#2 This is a solid state physics problem. ( I use this book : kittel introduction...
This is a solid state physics problem. ( I use this book : kittel introduction to soild state physocs ) thank you ! completely filled valence band. The electrons in this band have negative effective 4. Consider a E m. m Now an wavevector k is missing from this valence band electron with mass as in the figure, creating a hole. (a) What is the wavevector of this hole? [5] (b) If the energy of the electron with wavevector k...
Consider a trigonal lattice with a parameter a and angle α between the translation vectorsa1, a2, a3.1. Show that the reciprocal lattice is also trigonal. Find the length b of the translation vectors b1, b2, b3 of the reciprocal lattice as a function of a. Expressthe angle β between b1, b2 and b3 as a function of α.2. Check the correctness of the results by applying them to the particular cases of thesimple cubic lattice and FCC lattice, for which...
solid state physics 1. Consider a 1-dimensional chain of atoms with mass m. The force constant between atoms are alternately C and 10C. The distances between the nearest neighbors are a/2. Let u, and v, be the displacements of the s-th pair of atoms as shown in the figure below. lu lu Us lu s-1 s-1 s+1 s+1 10C 100 10C (a) Write down the equations of motion for u, and v,. [5] (b) Look for solutions in the form...
Consider harmonic vibrations of an atomic chain (1D crystal) consisting of alternating atoms of masses M1 and M2 with nearest-neighbor interactions.Find the amplitude ratio of the atoms for the optical and acoustic branches at K maxπ/a, a being the chain period. Show that at this value of K (zoneboundary) the two sublattices act as if decoupled: one sublattice remains at rest while the other sublattice vibration
3. Graphene bandstructure Graphene is a good example of 2D system with two atoms per unit cell (a) Write the simplified form of Hamiltonian using given vector notation. Consider the basis function is a Bloch wavefunction (b) From the eigenvalue equation, assume E(k) Eo ± |hol Which points in k-space satisfy ho = 0? 27T (c) One example of the answer for (b) is .(0,Using the Taylor expansion near that k-space point to simplify ho(kx,ky) and write the eigenvalue with...
4. A particle moves in a periodic one-dimensional potential, V(x a)-V(x); physically, this may represent the motion of non-interacting electrons in a crys- tal lattice. Let us call n), n - 0, +1, t2, particle located at site n, with (n'In) -Sn,Let H be the system Hamiltonian and U(a) the discrete translation operator: U(a)|n) - [n +1). In the tight- binding approximation, one neglects the overlap of electron states separated by a distance larger than a, so that where is...
11-8. Equation (11.4) is an expression for the energy levels of the delocalized MOs for a conjugated chain of N carbon atoms. In the limit of a very long chain of length L, with a LIN the distance between neighboring carbon atoms, this equation becomes E = α + 2β cos(ka), with k = π/L, 2π/L, 3 π/L, . NTIL Tla). (Yes, k is the wave number of the "waves" represented by equation (11.5)-see discussion at the end of Section...
Q1- The atoms in a crystal are modelled as hard spheres in contact. Calculate the Atomic radius in a fcc lattice with lattice constant 3.6 A Q2- (a) The atomic in a crystal are modelled as hard spheres in constant. Calculate the atomic radius in a fcc lattice with lattice constant 3.6 A. (b) Consider three-dimensional simple cubic lattice with lattice constant a. What is the distance from the center to a corner of the first Brillouin Zone in the...
16. A molecule of benzene is made up of six carbon atoms and six hydrogen atoms, linked together in a hexagonal shape as in Figure 13.28. (a) How many different compounds can be formed by replacing one or more of the hy- drogen atoms with a chlorine atom? (b) Find the number of different chemical compounds that can be formed by replacing three of the six hydrogen atoms in a benzene ring with a CH3 radical. We were unable to...
Consider a one-dimensional tight binding model of electrons hopping between atoms. Let the distance between atoms be called a, and here let us label the atomic orbital on atom ln) for n-1,..,N (you may assume orthonormality of orbitals, ie., (1m)- nm). n as Suppose there is an on-site energy e and a hopping matrix element -t. In other words, suppose (IH|m) = E for n-m and (1비m)=-t for n=m±1. (a) Derive and sketch the dispersion curve for electrons. (b) How...