Graphene nanoflakes in external electric and magnetic in-plane fields

Abstract

The paper discusses the influence of the external in-plane electric and magnetic field on the ground state spin phase diagram of selected monolayer graphene nanostructures. The calculations are performed for triangular graphene nanoflakes with armchair edges as well as for short pieces of armchair graphene nanoribbons with zigzag terminations. The Mean Field Approximation (MFA) is employed to solve the Hubbard model. The total spin for both classes of nanostructures is discussed as a function of external fields for various structure sizes, for charge neutrality conditions as well as for weak charge doping. The variety of nonzero spin states is found and their stability ranges are determined. For some structures, the presence of antiferromagnetic orderings is predicted within the zero-spin phase. The process of magnetization of nanoflakes with magnetic field at constant electric field is also investigated, showing opposite effect of electric field at low and at high magnetic fields

Hubbard pair cluster in the external fields. Studies of the polarization and susceptibility

“…At the same time, it has been noticed that the exact solutions to the model can be obtained for small clusters, consisting of several lattice sites [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84]. Intensive investigations of such systems have been carried out both from the point of view of static properties [48-50, 52, 58, 62, 64, 66-68, 71-73, 75-80, 82, 83, 85-88], as well as for dynamical description [54,59,61,70,81,84].…”

“…In case of very small atomic clusters, exact results for the Hubbard model have been obtained by analytical methods [48-50, 52, 54, 62, 66, 67, 71, 73-75, 79, 80, 82, 84, 85]. However, for larger clusters the numerical techniques turned out to be indispensable [58,64,65,72,[76][77][78]83]. It is worth mentioning that theoretical studies of finite clusters are becoming increasingly important for the development of experimental nanophysics and nanotechnology.…”

Ferrimagnetic and antiferromagnetic phase in bilayer graphene nanoflake controlled with external electric fields

“…It is composed of tight-binding part, describing the electron hopping between nearest-neighbouring carbon atoms labelled with i and j, both in-plane (with intraplanar hopping integral t i j = t = 3.0 eV [53]) and between the planes (with interplanar hopping integral t i j = t ⊥ = 0.4 eV [53] is supplemented with Hubbard term with U being an effective on-site Coulombic interaction energy between the electrons and the number of electrons is provided by the operator n i,σ = c † i,σ c i,σ . The Hubbard term is considered within Mean Field Approximation [54]. Further terms are responsible for introducing the external fields.…”

Transport through graphenelike flakes with intrinsic spin-orbit interactions

“…Usually only the first spin-diagonal part of Eq. (3) is taken into account [18,[23][24][25]. However, in the present anisotropic case the magnetization direction may be arbitrary, so the spin mixing term must not be skipped.…”