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ece495nf07hw6 - has a dispersion relation E k = 2 t cos ka...

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10/19/06 ECE 495N, Fall’07 MSEE B010, MWF 330P – 420P Fundamentals of Nanoelectronics Note: Exam II on Monday Nov.5 in class. All exercises, page numbers refer to S.Datta, Quantum Transport: Atom to Transistor, Cambridge (2005) HW#6: Due Monday Oct.30 in class. Please turn in a copy of your MATLAB codes for Problem 2. These should be your own, not cut and paste from the text. Problem 1: In class we have seen that an infinitely long linear 1-D lattice (lattice constant: a) with a Hamiltonian H = ε t 0 0 t ε t 0 0 t ε t ⋯ ⋯ ⋯
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Unformatted text preview: has a dispersion relation E ( k ) = + 2 t cos ka where -π < ka < + (1) Do the same problem using a unit cell of two atoms (instead of one) and show that E ( k ) = ± 2 t cos ka where -/2 < ka < + /2 (2) Are (1) and (2) equivalent? Explain. Problem 2: Exercise E.6.5, Page 154 Problem 3: Consider a uniform one dimensional wire with periodic boundary conditions having an E(k) relationship E = Bk 4 . Find the density of states as a function of energy....
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