Superconductivity at nanoscale - folk.uio.nofolk.uio.no/yurig/Nanotechnology/Superconductivity/... · In which way superconductivity manifests itself at nanoscale? Superconductivity

Superconductivity at nanoscale

Superconductivity in Nanosystems 2

Superconductivity is the result of the formation of a quantum condensate of paired electrons (Cooper pairs).

In small particles, the allowed energy levels are quantized and for sufficiently small particle sizes the mean energy level spacing becomes bigger than the superconducting energy gap.

It is generally believed that superconductivity is suppressed at this point (the Anderson Criterion)

Q: Is superconductivity important for nano-devices?

In which way superconductivity manifests itself at nanoscale?


Tunneling in superconductorsGenerally,


At the S-N interface,

S SN N

I

V

No single-electron tunneling possible until


Then, how the charge is transferred between the superconductor and normal metal?

p

Fermilevel

Hole-like excitation

Hole branch

Electron-hole representation

In a a normal metal


In a superconductor,

An electron can be reflected as a hole with oppositegroup velocity. In this way the charge 2e is transferred Andreev reflection


An electron (red) meeting the interface between a normal conductor (N) and a superconductor (S) produces a Cooper pair in the superconductor and a retroreflectedhole (green) in the normal conductor. Vertical arrows indicate the spin band occupied by each particle.

Reflected

Incident

Transmitted


In the presence of the tunneling barrier the Andreev reflection contains an extra tunneling amplitude.

However, at the single-particle tunneling is suppressed exponentially.

Andreev reflection is a way to bring Cooper pairs to a superconductor from a normal conductor in a coherent way.

e

e h

Cooper pair

For a perfect (non-reflecting) interface the probability of Andreev reflection is 1.

In general case both reflection channels normal and Andreev have finite probabilities.


Total Andreev Reflection in an N/S Phase

Boundary between semi-infinite N and S Layers

Normal Reflection in an N/S Phase Boundary

between semi-infinite N and S Layers


Parity effect

How much we pay to transfer N electrons to the box?

Coulomb energy:

We have taken into account that the electron charge is discrete.


We have arrived at the usual diagram for Coulomb blockade at some values of the gate voltage the electron transfer is free of energy cost!


Parity effect:

What happens in a superconductor?

Energy depends on the parity of the electron number!


The ground state energy for odd n is above the minimum energy for even n


Experiment (Tuominen et al., 1992, Lafarge et al., 1993)

Coulomb blockade of Andreev reflection

The total number of electrons at the grain is about109. However, the parity of such big number can be measured.


By Hergenrother et al., 1993

Stability diagram of Cooper pair box

Superconductivity in small systems manifests itself through energy scales of current-voltage curves

SET


Crossover from 2e periodicity to e periodicity can be observed in external magnetic field suppressing superconductivity

Observed in S-S-S systems, where the physics of Coulomb blockade is similar


How one can convey Cooper pairs between superconductors?


Stationary Josephson effect

What is the resistance of the junction?

IS S

V

Weak link two superconductors divided by a thin layer of insulator or normal conductor

For small currents, the junction is a superconductor!

Reason order parameters overlap in the weak link

B. Josephson


S S

AmplitudeSince superconductivity is the equilibrium state, the overlap leads to the change in the Gibbs free energy.

This energy difference is sensitive to the phase difference of the order parameter (the order parameter is complex).

We will show that it leads to the persistent currentthrough the junction the Josephson effect.


To calculate the current let us introduce an auxiliary small magnetic field with vector potential A which penetrates the junction. Then


Josephson interferometer

Denote:

Most sensitive magnetometer - SQUID

(after intergration)


y

x

Josephson junctions in magnetic field

1 2

Penetrated regions

Narrow junction > H= const

Therefore


In a wide junction the magnetic field created by the Josephson current becomes important. Then H and A become dependent on z

From the Maxwell equation

Ferrel-Prange equation

Josephson penetration length

Distribution of current in narrow and wide contacts

Josephson vortices

(fluxons)


Non-stationary Josephson effect

Due to the gauge invariance the electric potential in a superconductor can enter only in combination

Thus, the phase acquires the additional factor

Here is the phase difference while V is voltage across the junction.


Thus, is the voltage V is kept constant, then

where is the Josephson frequency

This equation allows to relate voltage and frequency, which is crucial for metrology.


Dynamics of a Josephson junction: I-V curve

A particle with

In a washboard potential


Macroscopic quantum tunneling

A macroscopic Josephson junction can escape from

its ground state via quantum tunneling like the -decay in nuclear

physics.

Quantum effects were observed through the shape of an I-V curve


Suppose that one modulates the voltage as

Then

Important application detection of electromagnetic signals

Josephson junction in an a. c. field


Then one can easily show that at a

time-independent step appears in the I-V-curve, its

amplitude being

Shapira steps


Applications


Metrology, Volt standard

High frequency applications

Magnetometers, SQUIDs

Amplifiers, SQUIDs

Imaging, MRI, SQUIDs

Main Applications


Medicine, biophysics and chemistry

Biomagnetism

Biophysics:- Diagnostics by magnetic tagging of antibodies-Special frequency characteristics, no rinsing

MRI (Magetic Resonance Imaging)- Low frequency, low noise amplifiers, sc solenoids

NMR (Nuclear Magnetic Resonance)-Low frequency, small fields, sc solenoids

NQR (Nuclear Quadropole Resonance)- Low frequency, low noise amplifiers, sc solenoids


Summary

Andreev reflection allows coherent transformation of normal quasiparticles to Cooper pairs.

Cooper pairs can be transferred through tunneling barriers via Josephson effect.

Coulomb blockade phenomena manifest themselves as specific parity effect in superconductor grains.

Manipulation Cooper pairs allow devices of a new type, e. g., serving as building blocks for quantum computation

Superconductivity at nanoscaleSlide Number 2Tunneling in superconductorsSlide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17How one can convey Cooper pairs between superconductors?Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Non-stationary Josephson effectSlide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Summary

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Superconductivity at nanoscale - folk.uio.nofolk.uio.no/yurig/Nanotechnology/Superconductivity/... · In which way superconductivity manifests itself at nanoscale? Superconductivity