Wednesday, December 12, 2012

Is ionic polarizability a primary or secondary cause in cuprates?

Distinguishing cause and correlation in complex systems is always a tricky matter.

There is an interesting preprint
Ion-size effects in cuprate superconductors - implications for pairing
B.P.P. Mallett, T. Wolf, E. Gilioli, F. Licci, G.V.M. Williams, A.B. Kaiser, N. Suresh, N.W. Ashcroft, J.L. Tallon

For a large family of cuprates they observe correlations between the basal plane area of the unit cell, the Heisenberg antiferromagnetic exchange J, the maximum superconducting Tc, and the total electric polarizability of the ions.

The main result from this rather impressive systematic study is in the Figure below
The upper graph shows that Tc (max) decreases with increasing J, contrary to what one might expect from spin fluctuation mediated (or RVB) type pictures of superconducitivity (see e.g. this paper which found the pairing amplitude scaled roughly with J).

The lower graph shows that Tc (max) increases with increasing ionic polarizability. The authors then make the claim (first proposed by Neil Ashcroft, one of the authors) that the superconductivity results from pairing via collective excitations of ionic polarizability, rather than via spin fluctuations.

However, I wonder about a different and less radical interpretation.
Assume the maximum Tc does not simply scale with J. One might also worry about what is happening to the tight binding parameter t, since this will also decrease with decreasing unit cell area.

Then remember that the cuprates are charge transfer insulators. The one band t-J model is derived from a two-band model with both p (oxygen) and d (copper) orbitals. The effective J is given by
Background: the figure below taken from this review illustrates the underlying lattice and energy levels.

Hence, as the ions become more polarised the denominator will increase and J will decrease, as is observed here.
Is this less radical hypothesis consistent with the evidence?

1 comment:

  1. As one of the authors I would like to thank you Ross for your thoughts and comments on our work.

    The key message of this work is the possible central role of the ionic-polarisability in superconductivity in the cuprates.

    We are motivated by the opposite effect on Tc by compression of the crystal from external pressure or from ion-size substitution (`chemical’ or `internal’ pressure). We look for the salient difference between these two compressions using the Ln-(Ba,Sr)2-Cu3-O7-y family as a model (YBCO is the most famous member of this family). In this work we show it is not J - as the upper panel in our figure shows (we would agree with your assumption, “let’s assume the maximum Tc does not simply scale with J”). On the other hand, by considering the ionic polarisability of the non-CuO2 layers one can simply understand how these two ‘pressures’ have the opposite effect on Tc.

    Unfortunately, with only this information one cannot discriminate between polarisation-wave or repulsive-interaction pairing scenarios – with repulsive interactions the larger polarisability means more effective screening of longer (real-space) range interactions which are otherwise detrimental to superconductivity where the order parameter changes sign around the Fermi-surface (as happens in cuprates). Either way, these observations suggest that the polarisability plays a key role in the cuprates.