Point-contact spectroscopy (PCS) is an experimental tool used for investigations of the interaction mechanisms between electron-electron, electron-phonon, electron-magnon etc. in metallic systems. The Drude model which is based on the diffusive motion of electrons describes the resistivity of a normal metal for length scales greater than the mean free path l. But for length scales shorter than l, the electrons move ballistically and this regime can be accessed by tunnelling into a material from a point contact of size a << l. In a ballistic contact, information about the spectral weight of interactions like electron-phonon, electron-magnon etc. can be obtained by measuring the differential conductance (dI/dV) or its derivative w.r.t. the applied voltage V. However, new phenomena are observed when the point-contact is established between a superconductor (S) and N i.e. in a N/S junction. Below the transition temperature of the superconductor, the resistivity drops to zero and an energy gap △ = 10-3 eV opens up in the density of states (DOS). In a N/S point-contact transport measurement, three major processes can occur at the interface:
- Andreev reflection.
Process 1, i.e. transmission, occurs if the energy of the incident electron from the N side is less than the superconducting band gap, E > △. For the case of E < △ if the dimension of the point contact is such that a ≥ l process 2 is observed. However, for the case of small enough point contact in the ballistic regime, a ≪ l, process 3 i.e. Andreev reflection takes place at the N/S interface and the differential conductance increases by a factor of 2 from that above the gap.
Physically, the point contact Andreev reflection (PCAR), as shown in Figure 1, can be characterized as a process where for a spin up electron from the N side to be injected with E < △ and be transmitted in the S side, it is required to form a Cooper pair with an electron of opposite spin in the superconductor. Consequently, a hole is retroreflected back with opposite spin and momentum of the incident electron.
The measured (dI/dV) as a function of applied V is modelled according to the Blonder-Klapwijk-Tinkham (BTK) theory and the energy gap △, lower bounds for the BCS coherence length ξ and the Fermi velocity vF for a superconductor.
In our group we have developed indigenously a low temperature PCAR set up for studies of both BCS superconductors and high TC cuprates. The tips used are W, Au and Nb, where the superconducting Nb tip is also used for measurement of spin polarization of magnetic materials. The tip is moved using a programmable motor with sub-micron sensitivity. The electrical measurements are done using state-of-the-art Keithley electronic systems while a labview program is used to run the measuring devices.