Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents
نویسنده
چکیده
The ground state of an electron gas is characterized by the interparticle spacing to the effective Bohr radius ratio rs = a/a ∗ B. For polarized electrons on a two dimensional square lattice with Coulomb repulsion, we study the threshold value r∗ s below which the lattice spacing s becomes a relevant scale and rs ceases to be the scaling parameter. For systems of small ratios s/a ∗ B , s becomes only relevant at small rs (large densities) where one has a quantum fluid with a deformed Fermi surface. For systems of large s/a∗B, s plays also a role at large rs (small densities) where one has a Wigner solid, the lattice limiting its harmonic vibrations. The thermodynamic limit of physical systems of different a∗B is qualitatively discussed, before quantitatively studying the lattice effects occurring at large rs. Using a few particle system, we compare exact numerical results obtained with a lattice and analytical perturbative expansions obtained in the continuum limit. Three criteria giving similar values for the lattice threshold r∗ s are proposed. The first one is a delocalization criterion in the Fock basis of lattice site orbitals. The second one uses the persistent current which can depend on the interaction in a lattice, while it becomes independent of the interaction in the continuum limit. The third one takes into account the limit imposed by the lattice to the harmonic vibrations of the electron solid. PACS. 71.10.-w Theories and models for many-electron systems – 71.10.Fd Lattice fermion models – 73.20.Qt Electron solids
منابع مشابه
Electronic Properties of a Concentric Triple Quantum Nanoring
In this paper, we study the electronic properties of a concentric triple quantum ring using exact diagonalization technique. The energy spectra and magnetization for a single electron and two electrons, in the presence of an applied magnetic field, are calculated and discussed. It is shown that, for two-interacting electrons, the period of Aharonov-Bohm oscillations decreases to the half of tha...
متن کاملLattice numerical simulations of hydraulic fractures interacting with oblique natural interfaces
The hydraulic fracturing propagation is strongly influenced by the existence of natural fractures. This is a very important factor in hydraulic fracturing operations in unconventional reservoirs. Various studies have been done to consider the effect of different parameters such as stress anisotropy, toughness, angle of approach and fluid properties on interaction mechanisms including crossing, ...
متن کاملPersistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder
Using the persistent current I induced by an Aharonov-Bohm flux in square lattices with random potentials, we study the interplay between electronic correlations and disorder upon the ground state (GS) of a few polarized electrons (spinless fermions) with Coulomb repulsion. K being the total momentum, we show that I ∝ K in the continuum limit. We use this relation to distinguish between the con...
متن کاملThe Simultaneous Effect of Holding Safety Stock and Purchasing Policies on the Economic Production Quantity Model Subject to Random Machine Breakdown
In this paper, we develop an economic production quantity (EPQ) model under machine breakdown and two types of repair (corrective and preventive). also, study the simultaneous effect of holding safety stock and purchasing policy. In order to avoid shortages occurring as a result of the random repair time, in addition to keep safety stock, we suppose that the manufacturer could purchase some qua...
متن کاملInteracting lattice electrons with disorder in two dimensions: Numerical evidence for a metal-insulator transition with a universal critical conductivity
The Coulomb interaction between the electrons and the presence of disorder both strongly affect the properties of solids.1–5 Namely, electronic correlations and randomness are separate driving forces behind metal-insulator transitions (MITs) due to the localization and delocalization of particles. While the electronic repulsion may lead to a Mott-Hubbard MIT,6 the scattering of noninteracting p...
متن کامل