Dr. Vadim Cheianov

Fermi surface

by Vadim Cheianov

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The Fermi surface is a surface in the momentum space characterizing the ground state of a Fermi liquid. It is defined as the surface of discontinuity of the momentum distribution function of the constituent particles.
In the Fermi gas model, describing a homogeneous system of non-interacting fermions, the ground state distribution of particles is given by the Fermi-Dirac function
where is the energy of a particle as a function of its momentum and is the Fermi energy. The Fermi surface is found as a solution to the algebraic equation
In a system of interacting fermions the momentum distribution function is defined as the vacuum expectation value
where is the creation (annihilation) operator of a fermion with spin and momentum . Under conditions defining the Landau Fermi liquid experiences a jump at a surface in the reciprocal space defining the Fermi surface of the interacting system.
Of particular importance is the case of a spherical Fermi surface, which is called the Fermi sphere. The radius of the Fermi sphere in the reciprocal space is called the Fermi momentum . The Kohn-Luttinger theorem states that in the absence of spontaneously broken symmetries the radius of the Fermi sphere does not depend on interactions between particles. For a system of spin fermions at particle density the Fermi momentum is