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In a previous paper, the author has pointed out that metamaterial in fact is artificial phase transition. It has the singularity behaviour of the transport properties such as permeability for electromagnetic metamaterial and bulk modulus for acoustic metamaterial which is a characteristic of phase transition. Besides this there are works on topological phase transition in hyperbolic metamaterials which further illustrates that metamaterial is artificial phase transition. The advantage of artificial phase transition is to enable one to control and manipulate phase transition, such as to raise the critical temperature of superconductivity to produce high temperature superconductor which is not found in nature. The negative permeability of a classical metamaterial enables one to control and manipulate classical magnetism. The negative permeability of a quantum metamaterial enables one to control and manipulate superconductivity. Metamaterial as artificial phase transition will open up to a whole new world of new materials. Also the advantage pf artificial phase transition is to obtain exceptional properties unavailable in natural form. For instance, in classical metamaterial, in magnetism, the magnetic property can be enhanced with negative permeability. For an elastic material, the elasticity can be enhanced with negative bulk modulus. In this paper, the concept of topological phase transition will be used in quantum metamaterial for the design of artificial semiconductor. This is a continuation of my PhD thesis(1969) in which I first introduced topological phase transition by using a warped energy surface model for semiconductor instead of the spherical free electrons model used for metal. The warping of the energy surface will produce a drastic change in the electrical conductivity giving rise to phase transition from metal to semiconductor. Hence this is a form of topological phase transition. It is also meaningful that metamaterial is a composite that depends on the geometrical structure of the unit cells rather than the material's electronic structure. Topology is a study of the geometric structure. Here the quantum metamaterial has to be used. The unit cell or qubits will be made of semiconductor and the quantum circuits will be made of Josephson junctions with nonlinear property and there will be interactions between the unit cells. Here the energy surface can be engineered by tailoring the permittivity tensor of the metamaterial composite to have a negative value and to have a singularity behaviour and to produce a warping of the energy surface .
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