By

SAJAD AHMAD SHIEK

(SSVP-2016)

UNDER SUPERVIS ION - Dr. ARIJIT SAHA

18/07/2016

Introduction

BTK Model

Calculation of Probability Current Densities at NSJunction

NS Junction at Finite Bias Voltage (I-V Characteristics)

Calculation of Differential Conductance

Conclusion

Acknowledgment

Three Major Quantum Mechanical Scattering Processes at NS Interface

Andreev Reflection

Transmission

Normal Reflection

Andreev Reflection Process

in an energy diagram

Potential barrier at NS interface

Bogoliubov transformations

with

where uk and vk are the BCS coherence factors

\

V(x) - Potential

µ(x) - Chemical potential

∆(x) - Energy gap

Trial wave solutions

Boundary conditions:

C

f

f

In conclusion we have reviewed the BTK theory

and its assumptions.

A full account on BTK derivation of the I-V

equation using the Bogoliubov equations and the

boundary conditions provided.

The resultant electric current and differential

conductance have been calculated using the BTK

current equation.

I am very thankful to IOP for this wonderful opportunity to

do a summer research project here.

I would like to extend my thanks to Prof. Goutam Tripathy

for providing all the necessary facilities during the stay in

IOP.