Research Interests
Electronic Structure of Dirty D-Wave Superconductors:
The  high temperature superconductors (HTSC) have been around for about 15 years (they were discovered in 1986/87) and have been extensively studied since then.   Although a lot is known about them, the most fundamental questions (where does the superconductivity come from?) are not really resolved.
Over the years, it has become increasingly clear that imperfections (dirt and intrinsic defects) have a large influence on what experiments measure.   This is both good and bad;  intentionally damaging your crystal is one way of studying the superconducting state, and recently tunneling experiments with atomic resolution have found beautiful interference patterns that have the potential to say a great deal about the superconducting state.  On the other hand, most HTSC crystals are intrinsically dirty, and it is very difficult to separate the effects of the dirt from other interesting effects.
The figure shows a numerical simulation on a lattice of the effect of impurities on the superconducting state.  Superconductivity is destroyed locally near each impurity, and then rises to its bulk value over a few nanometres.

 
We have performed extensive numerical studies of dirty superconductors with the goal of understanding the limits of validity of the standard "T-Matrix" theory of disorder.   In our numerical work, we find that the low energy states differ substantially from those predicted by the T-Matrix theory.
The figure compares the numerical calculation of the density of states (black curves) with the predictions of the T-Matrix theory (red curves).  At the lowest energies, there is a clear depletion of states which increases with impurity concentration (2% to 10%).  The right-panels characterise the power-law behaviour of the numerical results.

Publications:

 Nesting Symmetries and Diffusion in Disordered d-Wave Superconductors,  A. G. Yashenkin, W. A. Atkinson, I. V. Gornyi, P. J. Hirschfeld, and D. V. Khveshchenko, Physical Review Letters 86, 5982 (2001).

 Details of Disorder Matter in 2D d-Wave Superconductors,  W. A. Atkinson , P. J. Hirschfeld,  A. H. MacDonald, and K. Ziegler,  Physical Review Letters 85, 3926--3929 (2000).

  Gap Inhomogeneities and the Density of States in Disordered d-Wave Superconductors, W. A. Atkinson , P. J. Hirschfeld, and A. H. MacDonald, Physical Review Letters 85, 3922--3925 (2000).

Last Modified: 08/15/01