(a) Suppose the system is subject to some uniform magnetic eld in the 163 direction.2 Calculate the cyclotron effective mass m: of a quasi-particle with energy E and wave number kg in the .663 direction. You will nd m: = mlm (6) which does not depend on e or k2. You may use the formula (12.44)j which says\" 2 8A(e k2) * k = '. W%(s .) 2T 36 (7) Here, A(e, k2) is dened as follows. Consider the wave vectors whose component in 1-7.3 is xed to be kz. They form a plane in the 1:: space. Each of them has some energy given by the dispersion relation, so we can nd some equipotential curve of energy E on this plane. A(e, k2) refers to the area of the part of the plane that is surrounded by this curve. (b) Let the Fermi energy be 61?. Compute the density of states D(eF) at this Fermi energy and the specic heat C = 1TgilcTDzp). How does this compare to the results for a free electron gas in 3D? You will nd that they are very similar; nothing changes except that we should replace the electron mass by some effective mass mz:mesma. (& Here are some geometry facts you may nd helpful. An ellipse whose semiaxes are a, b has area web. All ellipsoid whose semiaxes are a, b, c has area abc. (a) Suppose the system is subject to some uniform magnetic eld in the 163 direction.2 Calculate the cyclotron effective mass m: of a quasi-particle with energy E and wave number kg in the .663 direction. You will nd m: = mlm (6) which does not depend on e or k2. You may use the formula (12.44)j which says\" 2 8A(e k2) * k = '. W%(s .) 2T 36 (7) Here, A(e, k2) is dened as follows. Consider the wave vectors whose component in 1-7.3 is xed to be kz. They form a plane in the 1:: space. Each of them has some energy given by the dispersion relation, so we can nd some equipotential curve of energy E on this plane. A(e, k2) refers to the area of the part of the plane that is surrounded by this curve. (b) Let the Fermi energy be 61?. Compute the density of states D(eF) at this Fermi energy and the specic heat C = 1TgilcTDzp). How does this compare to the results for a free electron gas in 3D? You will nd that they are very similar; nothing changes except that we should replace the electron mass by some effective mass mz:mesma. (& Here are some geometry facts you may nd helpful. An ellipse whose semiaxes are a, b has area web. All ellipsoid whose semiaxes are a, b, c has area abc