Microscopic theory of a strongly correlated two-dimensional electron

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states $\mathcal N(T)$ and ratio $C(T)/T$ of the specific heat to the temperature, occurs at a very low temperature $T_{\diamond}$ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution $n(p, T)$ depends slightly on the temperature, which is manifested in the maximum of the specific heat $C(T)$ near $T_*$, appears through a crossover at temperatures $T\sim T_*>T_{\diamond}$. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states $\mathcal N(T)\propto T^{-\alpha}$ with the exponent $\alpha\simeq 2/3$.