Fermions under strong repulsion: from multiconnected Fermi surfaces to Fermi condensation

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We consider a system of fermions with mass m and model repulsive interaction U(q) = g/√q² + q₀², where q is the momentum transfer, q₀ the screening constant, and g > 0 the coupling constant. It is shown that at g > gcr > 3π²/m the system ground state is changed from fully occupied Fermi sphere to multiconnected Fermi sphere (MFS), consisting in N fully occupied spherical layers (icebergs) separated by empty spacers. An effective description is developed for such states at N >> 1, showing their tendency at N → ∞ to the Fermi condensate (FC) state known for the model U(q) = g/q [Khodel, Shaginyan, JETP Lett., 51, 553, 1990]. At finite temperatures, a crossover is predicted from the Fermi liquid behavior of MFS with effective mass m* m N/ln(N) to non-Fermi-liquid behavior with m* ∝ 1/T at T > T* TF ln(N)/N.