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My PhD thesis is the first work to extend magnetoacoustics from metal to semiconductor. To represent the different electronic properties between metal and semiconductor, a new energy surface model is used known as warped energy surface. Metal to semiconductor is a phase transition. The warping effect of the energy surface produces a drastic change in the electrical conductivity and illustrates the phase transition from metal to semiconductor. This is a topological change in the geometrical shape of the energy surface producing phase transition from metal to semiconductor. Hence this is topological phase transition. This work is my PhD work which is awarded in 1969, three years before the first paper of the Nobel physics prize work of David J Thouless et al. My PhD thesis derived the magnetoconductivity tensor and the ultrasound attenuation coefficient for the propagation of GHz sound wave in seumiconductor such as germanium and silicon in the presence of magnetic fields at low temperatures. Here the Boltzmann transport equation is solved using the Shockley tube integral method for two different cases of constant relaxation time and the relaxation time as a Fourier summation. The effect of a magnetic field on electrical conductivity can be represented by integrals by using the idea of tubes. The Shockley tube integral is then solved to determine the magnetoconductivity tensor. It is found that there is no magnetoacoustic effect for semiconductors unlike for metals. Magnetoacoustic effect was discovered by H Bommel in 1954 which showed the periodic variation of the ultrasonic attenuation coefficient versus the inverse magnetic field and that the period of this oscillatory curve is related to the diameter of the Fermi surface which can be used for the determination of the Fermi surface. This is known as magnetoacoustic effect. The absorption of sound wave by the material is measured while magnetic fields of various strengths are applied to it. My thesis is also the first application of statistical mechanics to ultrasound propagation in solids through the use of transport theory. The usual method is electron-phonon interaction of quantum fields theory. This is also the first introduction of transport theory to condensed matter physics. Before that transport theory was used only on neutron transport theory for the design of nuclear reactors. It has to be noted that Philip Anderson and Volker Heine changed the name of solid state theory group in Cavendish Lab, Cambridge University to condensed matter theory group to reflect the significant role of phase transition. Hence my thesis also played a role in the founding of the field of condensed matter physics.
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