Topological Theory of Electron-Phonon Interactions in High Temperature Superconductors

Abstract

There are large isotope effects in the phonon kinks observed in photoemission spectra (ARPES) of optimally doped cuprate high temperature superconductors (HTSC), but they are quite different (Gweon et al. 2004) from those expected for a nearly free electron metal with strong electron-phonon interactions (Tang et al. 2003). These differences, together with many other anomalies in infrared spectra, seem to suggest that other particles (such as magnons) must be contributing to HTSC. Here we use topological (non-Hamiltonian) methods to discuss the data, emphasizing nanoscale phase separation and the importance of a narrow band of quantum percolative states near the Fermi energy that is spatially pinned to a self-organized filamentary dopant array. Topological discrete, noncontinuum, nonperturbative methods have previously explained the form of HTSC phase diagrams without involving detailed microscopic assumptions, and they are especially useful in the presence of strong nanoscale disorder. These methods also explain the ``miracle'' of an ideal nearly free electron phonon kink in sharply defined nodal quasiparticle states in LSCO at the metal-insulator transition. Finally the universality of the kink energy and Fermi velocity in different cuprates is the result of the marginally elastic nature of these materials, and specifically the isostatic character of the CuO2 planes.

References in corpus (9)

• Electronic Phase Diagram of High-T_c Cuprate Superconductors from a Mapping of the In-Plane Resistivity Curvature
• An unusual isotope effect in a high-transition-temperature superconductor
• Universal scaling relation in high-temperature superconductors
• High-transition-temperature superconductivity in the absence of the magnetic-resonance mode
• Superconducting properties of MgB2 from first principles
• The Dichotomy between Nodal and Antinodal Quasiparticles in Underdoped (La${}_{2-x}$Sr${}_x$)CuO${}_4$ Superconductors
• Electron-phonon Interaction close to a Mott transition
• Manifestation of the magnetic resonance mode in the nodal quasiparticle lifetime in superconducting cuprates
• Superconductive Excitations and the Infrared Vibronic Spectra of BSCCO

Cited by in corpus (2)

• Self-Organization and the Physics of Glassy Networks
• Self-Organized Networks and Lattice Effects in High Temperature Superconductors