Fermi surface | EPFL Graph Search

Are you an EPFL student looking for a semester project?

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology. Consider a spin-less ideal Fermi gas of particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy is given by where, is the mean occupation number of the state is the kinetic energy of the state is the chemical potential (at zero temperature, this is the maximum kinetic energy the particle can have, i.e. Fermi energy ) is the absolute temperature is the Boltzmann constant Suppose we consider the limit . Then we have, By the Pauli exclusion principle, no two fermions can be in the same state. Therefore, in the state of lowest energy, the particles fill up all energy levels below the Fermi energy , which is equivalent to saying that is the energy level below which there are exactly states. In momentum space, these particles fill up a ball of radius , the surface of which is called the Fermi surface. The linear response of a metal to an electric, magnetic, or thermal gradient is determined by the shape of the Fermi surface, because currents are due to changes in the occupancy of states near the Fermi energy. In reciprocal space, the Fermi surface of an ideal Fermi gas is a sphere of radius determined by the valence electron concentration where is the reduced Planck's constant. A material whose Fermi level falls in a gap between bands is an insulator or semiconductor depending on the size of the bandgap. When a material's Fermi level falls in a bandgap, there is no Fermi surface. Materials with complex crystal structures can have quite intricate Fermi surfaces.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (24)

Related people (22)

Related concepts (14)

Related courses (9)

Related lectures (78)

, , , ,

The cascade of electronic phases in CsV3Sb5 raises the prospect to disentangle their mutual interactions in a clean, strongly interacting kagome lattice. When the kagome planes are stacked into a crys

AMER PHYSICAL SOC2022

Anisotropic and nonlinear transport in microstructured 3D topological semimetals

Xiangwei Huang

Topological semimetals are frequently discussed as materials platforms for future electronics that exploit the remarkable properties of their quasiparticles. These ideas are mostly based on dispersion

EPFL2022

, ,

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many electron wave funct

NATL ACAD SCIENCES2021

K·p perturbation theory

In solid-state physics, the k·p perturbation theory is an approximated semi-empirical approach for calculating the band structure (particularly effective mass) and optical properties of crystalline solids. It is pronounced "k dot p", and is also called the "k·p method". This theory has been applied specifically in the framework of the Luttinger–Kohn model (after Joaquin Mazdak Luttinger and Walter Kohn), and of the Kane model (after Evan O. Kane).

Angle-resolved photoemission spectroscopy

Angle-resolved photoemission spectroscopy (ARPES) is an experimental technique used in condensed matter physics to probe the allowed energies and momenta of the electrons in a material, usually a crystalline solid. It is based on the photoelectric effect, in which an incoming photon of sufficient energy ejects an electron from the surface of a material. By directly measuring the kinetic energy and emission angle distributions of the emitted photoelectrons, the technique can map the electronic band structure and Fermi surfaces.

Free electron model

In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.

The course is aimed at giving a general understanding and building a feeling of what electronic states inside a crystal are.

This course gives an introduction into Solid State Physics (crystal structure of materials, electronic and magnetic properties, thermal and electronic transport). The course material is at the level o

This lecture gives an introduction to Solid State Physics, namely to their crystal and electronic structure, their magnetic properties, as well as to their thermal and electric conductance. The level

Band Structure: Energy Levels and Fermi Sphere

Explains energy levels, Fermi sphere, and periodic potentials in different dimensions.

Quantum and Nanocomputing: Molecular Energy Spectrum and Conduction Mechanisms

Explores molecular energy spectrum analysis, conduction mechanisms in quantum dots, and transmission spectrum in molecular systems.

What drives superconductivity

Explores the quantum-mechanical nature of superconductivity, covering basic quantum mechanics, Cooper pair formation, and the energy gap in superconductors.