Andrzej Ptok

The Fulde-Ferrell-Larkin-Ovchinnikov phase in the presence of pair hopping interaction

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.

The Fulde-Ferrell-Larkin-Ovchinnikov state in pnictides

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(kx)⋅cos(ky) symmetry, to be the ground state of the system in a certain parameter range.

Coexistence of superconductivity and incommensurate magnetic order

The influence of incommensurate spin-density waves (SDW) on superconductivity in unconventional superconductors is studied by means of the Bogolubov-de Gennes (BdG) equations. Exploiting translational symmetries of a magnetically ordered two-dimensional system, we propose an approach that allows to solve the BdG equations on much larger clusters than it is usually possible for inhomogeneous systems. Applying this approach, we demonstrate that the presence of incommensurate spin-density waves induces real-space inhomogeneity of the superconducting order parameter even in the absence of external magnetic field. In this case, a homogeneous order parameter of the Bardeen-Cooper-Schrieffer-type superconducting state is slightly modulated, or equivalently, a small fraction of the charge carriers form Cooper pairs with nonzero total momentum. However, when a sufficiently strong magnetic field is applied, the homogeneous component of the order parameter is suppressed and the system transits to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where the order parameter oscillates changing sign. We show that for s-wave pairing, the presence of external magnetic field diminishes the destructive influence of the SDW order on superconductivity. A simple explanation of this effect is also proposed.

Change of the sign of superconducting intraband order parameters induced by interband pair hopping interaction in iron-based high-temperature superconductors

Iron based superconductors are characterized by the gap symmetry, where the gap changes its sign between pockets of the Fermi surface. We discuss another sign change mechanism of the superconducting order parameter (OP)?the interband Cooper pairs hopping interaction. In the minimal two-orbital model of iron based superconductors we show that this interaction can lead to a change of the sign of the intraband superconducting OP regardless of its symmetry.

Controlling the bound states in a quantum-dot hybrid nanowire

Recent experiments using the quantum dot coupled to the topological superconducting nanowire [M.T. Deng et al., Science 354, 1557 (2016)}] 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.

Multiple phase transitions in Pauli-limited iron-based superconductors.

Specific heat measurements have been successfully used to probe unconventional superconducting phases in one-band heavy-fermion and organic superconductors. We extend the method to study successive phase transitions in multi-band materials such as iron-based superconductors. The signatures are multiple peaks in the specific heat, at low temperatures and high magnetic field, which can lead to the experimental verification of unconventional superconducting states with non-zero total momentum.

GPU-based acceleration of free energy calculations in solid state physics

Abstract 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 19×speedup compared to the CPU (119×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. Program summary Program title: Free_Energy Catalogue identifier: AEVX_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVX_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License, version 3 No. of lines in distributed program, including test data, etc.: 786 No. of bytes in distributed program, including test data, etc.: 6304 Distribution format: tar.gz Programming language: Fortran, CUDA C. Computer: Any with a CUDA-compliant GPU. Operating system: No limits (tested on Linux). RAM: Typically tens of megabytes. Classification: 7, 6.5. Nature of problem: GPU-accelerated free energy calculations in multi-band iron-based superconductor models. Solution method: Parallel parameter space search for a global minimum of free energy. 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

Influence of s± symmetry on unconventional superconductivity in pnictides above the Pauli limit – two-band model study

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.

The ab initio study of unconventional superconductivity in CeCoIn5 and FeSe

Electronic structure and the shape of the Fermi surface are known to be of fundamental importance for the superconducting instability in real materials. We demonstrate that such an instability may be explored by static Cooper pair susceptibility renormalized by pairing interaction and present an efficient method of its evaluation using Wannier orbitals derived from ab initio calculation. As an example, this approach is used to search for an unconventional superconducting phase of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type in a heavy-fermion compound CeCoIn

Probe-type of superconductivity by impurity in materials with short coherence length: the s-wave and η-wave phases study

_5