Collapse of the vacuum in hexagonal graphene quantum dots: A comparative study between tight-binding and mean-field Hubbard models

Abstract

In this paper, we perform a systematic study on the electronic, magnetic, and transport properties of the hexagonal graphene quantum dots (GQDs) with armchair edges in the presence of a charged impurity using two different configurations: (1) a central Coulomb potential and (2) a positively charged carbon vacancy. The tight-binding and the half-filled extended Hubbard models are numerically solved and compared with each other in order to reveal the effect of electron interactions and system sizes. Numerical results point out that off-site Coulomb repulsion leads to an increase in the critical coupling constant to β c = 0.6 for a central Coulomb potential. This critical value of β is found to be independent of the GQD size, reflecting its universality even in the presence of electron-electron interactions. In addition, a sudden downshift in the transmission peaks shows a clear signature of the transition from subcritical β < β c to the supercritical β > β c regime. On the other hand, for a positively charged vacancy, collapse of the lowest bound state occurs at β c = 0.7 for the interacting case. Interestingly, the local magnetic moment, induced by a bare carbon vacancy, is totally quenched when the vacancy is subcritically charged, whereas the valley splittings in electron and hole channels continue to exist in both regimes.

Electronic and magnetic properties of graphene quantum dots with two charged vacancies

“…For the range of values studies in this work, is nearly constant. More importantly, is also found to be largely independent of finite size effects for dots larger than few thousands atoms, consistent with single charged impurity results [49] as seen in Fig. 1c, provided is smaller than the dot diameter.…”

“…This is due to the screening of charged impurities by electron-electron interactions. Also, value is increased to 0.36, consistent with single charged vacancy results where is increased from 0.5 to 0.7 [49].…”

“…The armchair edges make the system free of additional edge state effects. Moreover, the critical value for which the 1S state crosses the Dirac point is known to be independent of the size of the quantum dot both within effective mass approximation and mean-field Hubbard models [49,50]. Thus, the hexagonal GQD system provides us with a practical way to understand bulk properties as well.…”

Atomic Collapse in Disordered Graphene Quantum Dots

“…The main physics behind the model is to calculate a critical coupling constant β c = Z c α above which is referred to as the supercritical regime [12]. This critical value is estimated to be β c = 0.5 for a vacuum consisting of non-interacting massless Dirac fermions [4,5], and β c remains the same when these fermions are confined in smaller-sized graphene quantum dots (GQDs) [13,14]. A further extension of the problem takes electron interactions into account [15,16] for which the critical coupling constant is renormalized to β c = 0.6 due to off-site Coulomb repulsion among Dirac particles [14].…”

“…This critical value is estimated to be β c = 0.5 for a vacuum consisting of non-interacting massless Dirac fermions [4,5], and β c remains the same when these fermions are confined in smaller-sized graphene quantum dots (GQDs) [13,14]. A further extension of the problem takes electron interactions into account [15,16] for which the critical coupling constant is renormalized to β c = 0.6 due to off-site Coulomb repulsion among Dirac particles [14]. On the exceeding values of the coupling strength β, the lowest energy electron state is bound to the impurity as the 1S 1/2 state [5].…”