Peter Hirschfeld: extracting new kinds of information from recent STM data

Peter Hirschfeld

"Extracting new kinds of information from recent STM data"

Peter remarked that he was going to give an extremely rare type of STM talk - one without color pictures, presented on a blackboard. Two topics were presented :

• The extraction of life-times from STM data
• Modulation of the gap in response to the BSSCO supermodulation.

The first topic concerns a new method, developed by Aldridge et al. They have found, empirically, that one can fit the local density of states
with two variables, a local scatering rate, and a local gap. The fit form looks something like





Emprically, these two variables are correlated with the gap determined from the coherence peaks in N(r,E), i.e. Delta_1(r) is found to be basically the same as the former type of gap maps.
Now however, one can pull out a scattering rate as well. All of these variables follow the approximately 30A (five unit cell) correlation length seen in previous gap maps.

Hirschfeld argued that this indicates that the local DOS is therefore sensitive to disorder effects that must be on length scales that are shorter than 30A. The local Green function is determined by



and he argues that r-r1 and r-r2 must be smaller than about 30A for consistency.


One can also extract an effective scattering rate



What is the meaning of this?

Chandra Varma asked whether this is sensible, because the scattering is low-angle scattering?

Hirschfeld pointed out that the scattering rate extracted this way is about 10 times smaller than anisotropic scattering rates extracted from ARPES measurements. From STM

Gamma(max) = 10meV (p=0.08) - underdoped
Gamma(max) = 2 meV (p=0.02) - optimally doped

Comparable figures from Arpes are 100 and 40 meV respectively. The origins for this mismatch may be

• Broadening effects of the inhomogeneity in oxygen content
• Resolution of the ARPES

Hirschfeld then turned to the second topic. In Bisco, there is a 26A, or 4.8 unit cell modulation of the structure. Slezak et al have been able to map out the phase of the modulation, defining contours of constant phase across the maps, and from this, they are able to correlate the local gap with the phase of the modulation. It is found that the gap drops by 10% as the phase goes from zero to pi. In Boguilubov-de Gennes phenomenology, this corresponds to a reduction of the coupling constant by about 30% (?). Peter mentioned similar types of conclusion in a t-J model by Zhang and Rice.

Of course, perhaps if once one correlate this modulation of the gap with the structure, one can gain insight into the pairing mechanism of high Tc. Is this possible?

Hirschfeld pointed out that the supermodulation corresponds to a "tipping" of the octahedra, and that in the region where the gap is largest, the apical oxygens are furthest apart. This may cause the t' - next nearest neighbor hopping to be larger, giving rise to a large Delta.