Nanoscale superconductivity

I have been interested for many years in heavy fermion and, more recently, high temperature cuprate superconductivity. The heavy fermion materials are metals involving rare earth or actinide ions in which electrons behave as though they have masses much larger than their bare mass, sometimes as much as a proton mass. Transition temperatures are only about 1K. The cuprate materials, with Tc's of order 100K or above, typically have a layered perovskite structure, and superconductivity seems to be nearly 2D. Here's a recent New York Times assessment of their technological potential, and specifically a discussion of recent advances in making superconducting wires and tapes . In both classes of systems there is strong evidence that superconductivity is unconventional in the sense that the superconducting order parameter or pair wave function has symmetry less than the underlying crystal lattice. In particular it is now established that the cuprate materials have d-wave symmetry. Here is a recent review explaining why we think so. Nanoscale superconductivity is of interest due to 1) possible applications of ultrasmall superconducting devices; 2) new quantum effects which arise when the system dimensions become comparable to the coherence length; and 3) recent STM experiments indicate that at least some high-temperature superconductors are inhomogeneous on a length scale of 30 Angstrom or so. It may be possible to think of this system as a collection of weakly coupled nanoscale grains, although this picture is far from clear.

d-wave superconducting gap. Note "+" and "-" means the order parameter has this sign for these directions of k on the Fermi surface. The gap goes to zero in the (110) directions, and low-energy properties are dominated by single particle excitations near these nodes.

  Current projects

• Grain boundaries in high temperature superconductors

  The physics of grain boundaries in strongly correlated electron systems has developed into a fascinating and active field of experimental research in recent years. Because they are in many cases the single factor most important in limiting electrical current flow, and will almost certainly be present in large numbers in any commercial product, understanding what happens at grain boundaries is extremely important for device applications. Large angle grain boundary Josephson junctions are the primary components of RSFQ circuits with operating temperatures of 50-60K, and high-quality SQUIDs operating at 77K, which are already employed for a host of applications such as fetal heart monitoring or the inspection of devices in semiconductor fabrication lines. Texturing techniques to align grain boundaries in high-Tc wires have recently achieved millions of A/cm2 critical currents in prototype cables, and improvements along these lines will certainly be facilitated by careful modelling of the grain boundaries themselves. In addition, a whole set of theoretical questions about what happens in correlated systems at interfaces is largely unexplored. While a good deal of theoretical work has made predictions for the effect of the dx2-y2 nature of the order parameter on the critical current within simple BCS models, and some aspects of the qualitative behavior have been confirmed by experiment, there are serious discrepancies (see below), as well as fundamental open questions regarding the nature of the barrier at the interface and the role of interactions in the host materials. Questions include: can we understand the exponential dependence of the critical current on the grain boundary angle? What are the changes in electronic structure at the interfaces, and are they in fact generically underdoped as recent experiments suggest? Are such interfaces intrinsically magnetic due to disrupted magnetic correlations in the bulk materials? Recently, we have succeeded in understanding the exponential decay of the critical current with misorientation angle. This required an "end to end" style calculation which involved performing molecular dynamics simulations to reconstruct the structure of the interface, microscopic analysis of the resulting hopping matrix elements and local potentials due to interface inhomogeneity, mapping onto an effective Cu-only Hamiltonian, and calculation of the critical current in such a system. Our results are presented in arXiv:0912.4191. Molecular dynamics simulation of YBCO 410 grain boundary with typical structures identified Current distribution in a d-wave superconductor at 410 grain boundary. Theory vs. experiment for critical current vs. misorientation angle.

  Most superconducting tapes or wires consist of tiny oriented crystallites or grains connected by boundaries, which limit the maximum critical current which the wire can carry. Here's a closeup AFM image of a YBCO grain boundary grown intentonally on a strontium titanate bicrystal by Jochen Mannhart's group in Augsburg.

• Electronic structure of nanoscale grains

  
  

  Energy of local coherence peak ("gap size") determined by Cornell group on BSCCO-2212 sample a) underdoped, b) optimally doped. Note patches are about 25A in size. Several groups (Stanford, Berkeley/Cornell) have found that the electronic structure of the surface of BSCCO-2212, a high-temperature superconductor, is inhomogeneous at the nanoscale. As models for this inhomogeneity, some authors have proposed that the samples should be thought of as a collection of weakly coupled d-wave grains of roughly the size of the superconducting coherence length, or d-wave grains coupled to grains of another electronic phase. This discussion has highlighted the question of the electronic structure of d-wave superconductors in restricted geometries. The effect of level discretization on ordinary superconductivity in Cooper pair ``boxes" is well understood, and the fundamental additional feature in the d-wave case is the effect of surface pair breaking. One of the important problems in this field is the evolution of Andreev bound states, when the size of the superconducting grain becomes comparable to the coherence length. As is known, the Andreev surface states form on surfaces with orientations different from the antinodal directions of a d-wave superconductor, due to the sign change of the order parameter. My group, together with Yuri Barash and Sasha Bobkov of ISSP-Chernogolovka, have performed calculations of the electronic structure of restricted geometry systems, beginning with wires translationally invariant in 1 direction. The structure, in particular the weight of the zero-mode Andreev state, is found to be strongly dependent on the number parity of chains making up the wire. In addition, self-consistent treatments showed a tendency towards spin triplet pair formation at narrow widths. Earlier work on (100) wires was published as Phys. Rev. B 64, 054512 (2001) ( Phys. Rev. B 70, 144502 (2004) ). Current work available as cond-mat/0402607 .

  Geometry of d-wave quantum wire with nearest-neighbor hopping among sites on a square lattice (circles). Impurities (squares) are required to cut off transmission to make wire of N chains (circles).     Quasiparticle spectra and the LDOS for superconducting half-filled (110) wire with N=11. (b) Dispersive modes ky vs. w/t for N=11 near the edge of the Brillouin zone. (c) The local density of states on layers with indices n=2 (solid line), n=3 (dashed line). The peaks should be observable in STM experiments. Large peak centered at zero energy is dispersionless Andreev state.