lesson 10 Density of states RECIPROCAL SPACE DIRECT

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lesson 10: Density of states RECIPROCAL SPACE DIRECT SPACE (Brillouin zone for fcc) Solid

lesson 10: Density of states RECIPROCAL SPACE DIRECT SPACE (Brillouin zone for fcc) Solid State Physics M. Casalboni 2017/’ 18 V 1 V 2 < V 1 1/20

lesson 10: Density of states DENSITY OF STATES Solid State Physics M. Casalboni 2017/’

lesson 10: Density of states DENSITY OF STATES Solid State Physics M. Casalboni 2017/’ 18 why to introduce the density of state? 2/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 DENSITY OF

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 DENSITY OF STATE however: 3/20

lesson 10: Density of states E(k) Solid State Physics M. Casalboni 2017/’ 18 possible

lesson 10: Density of states E(k) Solid State Physics M. Casalboni 2017/’ 18 possible value of k 4/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 E(k) possible

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 E(k) possible states d. E dk d. Edk let us define two intervals dk d. E dk 5/20

lesson 10: Density of states but: Solid State Physics M. Casalboni 2017/’ 18 E(k)

lesson 10: Density of states but: Solid State Physics M. Casalboni 2017/’ 18 E(k) d. E dk dk 6/20

lesson 10: Density of states formally and in 3 D Solid State Physics M.

lesson 10: Density of states formally and in 3 D Solid State Physics M. Casalboni 2017/’ 18 7/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 2π/L in

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 2π/L in reciprocal space the k points are equispatially distributed in 3 D inside the Brillouin Zone 8/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 9/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 9/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 2π/L 10/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 2π/L 10/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 11/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 11/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 12/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 12/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 13/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 13/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 14/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 14/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 15/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 15/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 Near a

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 Near a critical point we expand the energy 1 D + - M 0 M 1 2 D ++ + - or - + -- M 0 M 1 M 2 +++ + + - or + - + or - + + + - - or - + - or - - + --- M 0 M 1 M 2 M 3 3 D 16/20

lesson 10: Density of states Near a critical point we expand the energy Solid

lesson 10: Density of states Near a critical point we expand the energy Solid State Physics M. Casalboni 2017/’ 18 1 D 2 D 3 D 17/20

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 1 D

lesson 10: Density of states Solid State Physics M. Casalboni 2017/’ 18 1 D 18/20

lesson 10: Density of states similarly (see textbook): 2 D Solid State Physics M.

lesson 10: Density of states similarly (see textbook): 2 D Solid State Physics M. Casalboni 2017/’ 18 logaritmic divergence at saddle point M 1 19/20

lesson 10: Density of states and (see textbook): 3 D Solid State Physics M.

lesson 10: Density of states and (see textbook): 3 D Solid State Physics M. Casalboni 2017/’ 18 20/20