| Tài liệu tham khảo |
Loại |
Chi tiết |
| [13.1] J. P. Hobson and W. A. Nierenberg, “The statistics of a two-dimensional, hexagonal net”, Phys. Rev. 89, 662 (1953) |
Sách, tạp chí |
| Tiêu đề: |
The statistics of a two-dimensional, hexagonalnet”,"Phys. Rev |
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| [13.5] C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene”, Rev. Mod. Phys. 80, 1337–1354 (2008).Exercises |
Sách, tạp chí |
| Tiêu đề: |
Colloquium: Andreev reflection and Klein tunneling ingraphene”,"Rev. Mod. Phys |
| Tác giả: |
5] C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene”, Rev. Mod. Phys. 80, 1337–1354 |
| Năm: |
2008 |
|
| 13.2 Use Eq. (13.21) to show that the graphene effective Hamiltonian for k near a Dirac point can be written asH = v F σ ã kwhere σ is the Pauli spin operator, k = k x e x + k y e y is the two-dimensional wavevector near a Dirac point, and v F is the group velocity at the Fermi level (i.e., at ! = 0). The operator σ appearing in the Hamiltonian above is called the pseudo-spin |
Sách, tạp chí |
| Tiêu đề: |
v"F σãkwhereσ is the Pauli spin operator,k ="k"x"e"x +k"y"e"y" is the two-dimensionalwavevector near a Dirac point, and"v |
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| 13.3 (a) Find an expression for the energy of the graphene energy bands including the overlap integral, S π , between nearest-neighbor p z orbitals. Assume S π > 0 and ( pp π) < 0.(b) Find the energy for k near a Dirac point.(c) Plot a graph of ( E − p ) versus ka along the lines → M → K in the Brillouin zone. Use S π = 0 . 13, ( pp π) = − 3 eV, and p = 0 |
Sách, tạp chí |
| Tiêu đề: |
S"π", between nearest-neighbor "p"z" orbitals. Assume"S"π ">0 and |
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| 13.4 For Exercise 13.3, show that the radial effective mass, m ∗ r , and the group velocity near a Dirac point do not depend on the overlap integral. r = (δ k x 2 + δk 2 y ) 1 / 2 and 2 /m r ∗ = ∂ 2 E /∂r 2 + (∂ E/∂r )/r |
Sách, tạp chí |
| Tiêu đề: |
m"∗"r", and the groupvelocity near a Dirac point do not depend on the overlap integral."r ="(δ"k"x"2+δ"k"2"y")1/2and2"/m"r"∗="∂"2"E/∂r"2+ |
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| 13.7 For Exercise 13.5 sketch the relative displacements for the row-2 E lattice vibration mode at K 1 using the sum of the lattice wave and its time-reversed state |
Sách, tạp chí |
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| 13.6 (a) For Exercise 13.5 find the lattice vibration eigenvectors for k along the symmetry line.(b) Give the frequencies in terms of the dynamic matrix |
Khác |
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