreases to nearly zero on cooling down to the superconducting transition. This behavior is consistent with a scenario in which the in-plane resistivity anisotropy in FeSe is dominated by inelastic scattering by anisotropic spin fluctuations.PACS numbers: 74.70. Xa, 74.25.Ld Electronic nematicity has emerged as a key concept in iron-based superconductors since the observation of inplane resistivity anisotropy in stress-detwinned crystals of Co-doped BaFe 2 As 2 [1, 2]. The fact that the resistivity anisotropy is much larger than what is expected from the small lattice distortion led to the proposal that the tetragonal-to-orthorhombic transition in the iron pnictides is driven not by phonons, but by an electronic nematic phase. Subsequent experiments revealed an intricate dependence of the resistivity anisotropy on doping (a sign change between electron-and hole-doped materials [2-6]), and disorder [7,8], sparking hot debates about its microscopic origins (see Refs. [9 and 10] for reviews).Electronic contributions involved in the in-plane resistivity anisotropy [10] can be separated into the Drude weight and/or of the scattering rate anisotropies. Fermisurface anisotropies arising, for instance, from the ferroorbital order triggered at the nematic transition, affect mostly the Drude weight [11][12][13]. Anisotropic scattering, can be due to elastic processes, such as the development of local magnetic order around an impurity [14,15], or inelastic processes, such as the scattering of electrons by anisotropic magnetic fluctuations [16,17] known to exist below T s [18]. Recent stress-dependent optical reflectivity studies in Co-doped BaFe 2 As 2 point to a dominant effect of the Drude weight [19,20]. However, stripe magnetic order appearing at the magnetic transition severely complicates the analysis. This is because the magnetic state breaks tetragonal symmetry leading to an anisotropic reconstruction of the Fermi surface [7,21] and to the appearance of "Dirac cones" [22], which may dramatically alter the resistivity anisotropy [23]. Disentangling these contributions is fundamental to reveal the origin of the resistivity anisotropy and, consequently, of the nematic state.In this context, the stoichiometric FeSe [24] is an ideal system. It is rather clean (residual resistivity ratios as high as 50 [25]) and its orthorhombic/nematic phase transition at T s ≈ 90 K is not accompanied by a longrange magnetic order [26] eliminating effects of Fermi surface folding.In this Letter we rep...