Week 6 Solid State Chemistry

conductivity formula

sigma= number of electrons x charge of electrons x mobility of electrons

conductivity and temperature

• in metals, increasing temp decreases conductivity

• in insulators, increasing temp very slightly increases conductivity

• in semiconductors, increasing temp greatly increases conductivity

resistivity and temperature

resistivity decreases with temperature

phonon

• a lattice vibration quantum particle

• at 0K, all phonons are frozen

• at high temperature, phonon-electron collisions are the source of resisitivity

• they are also responsible for the heat capacity of materials

• normally there is only a small fraction of electrons in the conduction band, even in good conductors

how to get close to 0K

• liquid nitrogen gets you to 85K

• liquid helium can get between 4K and 0.2K depending on the method and isotopes used

Resistivity at 0K

• even at near absolute zero, metals still show some slight resistivity

• they need to be purified to get rid of this

• mercury was the easiest to purify and it was found to be the first super conductor with 0 resistivity

can all metals be superconductors

• no not all metals can be semiconductors

• ferromagnetic materials cannot be superconductors

what can change superconductivity

• magnetic fields

• changing the temperature to a higher one

  

The 3 core concepts of BCS Theory

1. superconducting state must have a band gap

2. the process of super conduction must involve multiple electrons

3. The crystal lattice interacts and is involved in the process

Core 1

• the heat capacity of a SC needs to be measured

• in a normal meta, the curve is a linear straight line

• in a superconductor, the curve goes up exponentially and once critical temperature is reached, it drops again

• this is similar to how a semiconductor would behave, indicating super conductors must have some sort of very small band gap

Core 2

• the band gap that opens is very small (in the meV region)

• the closer we get to Tc, the small the gap gets until it vanishes

• this behaviour is similar to bond breaking

• band gap can be measured using microwaves

Core 3

• changing the isotope abundance changes Tc

• this should not happen

• this indicates that the lattice and phonons are actively involved in determining Tc

• 𝑇𝑐 ∝ 𝑀−𝛽, where beta is= 0.5 and M is the mass of the isotope

Cooper pairs

• a pair of electrons that exists due to indirect e-e interactions from the lattice

• act like bosons which are a type of quantum particle

• bosons are immune to pauli exclusion principle

• cooper pairs are what allow superconductors to attract with no resistance we believe

• the reason SC do not work above Tc and under magnetic fields is because you break the cooper pairs

• cooper pairs have spin and down so a magnetic field breaks them beause it wants them to be both spin up which is not possible

How are cooper pairs formed

at the very low temperatures, as the electron moves through the lattice, it slightly distorts the lattice and phonons, leaving behind a very rich positive charge which attracts a second electron, creating and moving as pairs

The Meissner Effect

• super conductors have perfect diamagnetism

• this means that they perfectly repel external magnetic fields

• all cooper pairs collapse into a quantum state and create screening currents that cancel out applied magnetic field

• this causes a material to float

Type I SC

• no magnetic field can pass through

• has a single critical magnetic point (after which material is no longer a SC)

• usually are most elemental SC

  

Type II SC

• there is a vortex which allows some of the magnetic field to pass through but not actually affect the material

• has higher Hc and Tc that type I

• mobility of vortex can be blocked by defects

• most alloys and doped materials are type II

• high temp SC can only be type II

• there are a few elemental SC that are type II

• have 2 Hc

  

High temperature SC

• are generally made from a rare earth metal (2-x), an alkali metal (x), and copper oxide

• no one knows how they actually work

• Tc bigger than 100K

• eg. YBaCuO or LaBaCuO

• it seems unlikely that they form cooper pairs as at higher temperature cooper pairs become too unstable

Cuprate superconductors

• arranged in different sheets which works well due to the variable oxidation states of copper

• CuO4 is a 2D layer and acts as an electron sink

• CuO5 is a 3D layer and acts as a storage point for charge carriers so the SC can work

• cuprate SC are highly defective in oxygen

• the more layers of copper oxide there are, the higher Tc is

adding holes to SC

• the most common way of doping

• helps increase Tc

• adding holes allows for electron to finally be able to move more freely around the lattice and form cooper pairs

adding electrons to SC

• extra electrons help ease/break the static arrangement

• this helps in creating more cooper pairs

• adding electrons however does not increase the Tc of SCs

Why adding holes and electrons is a sensitive process

there is a very small range for doping the material either with holes or electrons that actually works

Resonance valance bond theory (RVB) of HT SCs

• assumes electrons in unpaired Cu orbitals will pair with neighboring oxygen electrons and move

• Instead of staying in one fixed pair, the electrons exist in a "superposition"—meaning they are constantly switching which neighbor they are paired with. This creates a fluid-like state of shifting pairs.

• there is no external force or "glue" pulling them together.

• When you "dope" the material (add holes), these pre-existing pairs that were "stuck" suddenly gain the room to move around, creating the superconducting current.

Magnetic spin fluctuation exchange

• one electron creates a magnetic ripple in the material, and a second electron drops into that ripple.

• This magnetic partnership allows the electron pairs to glide through the crystal lattice entirely friction-free, enabling high-temperature superconductivity.

• this theory divides electrons into subsystems which is controversial

Electromagnets

• there is no current resistance

• current needs to be increased slowly

• there is quench protection which is there in the case that parts of the material slowly become non superconductive and all the excess energy releases causing an explosion

• The material has to be winded in small coils to

  maximise the high-current area

• high magnetic fields produced

magnetic levitating trains

• this concept is being developed in japan

• the lack of friction could allow for speeds up to 600K an hour

• Superconducting NbTi magnets are cooled to 4 K on the train tracks and are used for both levitation and propulsion

Superconducting QUantum Interference Devices (SQUID)

• consists of a superdonducting loop interupted by this insulating josephson junctions

• the device is used to measure incredibly thin magnetic fields and is in things such as brain imaging (EEG) and quantum computers

• cooper pairs cause uniform wave across the loop