1/ What is the most important sea in the universe? It is not the Mediterranean or Caspian, not the Dead sea or the sea of Galilee. It is the FERMI SEA. Without it, human society would be unrecognizable. But its existence remains among the deepest mysteries.

2/The Fermi sea is a hidden sea of electrons (directly visible in momentum space), typically with ~10^23 electrons/cm^3. Deformations of the surface of the Fermi sea from voltage, temperature, and chemical potential gradients are responsible for the crucial properties of metals.

3/ The Fermi sea is responsible for the extremely high, nearly perfect, electrical conductivity of metals. It is this high electrical conductivity that is responsible for their shiny appearance, making them appealing to use as currency and stores of value.

4/ The high electrical conductivity is also what allows us to transmit electrical power efficiently. It is also the reason we are able to create and transmit electrical signals through cables, and transmit and receive signals through electromagnetic waves using antennae.

5/ Even the act of cooking on a stove with pots and pans mostly relies on the high thermal conductivity of metals, which again originates from the Fermi sea.

6/ Semiconductors, like silicon, are defined by the fact that they have very small Fermi seas. So small that we are able to fully deplete them with the meager voltages that we are able to control in small devices.

7/ This allows us to build transistors, allowing us to control like a dam the flow of electrical current from Fermi sea to shiny Fermi sea. This in turn allows us to make switches that we can use to create logical circuits and enable the modern digital era.

8/ Magnetism at the macroscopic level is only ubiquitous in metals, like iron (although on rare occasion ferromagnetism is observed in insulators). The Fermi sea plays a crucial role in the spontaneous ordering of electron spins, leading to a macroscopic magnetic moment.

9/Magnetism is what allows compasses, which allowed us to navigate the Earth without relying on starlight. It is also the basic physics that we utilize in disk drives, which allows us to store massive amounts of information digitally, again enabling the modern era.

10/ Superconductors arise as an instability of the surface of the Fermi sea. Lattice vibrations induce an effective attractive interaction between electrons, causing them to pair up and Bose condense, leading to the spontaneous breaking of charge conservation symmetry.

11/ This effect leads to perfect electrical conduction, perfect diamagnetism, and the most precise quantization of magnetic flux. It can be thought of as effectively giving the photon a mass; a conceptually equivalent mechanism is responsible for all mass in the universe.

12/ Superconductors are useful for building powerful electromagnets, that can be used to power maglev trains and MRI machines. They are also crucial in many physical platforms for qubits, potentially enabling the much dreamed of quantum computing revolution.

13/ Now why is the Fermi sea so mysterious? From one point of view, it is extremely simple. If we ignore the fact that electrons interact with each other through the Coulomb interaction, the Fermi sea is a simple consequence of the Pauli exclusion principle.

14/ But why do its key properties continue to exist in the presence of the extremely strong electron-electron interactions?

15/ Our theory of metals, where we take into account electron-electron interactions is called Landau Fermi liquid theory. It is a far-reaching theory which was initially applied to liquid He-3 by Lev Landau, and later applied to electrons in metals.

16/ The basic idea of the Fermi liquid theory of metals is that interacting electrons can be thought of essentially as non-interacting electrons with some minor modifications, for example a modified effective mass.

17/ This is easy to justify if we assume that electron-electron interactions are extremely weak compared to the kinetic energy of the electrons. However real metals are in the opposite limit. The electron-electron interactions are almost 10 times as large as the kinetic energy.

18/ So we have no good justification for why Fermi liquid theory works in metals. It just does, and we have learned to live with it. Perhaps one day we will have a satisfactory answer.

19/ From a modern perspective, Fermi liquids are one of the most intriguing quantum states of matter. The electrons in a Fermi liquid are more highly entangled than in any other low temperature state of matter. This is the log violation of the area law of entanglement entropy.

20/ Fermi liquids also have the largest emergent symmetry seen in physics: an infinite dimensional symmetry, corresponding to the group of all possible maps from the surface of the Fermi sea to the circle. In two dimensions, this is the loop group of U(1), denoted LU(1).

21/ The surface of the Fermi sea is not smooth at zero temperature -- there is a step function singularity, like a cliff, where the electron density dramatically changes. This singularity is a key defining property of a Fermi liquid. It is surprisingly difficult to get rid of.

22/ It turns out it is easy to destroy the Fermi surface in one-dimensional systems, which gives us Luttinger liquids -- that is the subject for another day.

23/ People tried very hard, mainly in the early 1990s, to destroy the Fermi surface in higher dimensions. They were hoping that understanding this could be the key to unlocking the mysteries of high temperature superconductors.

24/ After all this work, we only know two basic ways of how to destroy the Fermi surface, neither of which we understand well enough. The first occurs when we tune certain parameters, like pressure or electron density, to induce a quantum phase transition.

25/ The other occurs in the fractional quantum Hall effect, and is known as the HLR state; it is one of the most striking quantum liquids ever seen, being described by an exotic version of quantum electrodynamics with an emergent gauge field coupled to an *emergent* Fermi sea.

26/ The question of understanding metals that are not Fermi liquids is so mysterious that we don't even know what to call them; we just call them "non-Fermi liquids." And only the bravest physicists dare to study them.

End of Thread.

#physics #quantum #condensedmatterphysics