Tunneling and Phonon Spectra in Superconductors Brad Westover

Background on Superconductors l Superconductors exhibit zero resistance below a critical temperature l Superconductors expel magnetic fields from the solid, or confine those fields to small vortices

Cooper Pairs When the temperature is a SC is low enough, the electrons can form bound states of two electrons, called Cooper pairs l Cooper pairs are bound by phonon exchange, that is by lattice interactions l Cooper pairs will only be formed under certain conditions, when phonon interactions can overcome Coulomb repulsion l

Cooper Pairs (cont. ) l Distance between electrons in a Cooper pair is many (~100) times the lattice spacing, so phonon are collective excitation, not single lattice displacements l Binding energy of the Cooper pairs is very weak, about 1 -10 me. V

Type I Superconductors l Pure elements l Niobium, Lead are some of the best Type I SC’s, with critical temperatures around 10 K ¡ They are poor conductors at room temperature l Copper, ¡ They gold, silver do not superconduct are good conductors at room temperature

Type II Superconductors l SC’s with critical temperature in the 1040 K range, higher than Type I SC’s l Nb-Ti has Tc about 10 K l Mg. B 2 has Tc about 40 K l Multi-bond, high frequency modes contribute to critical temperature l Do not expel fields entirely, but instead, fields penetrate in small, quantized flux tubes

Phonon Spectrum Critical temperature rises with increasing phonon energy (omega) l And greater electronphonon coupling (lambda) l And decreases with greater electron interaction (mu) l

Phonon Spectrum However, electronphonon coupling is reduced for high phonon energies l Gamma is phonon line-width l N(0) is density of states l

Energy gap l Since there is an interaction energy in the Cooper pairs, there is an energy gap in the material, slightly below the Fermi energy

Tunneling l Quantum mechanical effect that occurs when a barrier larger than particle energy is penetrated l Tunneling may occur if the barrier potential is higher than the particle energy, but not if the potential at the other side is higher than the particle energy

Superconducting Tunneling l Between SC and metal at low temp. ¡ l In order to overcome the band gap, a voltage must be applied Between SC and metal at high temp. ¡ Some electron will be thermally excited above the energy gap, and will tunnel, producing current

SC Tunneling l Between SC and SC at low temp. ¡ l Voltage applied must be equal to the sum of the band gaps Between SC and SC at higher temp. ¡ ¡ Voltage applied must be equal to the difference of the band gaps, or the sum Peaked will be observed in the IV spectrum

Temperature dependence of Tunneling l IV curve becomes straighter and more resistor-like as temperature approaches Tc of SC’s, and is fully resistive above Tc

Phonon or Photon assisted Tunneling The energy to overcome the energy gap and tunnel through the barrier, can be provided by an external electric potential, or by a particles, like photons or phonons l The energy of these particles must match the energy needed to over come the gap l Two or more particles could be involved l

Phonon Spectra from Tunneling Measurements The current due to phonons is proportional to the second derivative of the I-V curve l Peaks in the spectrum correspond to phonon modes at that energy l

Phonon Spectra from Tunneling Measurements (cont. ) l Second derivative can reveal very subtle features in the I-V curve

Josephson Tunneling Below some critical current, there can be current flow without any voltage drop, that is, without any resistance l The insulating barrier acts like a superconductor! l

DC Josephson Effect Below a critical current, no voltage drop is observed l The critical current is dependent on the magnetic field flux through the junction l Used to make very sensitive magnetometers l

AC Josephson Effect When a DC voltage is applied, the junction will radiate at a certain frequency l When an AC voltage is applied, higher modes can be excited l Applied AC signal produces DC voltage drops l Steps are observed in the I-V curve l

References l Pictures and equations from: ¡ Solymar, L. Superconducting Tunneling and Applications. 1972 ¡ Baron, A. , et al. “Phonon spectra in pure and carbon doped Mg. B 2 by inelastic x-ray scattering. ” Physica C: Superconductivity.