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Instabilities of a Fermi Gas with Nested Fermi Surfaces

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.