Tunneling current between graphene layers

The physical model that allows to calculate the values of the tunneling current be-tween graphene layers is proposed. The tunneling current according to the pro-posed model is proportional to the area of tunneling transition. The calculated value of tunneling conductivity is in qualitative agreement with experimental data.Comment: 4 page

Structure and energetics of carbon, hexagonal boron nitride and carbon/hexagonal boron nitride single-layer and bilayer nanoscrolls

Single-layer and bilayer carbon and hexagonal boron nitride nanoscrolls as well as nanoscrolls made of bilayer graphene/hexagonal boron nitride heterostructure are considered. Structures of stable states of the corresponding nanoscrolls prepared by rolling single-layer and bilayer rectangular nanoribbons are obtained based on the analytical model and numerical calculations. The lengths of nanoribbons for which stable and energetically favorable nanoscrolls are possible are determined. Barriers to rolling of single-layer and bilayer nanoribbons into nanoscrolls and barriers to nanoscroll unrolling are calculated. Based on the calculated barriers nanoscroll lifetimes in the stable state are estimated. Elastic constants for bending of graphene and hexagonal boron nitride layers used in the model are found by density functional theory calculations.Comment: 9 pages, 6 figure

Interlayer interaction, shear vibrational mode, and tribological properties of two-dimensional bilayers with a commensurate moir\'e pattern

The potential energy surface (PES) of interlayer interaction of infinite twisted bilayer graphene is calculated for a set of commensurate moir\'e patterns using the registry-dependent Kolmogorov-Crespi empirical potential. The calculated PESs have the same shape for all considered moir\'e patterns with the unit cell size of the PES which is inversely related to the unit cell size of the moir\'e pattern. The amplitude of PES corrugations is found to decrease exponentially upon increasing the size of the moir\'e pattern unit cell. An analytical expression for such a PES including the first Fourier harmonics compatible with the symmetries of both layers is derived. It is shown that the calculated PESs can be approximated by the derived expression with the accuracy within 1%. This means that different physical properties associated with relative in-plane motion of graphene layers are interrelated and can be expressed analytically as functions of the amplitude of PES corrugations. In this way, we obtain the shear mode frequency, shear modulus, shear strength and barrier for relative rotation of the commensurate twisted layers to a fully incommensurate state for the considered moir\'e patterns. This barrier may possibly lead to the macroscopic robust superlubricity for twisted graphene bilayer with a commensurate moir\'e pattern. The conclusions made should be valid for diverse 2D systems of twisted commensurate layers.Comment: 9 pages, 3 figures; Supplemental Material: 2 pages, 1 figur

AA stacking, tribological and electronic properties of double-layer graphene with krypton spacer

Structural, energetic and tribological characteristics of double-layer graphene with commensurate and incommensurate krypton spacers of nearly monolayer coverage are studied within the van der Waals-corrected density functional theory. It is shown that when the spacer is in the commensurate phase, the graphene layers have the AA stacking. For this phase, the barriers to relative in-plane translational and rotational motion and the shear mode frequency of the graphene layers are calculated. For the incommensurate phase, both of the barriers are found to be negligibly small. A considerable change of tunneling conductance between the graphene layers separated by the commensurate krypton spacer at their relative subangstrom displacement is revealed by the use of the Bardeen method. The possibility of nanoelectromechanical systems based on the studied tribological and electronic properties of the considered heterostructures is discussed

ТЕРМИЧЕСКАЯ ЭНЕРГИЯ АКТИВАЦИИ ПРЫЖКОВОЙ ε2-ЭЛЕКТРОПРОВОДНОСТИ ПО АТОМАМ БОРА В СЛАБО КОМПЕНСИРОВАННОМ КРЕМНИИ

The insulating side of the concentration insulator–metal phase transition (Mott’s transition) in p-type silicon crystals doped with acceptor (boron atoms) is considered under the conditions of stationary hopping electrical conduction. The boron atoms substitute silicon atoms in the crystal lattice and can be in one of the three charge states (−1, 0, +1), while the compensating impurity (donors) is in the charge state (+1). The distribution of impurity atoms is supposed to be random (Poisson’s distribution). The A0-band is formed from the energy levels of boron atoms in the charge states (0) and (−1), while the A+-band is formed from the energy levels of boron atoms in the charge states (+1) and (0). The decrease in the activation energy ε2 of thermally assisted tunneling transitions (hops) of holes between electrically neutral boron atoms, i. e. boron atoms that are in the charge state (0), is calculated. The ε2 quantity is approximately equal to an energy gap between A0- and A+-bands, i. e. Hubbard’s gap. In the quasi-classical approximation it is shown that the narrowing of the energy gap between A0- and A+-bands occurs due to: (i) the formation of a quasi-continuous band of allowed energy values for v-band holes from excited quantum states of boron atoms in the charge state (0), thus the value of the v-band shift into the band gap is determined by a maximum radius of the hole orbit in a boron atom, which does not exceed the half of the average distance between the nearest impurity atoms, and (ii) the splitting of the ground (non-excited) energy levels of the “molecular” pairs of boron atoms in the charge states (0) into triplet and singlet states of two holes. Calculations of ε2 without any adjustable parameters are quantitatively agree with the known experimental data on p-Si:B.Рассматривается изоляторная сторона концентрационного фазового перехода изолятор–металл (перехода Мотта) в легированных акцепторами (атомами бора) кристаллах кремния p-типа в условиях стационарной прыжковой электрической проводимости. Атомы бора замещают в кристаллической решетке атомы кремния и могут находиться в одном из трех зарядовых состояний (−1, 0, +1), а компенсирующая примесь (доноры) находится в зарядовом состоянии (+1). Распределение атомов примесей по кристаллу предполагается случайным (пуассоновским). Из уровней энергии атомов бора в зарядовых состояниях (0) и (−1) формируется A0-зона, а из уровней энергии атомов бора в зарядовых состояниях (+1) и (0) формируется A+-зона. Рассчитывается уменьшение энергии активации ε2 термически ассистированных туннельных переходов (прыжков) дырок между электрически нейтральными атомами бора, т. е. находящимися в зарядовых состояниях (0). Величина ε2 примерно равна энергетической ширине щели между A0- и A+-зонами, т. е. щели Хаббарда. В квазиклассическом приближении показано, что сужение энергетической щели между A0- и A+-зонами происходит вследствие: 1) формирования из возбужденных квантовых состояний атомов бора в зарядовом состоянии (0) квазинепрерывной зоны разрешенных значений энергии для дырок v-зоны, так что величина смещения потолка v-зоны в глубь запрещенной зоны определяется максимальным радиусом орбиты дырки в атоме бора, не превышающим половины среднего расстояния между ближайшими атомами примесей, 2) расщепления основных (невозбужденных) уровней энергии «молекулярных» пар атомов бора в зарядовых состояниях (0) на триплетное и синглетное состояния двух дырок. Расчеты ε2 без подгоночных параметров количественно согласуются с имеющимися экспериментальными данными для p-Si:B

Effect of Peierls transition in armchair carbon nanotube on dynamical behaviour of encapsulated fullerene

The changes of dynamical behaviour of a single fullerene molecule inside an armchair carbon nanotube caused by the structural Peierls transition in the nanotube are considered. The structures of the smallest C20 and Fe@C20 fullerenes are computed using the spin-polarized density functional theory. Significant changes of the barriers for motion along the nanotube axis and rotation of these fullerenes inside the (8,8) nanotube are found at the Peierls transition. It is shown that the coefficients of translational and rotational diffusions of these fullerenes inside the nanotube change by several orders of magnitude. The possibility of inverse orientational melting, i.e. with a decrease of temperature, for the systems under consideration is predicted.Comment: 9 pages, 6 figures, 1 tabl

Multiscale modeling strategy to solve fullerene formation mystery

Since fullerene formation occurs under conditions where direct observation of atomic-scale reactions is not possible, modeling is the only way to reveal atomistic mechanisms which can lead to selection of abundant fullerene isomers (like C-I). In the present paper we review the results obtained for different atomistic mechanisms by various modeling techniques. Although it seems that atomic-scale processes related to odd fullerenes (such as growth by consecutive insertions of single carbon atoms and rearrangements of the sp structure promoted by extra sp atoms) provide the main contribution to selection of abundant isomers, at the moment there is no conclusive evidence in favor of any particular atomistic mechanism. Thus, the following multiscale modeling strategy to solve the mystery of the high yield of abundant fullerene isomers is suggested. On the one hand, sets of reactions between fullerene isomers can be described using theoretical graph techniques. On the other hand, reaction schemes can be revealed by classical molecular dynamics simulations with subsequent refinement of the activation barriers by ab initio calculations. Based on the reaction sets with the reaction probabilities derived in this way, the different atomistic mechanisms of abundant fullerene isomer selection can be compared using kinetic models.AMP acknowledges the Russian Foundation of Basic Research (Grant No. 20-52-00035). IVL acknowledges the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143). SAV and NAP acknowledge the Belarusian Republican Foundation for Fundamental Research (Grant No. F20R-301) and Belarusian National Research Program “Convergence-2025.