We present a theory that is a non-Fermi-liquid counterpart of the Abrikosov-Gor'kov pair-breaking theory due to paramagnetic impurities in superconductors. To this end we analyze a model of interacting electrons and phonons that is a natural generalization of the Sachdev-Ye-Kitaev-model. In the limit of large numbers of degrees of freedom, the Eliashberg equations of superconductivity become exact and emerge as saddlepoint equations of a field theory with fluctuating pairing fields. In its normal state the model is governed by two non-Fermi liquid fixed points, characterized by distinct universal exponents. At low temperatures a superconducting state emerges from the critical normal state. We study the role of pair-breaking on T c , where we allow for disorder that breaks time-reversal symmetry. For small Bogoliubov quasi-particle weight, relevant for systems with strongly incoherent normal state, T c drops rapidly as function of the pair breaking strength and reaches a small but finite value before it vanishes at a critical pair-breaking strength via an essential singularity. The latter signals a breakdown of the emergent conformal symmetry of the non-Fermi liquid normal state.Keywords: Eliashberg Theory, Superconductivity, Non-Fermi Liquid, Sachdev-Ye-Kitaev Model, Pair Breaking IntroductionThe dynamical theory of phonon-mediated superconductivity was formulated by Gerasim Matveevich Eliashberg in a pioneering tour de force of quantum many-body theory [1,2]. Considering the regime where phonon frequencies are much smaller than the Fermi energy of the electrons, electrons follow the lattice motion almost instantly. In this limit, Migdal had shown that electron-phonon vertex corrections become small [3]. Then a complicated intermediate-coupling problem suddenly becomes tractable. A closed, selfconsistent dynamical theory emerges that is not limited to the regime of weak electron-phonon interactions. The Eliashberg formalism follows the Gor'kov-Nambu description of superconductivity [4,5], reflecting the broken global U (1) symmetry, associated with charge conservation. The propagation of particles and the conversion of particles into holes are described by two self energies Σ (ω) and Φ (ω), respectively. Using the Eliashberg theory, important advances were made in understanding the physical properties of superconductors with a dimensionless electron-phonon coupling of order unity [6][7][8][9][10][11][12].The Eliashberg formalism has been applied to study superconductivity in problems that go significantly beyond the original electron-phonon problem [13][14][15][16][17][18][19][20][21][22][23]. When an electronic system becomes quantum critical, soft degrees of freedom emerge. The retarded nature of the coupling to such soft excitations makes an analysis in the spirit Eliashberg's approach, with a dynamical pairing field Φ (ω), natural. Since realistic models of quantum critical pairing usually possess no natural small parameter, a controlled approach that leads to an Eliashberg-like formalism is highly desirable....

In situ RHEED enables a height-resolved determination of the crystal structure of vertical nanowires via self-shadowing and ensemble shadowing.

Electrical conductivity relaxation was measured to investigate the kinetics of oxygen incorporation (in-diffusion process) and excorporation (out-diffusion process) in different epitaxial REBa2Cu3O7−δ thin films prepared by chemical solution deposition. The oxygen diffusion in these compounds happens in two distinct regimes with different activation energies, which depend on the compound. As the detailed X-ray analysis of similarly processed REBa2Cu3O7−δ films revealed, the transition temperature between these two regimes is compatible with a transition in the oxygen ordering in the Cu–O chains from the Ortho-II phase to the Ortho-I phase. These transitions may be of great importance for further optimization of the oxygenation process during the synthesis of these compounds but may depend not only on the rare-earth (RE) element but also on further factors such as variations of stoichiometry. The presented electrical conductivity measurements provide easy access to the determination of these transition temperatures.

Design of novel nanowire (NW) based semiconductor devices requires deep understanding and technological control of NW growth. Therefore, quantitative feedback over the structure evolution of the NW ensemble during growth...