Chene Tradunsky & Or Cohen with the great help of Ariel Amir.

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Presentation transcript:

Chene Tradunsky & Or Cohen with the great help of Ariel Amir

Square Lattice of Atoms Using "Tight Binding" method we created a matrix representing the Hamiltonian for the entire lattice ( Size - N 2 *N 2 ) After finding Eigen Values and Eigen States we got…

Energy Band in Various Magnitic Fields – Butterfly in Square Lattice E B E0E0 E 0 -4t E 0 +4t

Evolution of an eigen state B E - Notice the edge states that don't exist for calculations infinite N

Evolution of an eigen state

Classical Explanation for Edge States Magnetron Radius

Quantum Equivalent for Edge States

Hexagonal Lattice Same method – “Tight Binding”, putting in a matrix… but look what happens now !

Hexagonal Butterfly E0E0 E 0 -4t E 0 +4t B E

Some physical explanation for Low Magnetic Field Dispersion in square lattice (B=0) : Behaves like free particle in 2D with effective mass ! Free particle in homogenous magnetic field receives extra energy – Landau Levels :

Landau Levels In Square Lattice B E

What happens in hexagonal lattice ? Dispersion in square lattice (B=0) : For certain K behaves like relativistic particle : A correction to the energy can be calculated which is similar to the Landau Levels :

Energy Levels In Hexagonal Lattice B E