Inferring effective interactions from the local density of states: application to STM data from Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

Abstract

While the influence of impurities on the local density of states (LDOS) in a metal is notoriously non-local due to interference effects, low order moments of the LDOS in general can be shown to depend only on the local structure of the Hamiltonian. Specifically, we show that an analysis of the spatial variations of these moments permits one to ``work backwards'' from scanning tunneling microscopy (STM) data to infer the local structure of the underlying effective Hamiltonian. Applying this analysis to STM data from the high temperature superconductor, Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$, we find that the variations of the electro-chemical potential are remarkably small (i.e., the disorder is, in a sense, weak) but that there are large variations in the local magnitude of the d-wave gap parameter.

arXiv comment7 pages, 7 figures

References in corpus (20)

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Cited by in corpus (6)

• A Systematic Study of Electron-Phonon Coupling to Oxygen Modes Across the Cuprates
• Disappearance of antiferromagnetic spin excitations in over-doped La${}_{2-x}$Sr${}_x$CuO${}_4$
• Spectral signatures of modulated d-wave superconducting phases
• s-wave Superconductivity Phase Diagram in the Inhomogeneous Two-Dimensional Attractive Hubbard Model
• Cold-spots and glassy nematicity in underdoped cuprates
• Effects of inhomogeneities and thermal fluctuations on the spectral function of a model d-wave superconductor