Magnetic Breakdown: Effective Hamiltonian and de Haas-van Alphen Effect

Abstract

The influence of magnetic breakdown on the usual effective-Hamiltonian theory for Bloch electrons in a magnetic field is discussed using a simple two-dimensional rectangular model. The theory is based upon an expansion of the wave function in Wannier functions, but these have to be replaced by generalized Wannier functions (suggested by Blount) to handle breakdown. It is shown how to construct a linear network essentially equivalent to the network derived previously by the author for a nearly-free-electron model. The de Haas-van Alphen effect is discussed by expressing the energy density of states in terms of a time-independent Green's function on the network. It is shown how to construct a wave function lying on a twodimensional network as used by Pippard.* J. M. Luttinger, Phys. Rev. 84, 814 (1951). 3 E. Brown, Phys. Rev. 133, A1038 (1964.

Stage III Annealing Study of Electron-Irradiated Pure Aluminum

“…Frois and Dimitrov 5,6 have reported the recovery of pure Al after neutron irradiation at liquid-nitrogen temperatures. They obtained an activation energy of 0.56±0.06 eV for Stage III recovery.…”

“…Pippard 2 ' 3 has discussed the consequences of breakdown in terms of network models and the author has attempted to justify this approach in terms of a nearly-free-electron model 4 and in terms of the theory of the effective Hamiltonian. 5 A modified theory of the de Haas-van Alphen effect was developed by Falicov and Stachowiac 6 in terms of a time-dependent Green's function and a similar theory was later developed by the author in terms of a time-independent Green's function. 4,5 Both approaches treat the Green's function as a propagator on a Pippard network.…”

“…5 A modified theory of the de Haas-van Alphen effect was developed by Falicov and Stachowiac 6 in terms of a time-dependent Green's function and a similar theory was later developed by the author in terms of a time-independent Green's function. 4,5 Both approaches treat the Green's function as a propagator on a Pippard network.…”

“…[1][2][3][4][5][6][7][8][9] Federighi et al}~A in a series of experiments irradiated pure Al and Al alloys with neutrons. Recovery spectra in the Stage II and Stage III regions were investigated.…”

Theory of Bloch Electrons in a Magnetic Field

“…) and the localization of the Wannier function a,(z)[44].Both are closely connected withfhe analytic structure of Bloch bands [36, 381. There are no reliable estimates up to now [39,44].…”