Spin and electronic correlations in gated graphene quantum rings

Abstract

Spin and electronic correlations in gated graphene quantum ringsWe present a theory of graphene quantum rings designed to produce degenerate shells of single-particle states close to the Fermi level. We show that populating these shells with carriers using a gate leads to correlated ground states with finite total electronic spin. Using a combination of tight-binding and configuration-interaction methods, we predict the ground state and the total spin of the system as a function of the filling of the shell. We show that for smaller quantum rings, the spin polarization of the ground state at half filling depends strongly on the size of the system but reaches a maximum value beyond a critical size.

Jastrow-correlated wave functions for flat-band lattices

“…We find that the wavefunction accurately captures an intriguing transition from a Wigner crystal to a Jastrow correlated liquid, driven entirely by interactions. Our method can be generalized to accurately model graphene nanoribbons and other flatband lattice structures [5][6][7][8][9][10][11][12][13] and can be adapted to study magnetism recently explored in experiments on graphene nanoribbons. 25 The Jastrow-correlated wavefunctions constructed here are versatile.…”

“…For example, the π z Slater orbitals of carbon atoms could be used instead. 7 These orbitals are, in contrast, exponentially localized and loosely correspond to β ∼ 1. We expect less localization (larger β) in carbon structures with adsorbates (e.g., hydrogen 8 ).…”

“…Detailed calculations show flat bands in a variety of physically relevant contexts, including: the edges of two-dimensional (2D) graphene, 5 one-dimensional (1D) graphene nanoribbons, [5][6][7] hydrogenated graphene nanoribbons, 8 collapsed carbon nanotubes, 9 hydrogenated nanotubes, 10 graphene dots, 11 and graphene antidots. 12 Flat bands can also be found in a wealth of other compounds and engineered in optical lattices.…”

Effects of long-range disorder and electronic interactions on the optical properties of graphene quantum dots

“…We take onsite interaction parameter as U = 16.522/κ eV and long-range interaction parameters V ij = 8.64/κ and V ij = 5.33/κ for the first and second nearest neighbours with effective dielectric constant κ = 6 [48], respectively. Distant neighbor interaction is taken to be 1/d ij κ and interaction matrix elements are obtained from numerical calculations by using Slater π z orbitals [49]. Last term corresponds to impurity potential V imp (i) account for substrate effects.…”

Magnetic phases of graphene nanoribbons under potential fluctuations

“…Here, U is taken to be 16.522/κ eV, where κ is an effective dielectric constant taken to be as a control parameter. The long-range interaction parameters V ij are taken to be 8.64/κ eV and 5.33/κ eV (the Coulomb matrix elements are calculated numerically by using Slater π z orbitals [35]) for the first two neighbors, and 1/d ij κ for distant neighbors. V imp (i) represents a smooth long-ranged potential fluctuation, which can be attributed to charge impurities in the substrate.…”