PERHITUNGAN NUMERIK RAPAT KEADAAN GRAPHENE BILAYER DENGAN MODEL TIGHT-BINDING MENGGUNAKAN METODE RAMBATAN WAKTU TROTTER-SUZUKI

Abstract

ABSTRAK Perhitungan rapat keadaan (density of states/DOS) material graphene bilayer model ikatan kuat atau Tight-Binding (TB) melalui penyelesaian persamaan Schrӧdinger Gayut Waktu (PSGW) telah dilakukan dengan menggunakan metode rambatan waktu Trotter-Suzuki. Fungsi gelombang awal dibangkitkan dengan menggunakan bilangan acak kompleks sebagai fungsi superposisi dari basis tiap-tiap site atom berstruktur heksagonal untuk memperoleh fungsi korelasi. Nilai rapat keadaan dihitung dengan mentransformasi Fourier fungsi korelasi yang sudah didapatkan. Penelitian ini terfokus pada perhitungan rapat keadaan dari graphene bilayer model AA-Stacking. Hasil penelitian menunjukkan bahwa metode rambatan waktu Trotter-Suzuki sangat efisien digunakan untuk menghitung rapat keadaan dari sistem atom yang besar. Model TB dapat menjelaskan rapat keadaan material graphene bilayer dengan variasi ukuran sistem dan hopping parameter. Banyaknya jumlah atom (site) yang ditinjau mempengaruhi keteraturan hasil perhitungan rapat keadaan. Semakin banyak atom yang ditinjau, semakin teratur perhitungan rapat keadaan yang dihasilkan. Variasi nilai hopping interlayer mengakibatkan munculnya singularitas van Hove di level tenaga Fermi untuk t1=t2 dan bertambahnya sifat metallicity akibat bertambahnya nilai DOS pada level tenaga Fermi untuk t1<t2. Kata kunci: graphene bilayer, rapat keadaan, dan metode Trotter-Suzuki, ABSTRACT The density of states (DOS) of the bilayer graphene material with Tight-Binding (TB) model has been calculated by solving the Time Dependent Schrӧdinger Equation (TDSE) with Trotter-Suzuki formula. The generation of the initial wave function is carried out by using a random complex number as a superposition function of the base of each hexagonal structure atomic site to obtain the correlation function. The results of the calculation of the correlation function are then Fourier transformed to calculate the density of the state. This research focuses on calculating the state density of the graphene bilayer AA-Stacking. The results showed that the Trotter-Suzuki method was very efficient in calculating the state density of large atomic systems. The TB model can explain the density of states of the bilayer graphene material with variations in system size and hopping parameters. The number of atoms (sites) reviewed affects the regularity of the DOS calculation results. The more atoms that are reviewed, the more orderly the DOS calculations will be generated. The variation of the hopping interlayer value would be appearing van Hove singularity at the Fermi level for t1=t2 and increase in the metallicity properties with the increase in the DOS value at the Fermi level for t1<t2. Keywords: bilayer graphene, density of states, Trotter-Suzuki formula

Keywords

• bilayer graphene
• density of states
• Trotter-Suzuki formula