Condensed matter physics

Includes fun things like:

As of 2020, this is the other "fundamental branch of physics" besides to particle physics/nuclear physics.

Condensed matter is basically chemistry but without reactions: you study a fixed state of matter, not a reaction in which compositions change with time.

Just like in chemistry, you end up getting some very well defined substance properties due to the incredibly large number of atoms.

Just like chemistry, the ultimate goal is to do de-novo computational chemistry to predict those properties.

And just like chemistry, what we can actually is actually very limited in part due to the exponential nature of quantum mechanics.

Also since chemistry involves reactions, chemistry puts a huge focus on liquids and solutions, which is the simplest state of matter to do reactions in.

Condensed matter however can put a lot more emphasis on solids than chemistry, notably because solids are what we generally want in end products, no one likes stuff leaking right?

But it also studies liquids, e.g. notably superfluidity.

One thing condensed matter is particularly obsessed with is the fascinating phenomena of phase transition.

Bibliography:

AMO is a slightly more general area than condensed matter physics, including related phenomena with smaller numbers atoms and optics. The two terms are however sometimes used as synonyms. The term AMO has gained wide usage and acceptability, see e.g.:

If Ciro had had greater foresight, this might have been what he studied at university!

Affiliation: University of São Paulo.

How are the bands measured experimentally?

Why are there gaps? Why aren't bands infinite? What determines the width of gaps?

Bibliography:

The basis of 1970-20XX computers, gotta understand them I guess.

Most notable example: gallium arsenide, see also: gallium arsenide vs silicon.

An important class of semiconductors, e.g. there is a dedicated III-V lab at: École Polytechnique: www.3-5lab.fr/contactus.php

Experiments:

Lectures:

Media:

Transition into superconductivity can be seen as a phase transition, which happens to be a second-order phase transition.

As of 2020, basically means "liquid nitrogen temperature", which is much cheaper than liquid helium.

Upside: superconducting above 92K, which is above the 77K of liquid nitrogen, and therefore much much cheaper to obtain and maintain than liquid helium.

Downside: it is brittle, so how do you make wires out of it? Still, can already be used in certain circuits, e.g. high temperature SQUID devices.

Discovered in 1988, the first high-temperature superconductor which did not contain a rare-earth element.

Superconductivity is one of the key advances of 21st century technology:

TODO, come on, Internet!

Bibliography.

No, see: superconductor I-V curve.

Bibliography:

Main theory to explain Type I superconductors very successfully.

TODO can someone please just give the final predictions of BCS, and how they compare to experiments, first of all? Then derive them.

High level concepts:

Discrete quantum effect observed in superconductors with a small insulating layer, a device known as a Josephson junction.

To understand the behaviour effect, it is important to look at the Josephson equations consider two cases separately:

A good summary from Wikipedia by physicist Andrew Whitaker:

at a junction of two superconductors, a current will flow even if there is no drop in voltage; that when there is a voltage drop, the current should oscillate at a frequency related to the drop in voltage; and that there is a dependence on any magnetic field

Bibliography:

This is what happens when you apply a DC voltage across a Josephson junction.

It is called "AC effect" because when we apply a DC voltage, it produces an alternating current on the device.

By looking at the Josephson equations, we see that $V(t)=k$ a positive constant, then $\phi$ just increases linearly without bound.

Therefore, from the first equation: we see that the current will just vary sinusoidally between $\pm I_c$.

This meas that we can use a Josephson junction as a perfect voltage to frequency converter.

Wikipedia mentions that this frequency is $484GHz/mV$, so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.

Also it is likely not going to be very useful for many practical applications in this mode.

An I-V curve can also be seen at: Figure 4. "Electron microscope image of a Josephson junction its I-V curve".

If you shine microwave radiation on a Josephson junction, it produces a fixed average voltage that depends only on the frequency of the microwave. TODO how is that done more preciesely? How to you produce and inject microwaves into the thing?

It acts therefore as a perfect frequency to voltage converter.

The Wiki page gives the formula: en.wikipedia.org/wiki/Josephson_effect#The_inverse_AC_Josephson_effect You get several sinusoidal harmonics, so the output is not a perfect sine. But the infinite sum of the harmonics has a fixed average voltage value.

And en.wikipedia.org/wiki/Josephson_voltage_standard#Josephson_effect mentions that the effect is independent of the junction material, physical dimension or temperature.

All of the above, compounded with the fact that we are able to generate microwaves with extremely precise frequency with an atomic clock, makes this phenomenon perfect as a Volt standard, the Josephson voltage standard.

TODO understand how/why it works better.

Two equations derived from first principles by Brian Josephson that characterize the device, somewhat like an I-V curve: where:

Note how these equations are not a typical I-V curve, as they are not an instantaneous dependency between voltage and current: the history of the voltage matters! Or in other words, the system has an internal state, represented by the Josephson phase at a given point in time.

To understand them better, it is important to look at some important cases separately:

Maximum current that can flow across a Josephson junction, as can be directly seen from the Josephson equations.

Is a fixed characteristic value of the physical construction of the junction.

A function $\mathbb{R}\to \mathbb{R}$ defined by the second of the Josephson equations plus initial conditions.

It represents an internal state of the junction.

A device that exhibits the Josephson effect.

The inverse of the magnetic flux quantum.

The most practical/precise volt standard.

It motivated the definition of the ampere in the 2019 redefinition of the SI base units

Quick NIST article about it: www.nist.gov/news-events/news/2013/04/primary-voltage-standard-whole-world (archive)

The wiki page en.wikipedia.org/wiki/Josephson_voltage_standard contains amazing schematics of the device, apparently made by the US Government.

Can be used as a very precise magnetometer.

There are high temperature yttrium barium copper oxide ones that work on liquid nitrogen.

Two parallel Josephson junctions.

In Ciro's ASCII art circuit diagram notation:

Specific type of Josephson junction. Probably can be made tiny and in huge numbers through photolithography.

Inward Bound by Abraham Pais (1988) page 282 shows how this can be generalized from the Maxwell-Boltzmann distribution

Mentioned a lot in the context of superconducting quantum computers, e.g. youtu.be/t5nxusm_Umk?t=268 from Video "Quantum Computing with Superconducting Qubits by Alexandre Blais (2012)",

Mentioned at: Video "Quantum Computing with Light by Quantum Light University of Sheffield (2015)" youtu.be/nyK-vhoOBpE?t=185.

www.youtube.com/watch?v=PbuiIhr0LVA 7 Different Types of Plastic and Their Uses by Orange Plastics Academy (2018) Does not mention packaging foams.

The wiki comments: en.wikipedia.org/w/index.php?title=Ferromagnetism&oldid=965600553#Explanation

The Bohr–van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.

Also has some funky relations to renormalization TODO.

A tiny idealized magnet! Likely a good approximation for electron spin in many cases.

Wikipedia has done well for once:

The current to the coil windings is provided by a high current, very low voltage DC power supply, since in steady state the only voltage across the magnet is due to the resistance of the feeder wires. Any change to the current through the magnet must be done very slowly, first because electrically the magnet is a large inductor and an abrupt current change will result in a large voltage spike across the windings, and more importantly because fast changes in current can cause eddy currents and mechanical stresses in the windings that can precipitate a quench (see below). So the power supply is usually microprocessor-controlled, programmed to accomplish current changes gradually, in gentle ramps. It usually takes several minutes to energize or de-energize a laboratory-sized magnet.

Used to explain the black-body radiation experiment.

Published as: On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).

The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):

Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'

This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.

TODO how can it be derived from theoretical principles alone? There is one derivation at; en.wikipedia.org/wiki/Planck%27s_law#Derivation but it does not seem to mention the Schrödinger equation at all.

Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.

One important quantum mechanics experiment, which using quantum effects explain the dependency of specific heat capacity on temperature, an effect which is not present in the Dulong-Petit law.

This is the solid-state analogue to the black-body radiation problem. It is also therefore a quantum mechanics-specific phenomenon.

Observation that all solids appear to have the same constant heat capacity per mole.

It can be seen as the limit case of an Einstein solid at high temperatures. At lower temperatures, the heat capacity depends on temperature.

Wikipedia mentions that it is completely analogous to Planck's law, since both are

The key advantages of lasers over other light sources are:

Bibliography:

The type of laser described at: Video 16. "How Lasers Work by Scientized (2017)", notably youtu.be/_JOchLyNO_w?t=581. Mentioned at: youtu.be/_JOchLyNO_w?t=759 That point also mentions that 4-level lasers also exist and are more efficient. TODO dominance? Alternatives?

You could put an LED in a cavity with a thin long hole but then, most rays, which are not aligned with the hole, will just bounce inside forever producing heat.

So you would have a very hot device, and very little efficiency on the light output. This heat might also behave like a black-body radiation source, so you would not have a single frequency.

The beauty of lasers is the laser cavity (two parallel mirrors around the medium) selects parallel motion preferentially, see e.g.: youtu.be/_JOchLyNO_w?t=832 from Video 16. "How Lasers Work by Scientized (2017)"

Sample usages: