Condensed matter physics

Condensed matter physics is one of the best examples of emergence. We start with a bunch of small elements which we understand fully at the required level (atoms, electrons, quantum mechanics) but then there are complex properties that show up when we put a bunch of them together.

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.

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!

Bibliography:

Previously on EdX: www.edx.org/learn/quantum-physics-mechanics/delft-university-of-technology-topology-in-condensed-matter-tying-quantum-knots "DelftX: Topology in Condensed Matter: Tying Quantum Knots".

But then they regained their sanity and put the source code on GitHub: github.com/topocm/topocm_content and is CC BY-SA.

Uses an ungodly combination of Jupyter notebooks and Pelican.

How are the bands measured experimentally?

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

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Ciro Santilli distinctly remembers being taught that at basic electrical engineering school during Ciro Santilli's undergrad studies at the University of São Paulo.

It really allows you to do alternating current calculations much as you'd do DC calculations with resistors, quite poweful. It must have been all the rage in the 1950s.

If you adda bit of impurities to certain materials, at low temperatures of a few Kelvin their resistivity actually starts increasing if you go below a certain critical temperature.

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:

Lecture notes:

Media:

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

andor.oxinst.com/learning/view/article/measuring-resistance-of-a-superconducting-sample-with-a-dry-cryostat Not a video, but well done, by Oxford Instruments.

TODO!!! Even this is hard to find! A clean and minimal one! Why! All we can find are shittly levitating YBCO samples in liquid nitrogen! Maybe because liquid helium is expensive?

We know that superfluidity happens more easily in bosons, and so electrons joins in Cooper pairs to form bosons, making a superfluid of Cooper pairs!

Isn't that awesome!

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

The dream of course being room temperature and pressure superconductor.

LK-99:

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:

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As of 2023 the most important ones economicaly were:The main application is Magnetic resonance imaging. Both of these are have to be Liquid helium, i.e. they are not "high-temperature superconductor" which is a pain. One big strength they have is that they are metallic, and therefore can made into wires, which is crucial to be able to make electromagnetic coils out of them.

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 the following Josephson effect regimes 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:

In 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling (1963, Prediction of the Josephson effect)".

In 1963 Philip W. Anderson and John M. Rowell published their paper that first observed the effect as Section "Possible new effects in superconductive tunnelling (1963, Prediction of the Josephson effect)".

Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:

We were all - Josephson, Pippard and myself, as well as various other people who also habitually sat at the Mond tea and participated in the discussions of the next few weeks - very much puzzled by the meaning of the fact that the current depends on the phase

As part of the course Anderson had introduced the concept of broken symmetry in superconductors. Josephson "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally."

The inaugural that predicted the Josephson effect.

Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.

Paywalled by Elsevier as of 2023 at: www.sciencedirect.com/science/article/abs/pii/0031916362913690

Paper by Philip W. Anderson and John M. Rowell that first (?) experimentally observed the Josephson effect.

Paywalled by the American Physical Society as of 2023 at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.10.230

DOI: doi.org/10.1103/PhysRevLett.10.230

TODO understand the graphs in detail.

They used tin-oxide-lead tunnel at 1.5 K. TODO oxide of what? Why two different metals? They say that both films are 200 nm thick, so maybe it is:

A reconstruction of their circuit in Ciro's ASCII art circuit diagram notation TODO:

There are not details of the physical construction of course. Reproducibility lol.

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 7. "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.

TODO is there any relationship between this and the Josephson effect?

Experimental observation published as Experimental Evidence for Quantized Flux in Superconducting Cylinders.

This appears to happen to any superconducting loop, because the superconducting wave function has to be continuous.

Video "Superconducting Qubit by NTT SCL (2015)" suggests that anything in between gets cancelled out by a superposition of current in both directions.

Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43

The first published experimental observation of the magnetic flux quantum.

The paper that follows it in the journal is also of interest, "Theoretical Considerations Concerning Quantized Magnetic Flux In Superconducting Cylinders" by N. Byers and C. N. Yang, it starts:

In a recent experiment, the magnetic flux through a superconducting ring has been found to be quantized in units of ch/2e. Quantization in twice this unit has been briefly discussed by London' and by Onsager. ' Onsager' has also considered the possibility of quantization in units ch/2e due to pairs of electrons forming quasi-bosons.

So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.

Dumping the fitures at: archive.org/details/experimental-evidence-for-quantized-flux-in-superconducting-cylinders One day we can also dump the paper scans when it goes into the public domain in 2056! Public domain scientific paper by year.

The inverse of the magnetic flux quantum.

As mentioned in True Genius: The Life and Science of John Bardeen page 224, the idea of symmetry breaking was a major motivation in Josephson's study of the Josephson effect.

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

TODO WTF is this? How is it built? What is special about it?

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.

Toy model of matter that exhibits phase transition in dimension 2 and greater. It does not provide numerically exact results by itself, but can serve as a tool to theorize existing and new phase transitions.

Each point in the lattice has two possible states: TODO insert image.

As mentioned at: stanford.edu/~jeffjar/statmech/intro4.html some systems which can be seen as modelled by it include:

Also has some funky relations to renormalization TODO.

Bibliography:

TODO what it means to solve an Ising model in general?

stanford.edu/~jeffjar/statmech/lec4.html gives some good notions:

Bibliography:

A tiny idealized magnet! It is a very good model if you have a small strong magnet interacting with objects that are far away, notably other magnetic dipoles or a constant magnetic field.

The cool thing about this model is that we have simple explicit formulas for the magnetic field it produces, and for how this little magnet is affected by a magnetic field or by another magnetic dipole.

This is the perfect model for electron spin, but it can also be representative of macroscopic systems in the right circumstances.

The intuition for the name is likely that "dipole" means "both poles are on the same spot".

Applications: produce high magnetic fields forAs of the early 2020s, superconducting magnets predominantly use low temperature superconductors Nb-Ti and Nb-Sn, see also most important superconductor materials, but there were efforts underway to create practical high-temperature superconductor-based magnets as well: Section "High temperature superconductor superconducting magnet (HTS magnet)".

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.

They are pioneers in making superconducting magnets, physicist from the university taking obsolte equipment from the uni to his garage and making a startup kind of situation. This was particularly notable for this time and place.

They became a major supplier for Magnetic resonance imaging applications.

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 20. "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?

Bibliography:

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 20. "How Lasers Work by Scientized (2017)"

Sample usages:

The opposite of elementary particle.

As a phisicist once amazingly put it in a talk Ciro watched:

It all depends on how much energy you have to probe nature with. Previously, we thought protons were elementary particles. But then we used more energy and found that they aren't.

If some alien race had even less energy, they might not know about electrons at all, and could think that anyons are actually elementary.

Being an "elementary particle" is always a possibly temporary label.

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Affiliation: University of São Paulo.