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In this lectures I discuss the electronic liquid crystal (ELC) phases in correlated electronic systems, what these phases are and in what context they arise. I will go over the strongest experimental evidence for these phases in a variety…
When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a…
We report first ab initio relativistic correlation calculations of potential curves for ten low-lying electronic states, effective electric field on the electron and hyperfine constants for the ^3\Delta_1 state of cation of a heavy…
We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor $\nu \gg 1$ and in the presence of a quenched disorder. In the framework of the Hartree-Fock approximation, we obtain the…
When magnetic field is applied to metals and semimetals quantum oscillations appear as individual Landau levels cross the Fermi level. Quantum oscillations generally do not occur in superconductors (SC) because magnetic field is either…
We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy…
The electron states in a size-quantaized coated semiconductor wire in a uniform magnetic field applied parallel to the wire axis is considered. The wave functions are found and the equation for determination of energy eigenvalues depending…
We present an effective theory describing the low-energy properties of an interacting 2D electron gas at large non-integer filling factors $\nu\gg 1$. Assuming that the interaction is sufficiently weak, $r_s < 1$, we integrate out all the…
We investigate non-perturbative features of a three-dimensional Abelian Higgs model with singly- and doubly-charged scalar fields coupled to a single compact Abelian gauge field. The model is pretending to describe various planar systems of…
Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of…
Energies and wave functions of edge states in twodimensional electron gas are evaluated for a finite step potential barrier model. The spectrum, instead of smooth bending of Landau branches in the vicinity of the barrier acquires a steplike…
We review the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field. One of its most salient features is the relativistic quantum Hall effect the observation of which has been the…
When a gas of electrons is confined to two dimensions, application of a strong magnetic field may lead to startling phenomena such as emergence of electron pairing. According to a theory this manifests itself as appearance of the fractional…
Electron sheaths form near the surface of objects biased more positive than the plasma potential, such as in the electron saturation region of a Langmuir probe trace. Generally, the formation of electron sheaths requires that the…
Coupled semiconductor quantum dots form artificial molecules where relevant energy scales controlling the interacting ground state can be easily tuned. By applying an external magnetic field it is possible to drive the system from a weak to…
What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should…
Superfluidity of spatially separated electrons and holes and unbalanced two-layer electron system in high magnetic field is considered. The temperature of the Kosterlitz-Thouless transition to a superfluid state is obtained as a function of…
We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the…
The quantum dynamics of quasi-one-dimensional ring with varying electron filling factor is investigated in presence of external electric field. The system is modeled within Hubbard Hamiltonian with attractive Coulomb correlation, which…
We study the behavior of the extended states of a two-dimensional electron system in silicon in a magnetic field, B. Our results show that the extended states, corresponding to the centers of different Landau levels, merge with the lowest…