One of the outstanding problems of modern condensed matter physics is the phase diagram and properties of strongly-interacting and disordered electron systems. The fascinating physics of strong correlations unveils when the Coulomb interaction energy exceeds the Fermi energy. The theoretical description of 2D systems has not reached a predictive stage yet, very little is known about fundamentals of strong electron-electron interactions, and about quantum ground states of disordered interacting 2D systems. |

Even the ordinarytwo dimensionalelectron system exhibits nontrivial and beautiful properties, not yet fully explained within the existing theories. As interparticle interactions increase, the electron compressibility changes sign, the effective mass and *g*-factor Lande grow, and the spin susceptibility (Pauli) sharply raises. Therefore, the “electrons” in strongly interacting two-dimensional electron system tend to **become heavier**, and tend to **spontaneous spin magnetization. **These tendencies in the limit of strong interactions lead to the emergence of novel states of electronic matter. It is anticipated that the phase diagram of strongly interacting two-dimensional (2D) systems is remarkably rich: a multitude of electronic phases might lie between the limiting cases of a conventional paramagnetic Fermi liquid (FL) at high densities, Wigner crystal (low densities, weak disorder), and antiferromagnetic strongly localized state (strong disorder). In particular, we recently discovered spontaneous formation of ferromagnetic spin-polarized droplets (FSD), coexisting with 2D Fermi liquid. Due to interactions, the 2D system exhibits a metallic conduction, the behavior that in a sharp contrast with that for the noninteracting electron gas.

In a specially designed two-dimensional system with an equal number of electrons and holes, the particles tends to form electron-hole pairs and to condense into more energetically favorable state of the exciton insulator.

(a) Schematic phase diagram of the excitonic insulator (EI). Vertical axis is the exciton binding energy, horizontal axis – energy gap between the electron and hole bands. (b) schematic temperature dependence of the resistivity temperature dependence for EI.

In the strongly interaction two-dimensional electron system subjected to an external quantizing magnetic field, a variety of novel phases emerge, such as Hall insulator, a state with fractionally quantized Hall resistance, reentrant transitions between the insulator and quantized Hall resistance state, composite state at half-integer filling of the Landau levels, etc. Under these conditions, the 2D system can be described as a gas of novel quasiparticles, the composite fermions consisting of electrons with flux quanta attached.

These wondering and unusual properties of strongly correlated low dimensional systems are studied in the SCES Laboratory.