Noriza Ahmad Zabidi

Energy band crossing points in multilayers of graphene

The monolayer of carbon atoms in a hexagonal lattice is called graphene. It is a monoatomic layer of graphite. The stacking of hexagons one over the other creates a variety of layers. We can stack in such a way that the hexagons of the first layer coincide with the hexagons of the next layer or they may be displaced. In this way we are able to make three types of layer stacks of graphene. These are called A, B and C types. We have found that a single layer of graphene shows a small gap of 27.212 meV. In the two layers of the AA type also the crossing is avoided. The energy from the apparent crossing point towards higher energies is not equal to that towards lower energies. The energy levels are not symmetric with respect to the apparent crossing point. In the AB type stacking for two layers the energy gap is 4.8 meV. The energy gap for a variety of stacking of layers has been obtained from the non‐relativistic Schrodinger theory.

Ab initio calculation of vibrational frequencies and Raman spectra of barium peroxide glass including comparison of tetrahedral BaO4 with GeO4 and SiO4.

We have calculated the vibrational frequencies of clusters of atoms from the first principles by using the density-functional theory in the local density approximation (LDA). We are also able to calculate the electronic binding energy for all of the clusters of atoms from the optimized structure. We have made clusters of BanOm (n, m=1-6) and have determined the bond lengths, vibrational frequencies as well as intensities in each case. We find that the peroxide cluster BaO2 occurs with the O-O vibrational frequency of 836.3 cm(-1). We also find that a glass network occurs in the material which explains the vibrational frequency of 67 cm(-1). The calculated values agree with those measured from the Raman spectra of barium peroxide and Ba-B-oxide glass. We have calculated the vibrational frequencies of BaO4, GeO4 and SiO4 each in tetrahedral configuration and find that the vibrational frequencies in these systems depend on the inverse square root of the atomic mass.

DFT Calculation of Band Structure of Carbon Chain Pulled from Graphene

A linear chain of five atoms of carbon is optimized for the minimum energy to determine the distance between atoms and its band structure is calculated. In the LDA the gap energy is found to vary from 4.66 eV at Q (0, 0.5, 0.5) to 22.86 eV at F (0, 0.5, 0). An incomplete hexagon with 5 atoms is attached to a linear chain which gives the gap of 1.14 eV at F point and 2.25 eV at Z (0, 0, 0.5). When two incomplete hexagons are attached to the two ends of the linear chain, the gap varies from 0.49 eV to 0.84 eV. The Fermi energy for the linear chain is 6.68 eV. For one incomplete hexagon attached to the chain it is 4.70 eV and for two incomplete hexagons attached to both the ends of the chain it is 4.34 eV. Thus the Fermi energy reduces in attaching hexagons to the chain. The energy gap is very large for the linear chain and much reduced values are found for hexagons attached to the chain.

The Electronic Structure of Co/Cu/Co interlayers

We have calculated the band structure of Co/Cu interlayers for four different models. (i) One layer of Co over one layer of Cu, (ii) four layers of atoms in the sequence CoCuCoCu, (iii) six layers, CoCuCoCuCoCu and (iv) eight layers as CoCuCoCuCoCuCoCu. We have optimized the bond lengths for the minimum energy in each case. We calculate the band structure by using the spin polarized as well as the unpolarized orbitals. We calculate the Fermi energy as well as the binding energy in each case. The Fermi energy is useful for the understanding of conductivity. We also discuss the dependence of resistivity on spin. There is an electron wave vector, k = 2 π/t, which matches with the layer thickness, t, leading to oscillations in the magnetoresistivity.

Clusters of Ge and O Atoms and the Raman Spectra of Vitreous GeO2

We have constructed the clusters of atoms of germanium and oxygen atoms by using the density‐functional theory. By optimizing the structures for the minimum energy of the Kohn‐Sham equation, we are able to calculate the bond lengths. We use the local density approximation to obtain the electronic binding energy for each cluster. We find the vibrational frequencies of each and every cluster and compare the calculated values with those measured from the Raman spectra of GeO2 glass. The glass involves clustering of atoms. Hence some of the calculated values match with those found in the experimental data. In this way, we find that Ge‐O2 (triangular), Ge‐O3 (pyramidal) and Ge‐O6 (pyramidal) clusters are present in the glassy state.

Electronic Structure of Fe and Cu Interlayers

We use the density‐functional theory to make layers of Fe and Cu atoms. We have found the band structure of interlayers upto 10 layers of atoms. We have calculated the structure and cell constants in all of the cases. The Fermi energy is found to depend on the number of layers of atoms. The value of d ln eF/d ln R = β has been calculated for pure Cu and pure Fe lattices. It is found that β = 0.004 for Cu and 0.002 for Fe in face centered cubic (f.c.c) structure. We have made the interlayers of Fe and Cu for which the value of β = 0.3. Thus, we find that the Fermi energy varies as a function of distance.

Ab Initio Study of Polonium

Polonium is the only element with a simple cubic (sc) crystal structure. Atoms in solid polonium sit at the corners of a simple cubic unit cell and no where else. Polonium has a valence electron configuration 6s26p4 (Z = 84). The low temperature α‐phase transforms into the rhombohedral (trigonal) β structure at ∼348 K. The sc α‐Po unit cell constant is a = 3.345 A. The beta form of polonium (β‐Po) has the lattice parameters, aR = 3.359 A and a rhombohedral angle 98°13′. We have performed an ab initio electronic structure calculation by using the density functional theory. We have performed the calculation with and without spin‐orbit (SO) coupling by using both the LDA and the GGA for the exchange‐correlations. The k‐points in a simple cubic BZ are determined by R (0.5, 0.5, 0.5), Γ (0, 0, 0), X (0.5, 0, 0), M (0.5, 0.5, 0) and Γ (0, 0, 0). Other directions of k‐points are Γ (0, 0, 0), X (0.5, 0, 0), R (0.5, 0.5, 0.5) and Γ (0, 0, 0). The SO splittings of p states at the Γ point in the GGA+SO scheme for α‐...

DFT Calculation of Clusters of Ba and O atoms and the Raman spectra of Barium Peroxide

We calculate the vibrational frequencies of clusters of atoms from the first principles by using the density functional theory in the local‐density approximation. We are also able to calculate the electronic binding energy. We have made clusters of BanOm(n = 1–5,m = 1–4) atoms and have determined the bond lengths, vibrational frequencies as well as intensities in each case. We find that the peroxide cluster BaO2 occurs with the O‐O vibrational frequency at 836.3 cm−1. We also find that a glass net work occurs in the material which explains the vibration at 67 cm−1. The calculated values agree with those measured from the Raman spectra of barium peroxide and Ba‐B‐oxide glass.

Band Structure of the Mn5Si3‐, Tb5Si3‐, and Tb5Ge3‐type Compounds

The results of the band structure studies on Tb5Si3 and Tb5Ge3 as well as Mn5Si3 single crystals are reported. The compounds Tb5Si3 and Tb5Ge3 are metamagnetic because of a strong effect of magnetic field on the magnetization. The spin polarized and nonpolarized calculations give similar results in band structure for all of the compounds. The Fermi energy of Mn5Si3 is higher compared to Tb5Si3 and Tb5Ge3 while binding energy for Mn5Si3 is lower than in the other two compounds. The band gaps found in the Mn5Si3 compound are a bit higher when spin polarization is introduced in the calculation. The densities of states calculations show no electrons in the conduction band. This is the special finding of the present work. The bands Tb5Si3 and Tb5Ge3 but not Mn5Si3 exhibit metamagnetic behavior assigned to valence band electrons.

The Electronic Structure Band Structure of KFe2As2

The layers of FeAs upon doping with K become superconducting. Hence we use the density functional theory to calculate the band structure of one layer of FeAs atoms by using spin polarized as well as impolarized orbitals. We find that the Fermi energy for unpolarized orbitals is 7.02 eV which changes to 6.87 eV whenpolarized orbitals are used. The gap energy for unpolarized orbitals varies from 7.76 meV at G points to 152.39 meV at Y points. At the Z point the gap is 25.17 meV for polarized orbitals. The DOS shows large concentrations at negative energies showing dominant insulating character. In order to find the effect of doping, we calculate the band structure of a unit cell of KFe2As2. It is very clear that there is a polarized effect of doping upon the population in the conduction band. The gap for polarized case is now 4.5 meV at G point and 125.18 meV at R point. We predict the anomaly at 25 meV observed in the photoemission spectroscopy.