Calculation of Cohesive Energies of 3-D Bismuth Selenide (Bi2Se3) and Bismuth Antimony BiSb Topological Insulators: DFT Study
E. C. Hemba
Department of Physics, Federal College of Education, Pankshin, Plateau State, Nigeria.
T. J. Ikyumbur *
Department of Physics, Benue State University, Makurdi, Benue State, Nigeria.
E. A. Trisma
Department of Physics, Federal College of Education, Pankshin, Plateau State, Nigeria.
F. Gbaorun
Department of Physics, Benue State University, Makurdi, Benue State, Nigeria.
F. Aungwa
Department of Physics, Nigeria Defence Academy, Kaduna, Kaduna State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The cohesive energies of 3-dimensional (3-D) topological insulators bismuth antimony (BiSb) and bismuth selenide (Bi2Se3) were calculated. The Fritz Haber Institute Ab-initio molecular simulations (FHI-aims) code was employed for this calculation. The output files of the FHI-aims code were used during the computation and the total energies at each number of iterations for single free atoms and bulk were then calculated. The results from this work revealed that bismuth atom becomes stable at 3rd iteration meanwhile both selenium and antimony atoms gain stability at the 5th iteration. The results also showed that bismuth antimony acquire stability at the 3rd iteration and bismuth selenide gain stability at 9th iteration. This implies that among the free atoms studied in this work bismuth atom is more stable and for the bulk bismuth antimony is more stable. The cohesive energies of BiSb and Bi2Se3 were calculated using the optimized parameters. The results obtained from the calculation of the cohesive energies in this work were 1.02eV and 1.76eV for BiSb and Bi2Se3 respectively. This results compared reasonably well with experimental results and have little percentage errors of 1.30% for bismuth antimony and 29.55% for bismuth selenide. The deviation observed in this work may be due to the DFT calculation of the solid rather than the atoms themselves.
Keywords: Cohesive energies, topological insulators, FHI-aims, bismuth selenide (Bi2Se3), bismuth antimony (BiSb) and DFT
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Kane CL, Mele EJ. Z2 topological order and the quantum spin Hall effect. Phys Rev Lett. 1468;9(14):146802.
Gu Z, Wen X. Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order. Phys Rev B. 2009;80(15):155131.
Pollmann F, Berg E, Turner AM, Oshikawa M. Symmetry Protection of Topological Phases in one –dimensional quantum spin systems. Phys Rev B. 2012;85(7):075125.
Chen X, Gu Z, Wen X. Classification of Gapped Symmetry Phases in 1D spin systems. Phys Rev B. 2011;83(3):035107.
Li CH, van ’t Erve OM, Robinson JT, Liu Y, Li L, Jonker BT. Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in Bi2Se3. Nat Nanotechnol. 2014;9(3):218-24.
Guhr Th, A, Muller-Groening HA, Weiden M. Random matrix theories in quantum physics: common concepts. Physics report Vd. 1998;299:189-425.
Zhang T, Cheng P, Chen X, Jia JF, Ma X, He K et al. Experimental demonstration of topological surface states protected by time-reversal symmetry. Phys Rev Lett. 2009;103(26):266803.
Hsieh D, Qian D, Wray L, Xia Y, Hor YS, Cava RJ et al. A Topological Dirac insulator in a quantum spin Hall phase. Nature. 2008;452(7190):970-4.
Hasan MZ, Kane CL. Colloquium: Topological insulators. Rev Mod Phys. 2010;82(4):3045-67.
Chadov S, Qi X, Kübler J, Fecher GH, Felser C, Zhang SC. Tunable Multifunctional Topological Insulators in termary Heusler compounds. Nat Mater. 2010;9(7):541-5.
Lin H, Andre-Wray L, Yuqi X, Suyan X, Shuang J, Robert JC et al. Half-Heusler termary compounds as new multifunction experimental platforms for Topological quantum Phenomena. Nat Mater. 2010;9(7):546-9.
Hsieh D, Xia Y, Qian D, Wray L, Meier F, Dil JH et al. Observation of time-reversal-protected single-Dirac-cone topological-insulator states in Bi2Te and Sb2Te3; 2009.
Kane C, Moore J. Topological insulators. Physics world archive. IOP publishing Ltd;2014. ISSN: 0953-8585.
Naylor AJ. Towards highly-efficient thermoelectric power harvesting Gerators [Ph.D. thesis]. In: the Faculty of Natural and Environmental Sciences, School of Chemistry. University of Southampton; 2014.
Yang XX, Zhou ZF, Wang Y, Jiang R, Zheng WT, Sun CQ. Raman Spectroscopy Determination of the Debye temperature and Atomic Cohesive energy of CdS. CdSe, Bi2Se3 and Sb2Te3 nanostructure. J Appl Phys. Physical Review Letters. 2012;112(8):0835008.
Verma AS, Sarkar BK, Jindal VK. Cohesive Energy of Zincblende (AIIIBV and AIIBVI) Structured solids. Pramana J Phys. 2010;74(5):851-5.
Krumrain J, Mussler G, Borisova S, Stoica T, Plucinski L, Schneider CM, et al. MBE growth optimization of topological insulator Bi2Te3 films. J Cryst Growth. 2011;324(1): 115-8.
He HT, Wang G, Zhang T, Sou IK, Wong GK, Wang JN, et al. Impurity effect on weak antilocalization in the topological insulator Bi2Te3. Phys. Rev Lett. 2011;106 (16):166805.
Perdew JP, Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys Rev B Condens Matter. 1992;45(23):13244-9.
Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett. 1996;77:3865-8.
Abdu SG, Adamu MA, Onimisi MY. DFT computations of the ground state energy per atom of fullerenes (C60). Sci World J. 2018;13(1):35-8.
Galadanci GSM, Garba B. Computation of the Ground State Cohesive Properties of Alas Crystalline Structure Using FHI-aims code. IOSR-JAP. 2013;4(5):85-95.
Bernevig BA, Hughes TL, Zhang SC. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science. 2006;314(5806):1757-61.
Kane CL, Mele EJ. Z2 topological order and the quantum spin Hall effect. Phys Rev Lett. 2005;95(14):146802.
König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp LW, et al. Quantum spin Hall insulator state in HgTe quantum wells. Science. 2007;318(5851): 766-70.
Giannozzi P. Density Functional Theory for electronic structure calculations structure della material. 2005;1.
Sholl DS, Steckel JA. Density functional theory: A practical introduction. John Wiley & Sons Inc Publication; 2009.
Tuckerman M 2004. Introduction to DFT. Maria Currie Tutorial Series. Modelling biomolecules.
Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X et al. Ab iniotio molecular simulations with numeric atom-centered orbitals. Comput Phys Commun. 2009; 180(11):2175-96.
Burke K, Friends M. The ABC of DFT; 2008. Book Available on Line at htt://chem [cited 15/5/2018].
Available: http://ps.uci.edu/kieron/dft/book/.
Kohn W, Sham LJ. Self-consistent equations including exchange and correlation effects. Phys Rev. 1965;140 (4A):A1133-8.
Mishra SK, Satpathy S, Jepsen O. Electronic Structure and Thermoelectric Properties of bismuth telluride and bismuth selenide. J Phys: Condens Matter. 1997; 9(2):461-70.
Havu V, Blum V, Havu P, Scheffler M. Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions. J Comp Phys. 2009;228(22):8367-79.
Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X et al. Ab initiomolecular simulations with numeric atom-centered orbitals. Comput Phys Commun. 2009;180 (11):2175-96.
Abdu SG, Adamu MA, Onimisi MY. DFT Computations of the lattice constant, stable atomic structure and the ground state energy per atom of fullerenes (c60). Sci World J. 2018;13(1).
ISSN 1597-6343
Viktor A, Oliver H, Sergey L. Hands-On Tutorial on ab initio Molecular Simulations, Tutorial I: Basics of Electronic-Structure Theory, Fritz-Haber-Institut der. Berlin: Max-Planck-Gesellschaft; 2011.
De Max-Planck-Gessellschaf B. Ab initio molecular simulations. Fritz Haber Institute (FHI aims). All-electron structure theory with numeric Atomcentered basis functions; 2011.
Francis A, Ahoume BA, Eli D. Cohesive energies calculation of gallium-arsenide and aluminium-arsenide: DFT study. J Niger Assoc Math Phys; 2017.
Abdu SG. Hartree-Fock Solutions of the hydrogen, helium, lithium, beryllium and Boron atoms. Niger J Phys. 2010; 21(2).
Kelly J. Magnetotransport of topological insulators: bismuth selenide and bismuth telluride. National Stroke Foundation/REU Program, Physics Department, University of Notre Dame; 2011.