Evolution of the electronic excitation spectrum with strongly diminishing hole density in superconducting Bi2Sr2CaCu2O8+δ

Abstract

A complete knowledge of its excitation spectrum could greatly benefit efforts to understand the unusual form of superconductivity occurring in the lightly holedoped copper-oxides. Here we use tunnelling spectroscopy to measure the T→0 spectrum of electronic excitations N(E) over a wide range of hole-density p in superconducting Bi 2 Sr 2 CaCu 2 O 8+δ . We introduce a parameterization for N(E) based upon an anisotropic energy-gap ( ) ( ) 2 / ) ( ) ( 1 y x k Cos k Cos k − Δ = Δ r plus an effective scattering rate which varies linearly with energy E E α = Γ ) ( 2 . We demonstrate that this form of N(E) allows successful fitting of differential tunnelling conductance spectra throughout much of the Bi 2 Sr 2 CaCu 2 O 8+δ phase diagram. The resulting average Δ 1 values rise with falling p along the familiar trajectory of excitations to the 'pseudogap' energy, while the key scattering rate ) ( 1 2 * 2 Δ = Γ = Γ Eincreases from below ~1meV to a value approaching 25meV as the system is underdoped from 2 p~16% to p<10%. Thus, a single, particle-hole symmetric, anisotropic energy-gap, in combination with a strongly energy and doping dependent effective scattering rate, can describe the spectra without recourse to another ordered state.Nevertheless we also observe two distinct and diverging energy scales in the system: the energy-gap maximum Δ 1 and a lower energy scale Δ 0 separating the spatially homogeneous and heterogeneous electronic structures.Hole-doped copper-oxides have their highest superconducting critical temperature T c at hole-densities per CuO 2 of p~16%, and the superconductive state exhibits d-wave symmetry. By measuring STM tip-sample differential conductance dI/dV(r,V) ≡ g(r,V) at each location r and bias voltage V one can achieve energy resolved images of the localdensity-of-excitations N(E) because g(r,V) ∝ N(r,E=eV) (when the N(E) integrated to the junction formation bias is homogeneous 1 ). Near optimal doping, the g(V) spectra appear highly consistent with the theoretical N(E) of a d-wave superconductor; when superconductivity is suppressed by unitary scattering at a Zn atom 2,3 or at the center of a vortex core 3,4 , the two particle-hole symmetric peaks in g(V) are also suppressed as expected of the superconducting coherence peaks. Thus there can be little doubt that the measured N(E) near optimal doping is that of the d-wave superconducting state. But as p is reduced, the electronic excitations begin to exhibit 5,6,7 a 'pseudo' gap (PG) . This is a momentum-space anisotropic energy gap 5-9 in the excitation spectrum whose effects can be detected by numerous spectroscopic and thermodynamic techniques 6,7 far above the superconducting T c (which diminishes to zero as p→0). The PG energy scale increases linearly with diminishing p.Possible explanations for the PG include, for example, effects of hole-doping an antiferromagnetic Mott insulator 10 -14 . Different models for this situation yield an anisotropic energy-gap whose maximum diminishes linearly with increasing p (heuristically, one can view thi...

Strong-coupling analysis of scanning tunneling spectra in Bi2Sr2Ca2CuBerthod1, Fasano2, Maggio-Aprile3 et al. 2013Phys. Rev. B

“…Following pioneering studies, 3,4 the STM data analysis has remained mostly qualitative, or based on phenomenological approaches. In a few cases, a BCS d-wave model including a realistic band structure 5 and/or a phenomenological scattering rate 6 turned out to be appropriate. Such cases are the exception rather than the rule: These models will not capture, in particular, the "dip" feature ubiquitously present at energies above the superconducting gap.…”

Imaging nanoscale Fermi-surface variations in an inhomogeneous superconductor

“…ARPES sums signals from differently doped regions; as more highly doped regions yield higher signal, ARPES will overemphasize them. Coupled with the observation that the width of the gap (and hence doping) distribution scales with mean gap size 24 , and is thus smaller in overdoped than underdoped samples, inhomogeneity should have a stronger effect on ARPES measurements in underdoped than in overdoped samples. This effect is particularly apparent in Bi-2201, which is more inhomogeneous than Bi-2212 (ref.…”

Effect of Surface Morphology and Magnetic Impurities on the Electronic Structure in Cobalt-Doped BaFe2As2 Superconductors

“…However, such a large and energyindependent  leads to a zero-bias conductance far in excess of the values observed in Figures 2(b) and (d), and a d-wave expression does not yield a significantly better fit. Given this difficult situation, we recalled the work of Alldredge et al 20 , in which cuprate dI/dV curves were fit using a linear in energy -i.e. (E) = E, with  dependent on location.…”