

updated 2012.5.18 

* Daily schedule [#daily]
- 09:00-10:00 Discussion (1)
- 12:00-13:30 Lunch
- 13:30-14:30 Discussion (2)

* Goal of the project. [#goal]



* Assignment for discussion [#discussion]

- Monday: Saito (morning) subject introduction to our lab. Florian (afternoon), differential equations. 
- Tuesday: Nugraha (morning + afternoon), subject: concept of coherent phonon.
- Wednesday: Hasdeo (afternoon) subject is missing
- Thursday: Tatsumi (morning) subject: the structure of nanotubes   (afternoon) group meeting 
- Friday: Tastumi(morning) subject is missing

** Please note: [#notethat]
- If Eric-san asks you what he needs, please answer it with cc to me.
- If you do not have any material to need, please give him an easy question to solve.
- If Eric-san could not answer this question, it means that your question is bad (need some knowledge).
- If Eric-san can answer within 2min, it means that you gave not proper question (answer is trivial).

* What does Eric-san want to [#wishlist]

Please list here with some simple reason or detail. 
List from new to old. 







 Answer : (Tapsanit) Please consider my answers one by one in order to understand the Brillouin zone.
 1. What is the Bloch'theorem written in page. 17 of Saito's book?
  denoted by Psi(r) should satisfy the Bloch's theorem due to the periodicity 
  of the atoms in solid. The Psi is sometimes called the Bloch wave function. 
  It can be written as the phase factor exp(ikr) times the periodic function in 
  real space u(r), u(r+T) = u(r), : Psi(r) = exp(ikr)u(r). It is recommended to 
  check that the Psi(r)=exp(ikr)u(r) satisfies the Bloch's theorem.

 2. What is the Brillouin zone? (not solved)
  because the Brillouin zone is defined from the reciprocal lattice.

 3. What is the reciprocal lattice that define the Brillouin zone?
 A: As mentioned, the electron in solid is a kind of wave whose wave
  function satisfies the Bloch's theorem. This means that it has the  
  wavevector with amplitude and direction just like normal wave. The dimension 
  lattice. Then, reciprocal lattice is constructed to obtain the wavevector   
  of the electron. Please note that there are many wavevectors possibly 
  obtained from the reciprocal space. The unit vectors of the reciprocal 
  lattice (b1,b2,b3) are obtained from the unit vectors of the real lattice 
  (a1,a2,a3) by following relations 
  (* denotes  dot product of two vectors) :
  b1*a1 = 2*Pi, b2*a2 = 2*Pi, b3*a3 = 2*Pi and bi*aj = 0 if i /= j. 
  It is recommended to try to use this relations to derive the unit vectors of 
  reciprocal lattice, b1 and b2, of graphene in Eq. (2.23) of Saito's book 
  using a1 and a2 in Eq. (2.22).  

 Q2:  Copy machine: Can I use the copy machine or printer?  
 A2: (not solved)  

 Q1:  Library: I would like to know where is the library and how to use it. 
 A1: (not solved) or (solved) Hasdeo-san brought me to the library directly etc. 

* Report [#report]


Check that the ?(r)=e^(ik?r) u(r) satisfies the Bloch's theorem:
Bloch?s theorem is: T_a ?=e^(ik?a) ?
T ?_(a ?_i )is a translation operator ? T ?_(a ?_i ) ?(r ?)= ?(r ?+a ?_i)
r ?+(a_i ) ?=r ? because (a_i ) ? is a lattice vector.
u(r) is a periodic function.
e^(ik?(r ?+(a_i ) ? ) ) u(r ?+(a_i ) ?)= e^(ik?((a_i ) ? ) ) [e^(ik?(r ? ) ) u(r ?+(a_i ) ?)]=e^(ik?((a_i ) ? ) ) [e^(ik?(r ? ) ) u(r ?)]
Theorem is satisfied.

Derive the unit vectors of reciprocal lattice, b1 and b2, of graphene in Eq. (2.23) of Saito's book using a1 and a2 in Eq. (2.22).
	a ?_i=unit vector of real lattice
	 b ?_i=unit vector or reciprocal lattice
	a ?_i?b ?_i=2? 
	a ?_i?b ?_j=0 if i?j
	from eqn 2.22 in CN book: 

** June 5 (Hasdeo teaches XX and YY. from 9:00-9:34) etc [#rep20120605] 
- Who gave what? (XX min) 
- What isr the home work?
- The answer of the home work should be put here.
- Evaluation of the answer by teacher
- Evaluation by Saito

** June 4 [#rep20120604]
- task 1
- task 2
- etc...

- task 4
- etc...
