Fe-based superconductors (FeSC) exhibit all the properties of systems that allow the formation of a superconducting phase with oscillating order parameter, called the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. By the analysis of the Cooper pair susceptibility in two-band FeSC, such systems are shown to support the existence of a FFLO phase, regardless of the exhibited order parameter symmetry. We also show the state with nonzero Cooper pair momentum, in superconducting FeSC with ∼ cos(k x ) · cos(k y ) symmetry, to be the ground state of the system in a certain parameter range.

Recent experiments using the quantum dot coupled to the topological superconducting nanowire [M.T. Deng et al., Science 354, 1557] revealed that zero-energy bound state coalesces from the Andreev bound states. Such quasiparticle states, present in the quantum dot, can be controlled by the magnetic and electrostatic means. We use microscopic model of the quantum-dot-nanowire structure to reproduce the experimental results, applying the Bogoliubov-de Gennes technique. This is done by studying the gate voltage dependence of the various types of bound states and mutual influence between them. We show that the zero energy bound states can emerge from the Andreev bound states in topologically trivial phase and can be controlled using various means. In non-trivial topological phase we show the possible resonance between this zero energy levels with Majorana bound states. We discuss and explain this phenomena as a result of dominant spin character of discussed bound states. Presented results can be applied in experimental studies by using the proposed nanodevice.

Abstract. The theoretical analysis of the Cooper pair susceptibility shows the two-band Fe-based superconductors (FeSC) to support the existence of the phase with nonzero Cooper pair momentum (called the Fulde-Ferrel-Larkin-Ovchinnikov phase or shortly FFLO), regardless of the order parameter symmetry. Moreover this phase for the FeSC model with s± symmetry is the ground state of the system near the Pauli limit. This article discusses the phase diagram h-T for FeSC in the two-band model and its physical consequences. We compare the results for the superconducting order parameter with s-wave and s±-wave symmetry -in first case the FFLO phase can occur in both bands, while in second case only in one band. We analyze the resulting order parameter in real space -showing that the FeSC with s±-wave symmetry in the Pauli limit have typical properties of one-band systems, such as oscillations of the order parameter in real space with constant amplitude, whereas with s-wave symmetry the oscillations have an amplitude modulation. Discussing the free energy in the superconducting state we show that in absence of orbital effects, the phase transition from the BCS to the FFLO state is always first order, whereas from the FFLO phase to normal state is second order.

Recent experiments on CeCoIn 5 suggest an unusual interplay between superconducting and magnetic orders that gives rise to a multicomponent ͑magnetosuperconducting͒ phase. We demonstrate that characteristics of CeCoIn 5 make this system particularly well suited for the onset of such a phase. Based on general considerations, we show that superconductivity with nonzero Cooper-pair momentum may lead to an enhancement of the spin-spin response function and, simultaneously, incommensurate spin-density wave may enhance the Cooper-pair susceptibility.

Obtaining a thermodynamically accurate phase diagram through numerical calculations is a computationally expensive problem that is crucially important to understanding the complex phenomena of solid state physics, such as superconductivity. In this work we show how this type of analysis can be significantly accelerated through the use of modern GPUs. We illustrate this with a concrete example of free energy calculation in multi-band iron-based superconductors, known to exhibit a superconducting state with oscillating order parameter (OP). Our approach can also be used for classical BCS-type superconductors. With a customized algorithm and compiler tuning we are able to achieve a 19x speedup compared to the CPU (119x compared to a single CPU core), reducing calculation time from minutes to mere seconds, enabling the analysis of larger systems and the elimination of finite size effects.Keywords: FFLO, pnictides, NVIDIA CUDA, PGI CUDA Fortran, superconductivity PROGRAM SUMMARYManuscript Title: GPU-based acceleration of free energy calculations in solid state physics Authors: Micha l Januszewski, Andrzej Ptok, Dawid Crivelli, Bart lomiej Gardas Journal Reference: Catalogue identifier: Licensing provisions: LGPLv3 Programming language: Fortran, CUDA C Computer: any with a CUDA-compliant GPU Operating system: no limits (tested on Linux) RAM: Typically tens of megabytes. Keywords: superconductivity, FFLO, CUDA, OpenMP, OpenACC, free energy Classification: 7, 6.5 Nature of problem: GPU-accelerated free energy calculations in multi-band iron-based Email addresses: michalj@gmail.com (Micha l Januszewski), aptok@mmj.pl (Andrzej Ptok) February 4, 2015 superconductor models. Solution method: Parallel parameter space search for a global minimum of free energy. Preprint submitted to Computer Physics Communications Unusual features:The same core algorithm is implemented in Fortran with OpenMP and OpenACC compiler annotations, as well as in CUDA C. The original Fortran implementation targets the CPU architecture, while the CUDA C version is hand-optimized for modern GPUs.Running time: problem-dependent, up to several seconds for a single value of momentum and a linear lattice size on the order of 10 3 .

We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional (1D) optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model (AHM) in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground state phase diagrams including some unconventional superconducting phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and the η phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. It allows to determine optimal regimes for the FFLO phase as well as η-pairing stability. We also investigate the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, at T = 0. Finally, the obtained results show that despite of the occurrence of the Lifshitz transition induced by an external magnetic field, the superconducting state can still exist in the system, at higher magnetic field values.

The recent experimental support for the presence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in CeCoIn(5) directed attention towards the mechanisms responsible for this type of superconductivity. We investigate the FFLO state in a model where on-site/inter-site pairing coexists with the repulsive pair hopping interaction. The latter interaction is interesting in that it leads to pairing with non-zero momentum of the Cooper pairs even in the absence of the external magnetic field (the so-called η pairing). It turns out that, depending on the strength of the pair hopping interaction, the magnetic field can induce one of two types of the FFLO phase with different spatial modulations of the order parameter. It is argued that the properties of the FFLO phase may give information about the magnitude of the pair hopping interaction. We also show that η pairing and d-wave superconductivity may coexist in the FFLO state. It holds true also for superconductors which, in the absence of magnetic field, are of pure d-wave type.

In this paper we address Lifshitz transition induced by applied external magnetic field in a case of iron-based superconductors, in which a difference between the Fermi level and the edges of the bands is relatively small. We introduce and investigate a two-band model with intra-band pairing in the relevant parameters regime to address a generic behaviour of a system with hole-like and electron-like bands in external magnetic field. Our results show that two Lifshitz transitions can develop in analysed systems and the first one occurs in the superconducting phase and takes place at approximately constant magnetic field. The chosen sets of the model parameters can describe characteristic band structure of iron-based superconductors and thus the obtained results can explain the experimental observations in FeSe and Co-doped BaFe2As2 compounds.