Abstract: Using the continuum model, we investigate the confined states and the corresponding wave functions of ABC-stacked trilayer graphene (TLG) quantum dots (QDs). First, a general infinite-mass boundary condition is derived and applied to calculate the electron and hole energy levels of a circular QD in both the absence and presence of a perpendicular magnetic field. Our analytical results for the energy spectra agree with those obtained by using the tight-binding model, where a TLG QD is surrounded by a staggered potential. Our findings show that (i) the energy spectrum exhibits intervalley symmetry E-K(e)(m) = -E-K'(h)(m) for the electron (e) and hole (h) states, where m is the angular momentum quantum number, (ii) the zero-energy Landau level (LL) is formed by the magnetic states with m <= 0 for both Dirac valleys, that is different from monolayer and bilayer graphene QD with infinite-mass potential in which only one of the cones contributes, and (iii) groups of three quantum Hall edge states in the tight-binding magnetic spectrum approach the zero LL, which results from the layer symmetry in TLG QDs.

Abstract: The electron energy spectrum in monolayer-bilayer-monolayer and in bilayer-monolayer-bilayer graphene structures is investigated and the effects of a perpendicular magnetic field and electric bias are studied. Different types of monolayer-bilayer interfaces are considered as zigzag (ZZ) or armchair (AC) junctions which modify considerably the bulk Landau levels (LLs) when the spectra are plotted as a function of the center coordinate of the cyclotron orbit. Far away from the two interfaces, one obtains the well-known LLs for extended monolayer or bilayer graphene. The LL structure changes significantly at the two interfaces or junctions where the valley degeneracy is lifted for both types of junctions, especially when the distance between them is approximately equal to the magnetic length. Varying the nonuniform bias and the width of this junction-to-junction region in either structure strongly influence the resulting spectra. Significant differences exist between ZZ and AC junctions in both structures. The densities of states (DOSs) for unbiased structures are symmetric in energy whereas those for biased structures are asymmetric. An external bias creates interface LLs in the gaps between the LLs of the unbiased system in which the DOS can be quite small. Such a pattern of LLs can be probed by scanning tunneling microscopy.

Abstract: Using the simplified linear combination of atomic orbitals (LCAO) method in combination with ab initio calculations, we construct a tight-binding (TB) model for two different crystal structures of monolayer gallium: a(100)- and b(010)-Gallenene. The analytical expression for the Hamiltonian and numerical results for the overlap matrix elements between different orbitals of the Ga atoms and for the Slater and Koster (SK) integrals are obtained. We find that the compaction of different structures affects significantly the formation of the orbitals. The results for a(100)-Gallenene can be very well explained with an orthogonal basis set, while for b(010)-Gallenene we have to assume a non-orthogonal basis set in order to construct the TB model. Moreover, the transmission properties of nanoribbons of both monolayers oriented along the AC and ZZ directions are also investigated and it is shown that both AC- and ZZ-b(010)-Gallenene nanoribbons exhibit semiconducting behavior with zero transmission while those of a(100)-Gallenene nanoribbons are metallic.

Abstract: We present the Tight-Binding Studio (TB Studio) software package that calculates the different parameters of a tight-binding Hamiltonian from a set of Bloch energy bands obtained from first principle theories such as density functional theory, Hartree-Fock calculations or semi-empirical band-structure theory. This will be helpful for scientists who are interested in studying electronic and optical properties of structures using Green's function theory within the tight-binding approximation. TB Studio is a cross-platform application written in C++ with a graphical user interface design that is user-friendly and easy to work with. This software is powered by Linear Algebra Package C interface library for solving the eigenvalue problems and the standard high performance OpenGL graphic library for real time plotting. TB Studio and its examples together with the tutorials are available for download from tight-binding.com. Program summary Program Title: Tight-Binding Studio Program Files doi:http://dx.doi.org/10.17632/j6x5mwzm2d.1 Licensing provisions: LGPL Programming language: C++ External routines: BLAS, LAPACK, LAPACKE, wxWidgets, OpenGL, MathGL Nature of problem: Obtaining Tight-Binding Hamiltonian from a set of Bloch energy bands obtained from first-principles calculations. Solution method: Starting from the simplified LCAO method, a tight-binding model in the two-center approximation is constructed. The Slater and Koster (SK) approach is used to calculate the parameters of the TB Hamiltonian. By using non-linear fitting approaches the optimal values of the SK parameters are obtained such that the TB energy eigenvalues are as close as possible to those from first-principles calculations. We obtain the expression for the Hamiltonian and the overlap matrix elements between the different orbitals of the different atoms in an orthogonal or non-orthogonal basis set. (C) 2020 Elsevier B.V. All rights reserved.