In a BEC, all particles occupy the lowest energy state, known as the ground state, resulting in a state of matter with unique properties.

Cooper pairing, where electrons form pairs and behave as bosons, is the underlying mechanism for superconductivity, allowing electrons to flow without resistance.

The critical temperature (Tc) is the temperature above which a superconductor loses its superconducting properties and transitions to a normal state.

The Fractional Quantum Hall Effect arises from the quantization of Hall resistance in two-dimensional electron systems, exhibiting plateaus at fractional values of the von Klitzing constant.

Quantum spin liquids are characterized by the absence of magnetic ordering due to competing interactions between spins, leading to a disordered magnetic state.

Copper oxide-based materials, also known as cuprates, are a class of materials that exhibit high-temperature superconductivity, with some compounds having critical temperatures above 100 Kelvin.

Non-Fermi liquids, unlike Fermi liquids, do not have a well-defined Fermi surface due to strong interactions between quasiparticles, leading to deviations from Fermi liquid behavior.

Majorana fermions, quasiparticles that are their own antiparticles, arise in topological superconductors, where the superconducting order parameter has a non-trivial topological structure.

Topological insulators are characterized by a conducting surface and an insulating bulk, with the surface states protected by topological invariants, leading to unique electronic properties.

Angle-resolved photoemission spectroscopy (ARPES) is a powerful technique for studying the electronic structure of quantum materials, providing information about the momentum and energy of electrons near the Fermi surface.

Mott insulators are characterized by strong electron-electron interactions that prevent electrons from hopping between lattice sites, leading to an insulating state, while band insulators arise from a filled valence band.

Excitons, quasiparticles consisting of an electron and a hole bound together by Coulomb attraction, are formed in semiconductors due to electron-hole recombination.

A quantum critical point is a phase transition where quantum fluctuations, rather than thermal fluctuations, drive the system's behavior, leading to unique and often unconventional phenomena.

Topological insulators are materials that exhibit the quantum spin Hall effect, where spin-polarized edge states conduct electricity while the bulk remains insulating.

Non-BCS superconductors, unlike BCS superconductors, do not have a gap in their excitation spectrum, meaning that there are no energy states below a certain energy level.