Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains
a formidable challenge. Fourier analysis is commonly used to analyze the underlying structure of fundamental motifs present in an image. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of a new algorithm based on nonconvex optimization, applicable to any microscopy modality, that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this novel algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material. Our phase sensitive quasiparticle interference imaging results indicate that the pairing symmetry in optimally doped NaFeAs is consistent with a sign-changing s+- order parameter.
Muon spin rotation and relaxation studies have been performed on a 111 family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic mome
nt size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with increasing x. The combination of magnetic and superconducting volumes implies that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reduction of both the ordered moment size and the volume fraction is observed below the superconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other iron pnictides in which one of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further enhanced with increased Ni doping, leading to a reentrant non-magnetic state below T_C for x = 1.3 %. The reentrant behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the same electrons. These observations are consistent with the sign-changing s-wave superconducting state, which is expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering temperature TN across a variety of iron-based superconductors. We argue that this linear relationship is consistent with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering.
Metal-to-insulator transitions (MITs) are a dramatic manifestation of strong electron correlations in solids1. The insulating phase can often be suppressed by quantum tuning, i.e. varying a nonthermal parameter such as chemical composi- tion or press
ure, resulting in a zero-temperature quantum phase transition (QPT) to a metallic state driven by quantum fluctuations, in contrast to conventional phase transitions driven by thermal fluctuations. Theories of exotic phenomena known to occur near the Mott QPT such as quantum criticality and high-temperature superconductivity often assume a second-order QPT, but direct experimental evidence for either first- or second-order behavior at the magnetic QPT associated with the Mott transition has been scarce and further masked by the superconducting phase in unconventional superconductors. Most measurements of QPTs have been performed by volume-integrated probes, such as neutron scattering, magnetization, and transport, in which discontinuous behavior, phase separation, and spatially inhomogeneous responses are averaged and smeared out, leading at times to misidentification as continuous second-order transitions. Here, we demonstrate through muon spin relaxation/rotation (MuSR) experiments on two archetypal Mott insulating systems, composition-tuned RENiO3 (RE=rare earth element) and pressured-tuned V2O3, that the QPT from antiferromagnetic insulator to paramagnetic metal is first-order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value across the phase diagram until it is suddenly destroyed at the QPT. These findings call for further investigation into the role of inelastic soft modes and the nature of dynamic spin and charge fluctuations underlying the transition.
