Superconductivity at the Nanoscale

1. Superconductivity at the Nanoscale D. Stroud and N. Trivedi • Why are nano superconductors useful/important? • How is superconductivity at the nanoscale modeled? • Behavior or nanoscale superconducting wires and devices Contact e-mail: trivedi@mps.ohio-state.edu

2. SmallJosephsonjunctionsasqubits What are nano superconductors good for? • Small superconductingsystems (e.g. Josephson junctions) -- among the most promising candidates for qubits • Only twoenergylevels (which behave like “1” or “0” bits) qubit or quantum bit: “coherent superposition” of “1” and “0” • Qubits will generate vastly more computing power than “classical” computers.

3. A superconductor is a material which can carry current with no resistance!! Tc Zero resistance is seen below a material dependent critical temperature Tc

4. Maximum Tc ~130K Achieved in the copper oxide high Tc materials -- useful because Tc> boiling pt. of liquid nitrogen Tc Nobel Prizes for studies of SC in 1913, 1972, 1973, 1987, 2003 SC’s useful as low-dissipation current carriers; valuable in producing ultra-high magnetic fields, and for microwave applications.

5. Types of nanoscale SC’s to be studied Zero-dimensional SC Two coupled zero-dimensional SC’s J One-dimensional SC (thin wire) Two-dimensional SC (nm layer thickness)

6. When superconductors are made very small or thin, they often lose the remarkable property of superconductivity. Why does this loss of superconductivity happen? Single electron tunneling SINGLE ELECTRON TRANSISTOR SC requires: mean level spacing < SC gap Effect of odd/even numbers of electrons seen! Ralph, Black and Tinkham, PRL 74, 3241 (1995)

7. Quantum Phase Fluctuations in nano SCs charging energy to put an electron on nano SC Capacitance of a grain C~d 10-20 nm dia causes quantum fluctuations of the phase Josephson coupling between two nano superconductors ~J Josephson “weak link” (nonlinear circuit element)

8. Nano SC wires of width ~5nm Bezryadin, Lau and Tinkham, Nature 404, 971 (2000) SC is destroyed in nanowires by thermal fluctuations, quantum phaseslips, and dissipation. Is there a universal resistance of the nano-wire above which the wire cannot superconduct?

9. Nanoscale superconductivity in 2D • The high-Tc SCs: stacks of CuO2 layers, with various other ions in between them. All the superconducting “action” occurs in the CuO2 layers. • Superconducting layers are inhomogeneous on a nanoscale: The superconducting energy gap varies from point to point within the layer, on a nanometer scale (seen in STM experiments). • Theoretical multiscale approach: • (i) Solve for superconducting properties using a the standard non-linear Bogoliubov-de Gennes differential equations, modified to include nanoscale inhomogeneity and phase fluctuations. • (ii) Treat inhomogeneity at a larger, but still close to nanoscale, using a mapping onto an effectively Josephson-coupled layer.

10. Generation of self organised nanoscale structure in a disordered superconductor Spatial dependence of pairing amplitude with increasing disorder in an inhomogeneous SC obtained by solving Bogoliubov deGennes equations Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 1450 (2002)

11. Scanning tunneling spectroscopy Ghosal, Randeria, Trivedi PRB 63, 20505 (2000) THEORY EXPT: J.C. Davis Nature 403, 746 (2000)