Phase-Space Approach to Wannier Pairing and Bogoliubov Orbitals in Square-Octagon Lattices

Abstract

Low-energy lattice models are the cornerstone for studying many-body physics and interactions between the system and measurement fields. A key challenge is identifying appropriate quasiparticle states that canonically transform between momentum and real space while retaining the correlation, entanglement, and geometric properties - generally called the Wannier obstruction. Here, we introduce a phase-space approach to bypass these obstructions. Instead of treating the phase space as a manifold, we embed a real space through a Bloch vector space at each momentum. Orbital and spin states are introduced through product states with the Bloch vector, while quantum statistics, correlations, topology, and entanglements are inherited from the Hamiltonian. We apply this framework to explore the unconventional pairing symmetry and the Bogoliubov-de Gennes (BdG) equation in phase space. Our findings demonstrate that while superconductivity exhibits global coherence, the local Wannier orbital symmetry primarily determines the pairing symmetry. We analytically solve the spin-fluctuation-mediated pairing symmetry on the phase space by engineering a flat band with artificial gauge fields. We validate the model on the square-octagon superconductor Lu${}_2$Fe${}_3$Si${}_5$ using density functional theory (DFT), revealing the coexistence of nodeless $s^{\pm }$ and nodal $s_{z^2}$ pairing symmetries. This phase-space framework provides a robust, obstruction-free lattice model for complex many-body systems and their exotic excitations.

23 (11 main) pages (double column), Accepted for publication in Phys. Rev. B

References in corpus (22)

• Strong electronic correlations from Hund's coupling
• Wannier representation of Z_2 topological insulators
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Dynamical mean-field theory using Wannier functions: a flexible route to electronic structure calculations of strongly correlated materials
• Orbital Selective Superconductivity in a Two-band Model of Infinite-Layer Nickelates
• Compactly-supported Wannier functions and algebraic $K$-theory
• Specific heat evidence for two-gap superconductivity in ternary-iron silicide Lu${}_2$Fe${}_3$Si${}_5$
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Quantum Spin Hall Effect in 2D Transition Metal Dichalcogenide Haeckelites
• Intermediate Coupling Model of the Cuprates
• Superconducting dome in MoS2 and TiSe2 generated by quasiparticle-phonon coupling
• Two energy scales in the magnetic resonance spectrum of electron and hole doped pnictide superconductors
• Two-gap superconductivity in single crystal Lu${}_2$Fe${}_3$Si${}_5$ from penetration depth measurements
• Symmetry of superconducting states with two orbitals on a tetragonal lattice: application to $La{O}_{1-x}{F}_{x}FeAs$
• Two-band superconductivity featuring different anisotropies in the ternary iron silicide Lu${}_2$Fe${}_3$Si${}_5$
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Disorder-sensitive superconductivity in the iron silicide Lu${}_2$Fe${}_3$Si${}_5$ studied by the Lu-site substitutions
• Time-reversal symmetry breaking in frustrated superconductor Re${}_2$Hf
• Superconductivity of anomalous pseudospin
• Coexisting pseudogap, charge transfer gap, and Mott gap energy scales in the resonant inelastic x-ray scattering spectra of electron-doped cuprates
• Electronic structure and Fermi surface of iron-based superconductors R2Fe3Si5 (R = Lu;Y;Sc) from first principles
• The electronic structure of rare-earth iron silicide R2Fe3Si5 superconductors