Abstract
In this paper, we report the results of our theoretical investigation on the interplay of superconductivity and disorder in two-dimensional (2D) systems. The effect of disorder on superconductivity of 2D systems was found analytically using Green’s function formalism. The results of our calculation revealed that disorder induced due to randomly distributed superconducting islands enhances decoherence of Cooper pairs and suppresses superconductivity. We have also determined the critical value of disorder at which the 2D system completely loses its superconducting properties. Below this critical value of disorder, the system acts as a superconductor, a system with zero electrical resistance. Above the critical value, it acts as an insulator, a system with infinite electric resistance. This is a fascinating result because a direct transition from the state of the infinite conductivity to the opposite extreme of infinite resistivity is unexpected in the theory of condensed matter physics.
Highlights
Superconductivity is a resistanceless state of matter first discovered in mercury by Onnes [1]. is paradoxical state of matter was described microscopically by Bardeen et al [2] in 1957
We have studied the superconductor-insulator quantum phase transition in two-dimensional systems
We mainly considered the effect of disorder-enhanced randomness in an on-site chemical potential on the superconductivity of 2D thin films
Summary
Superconductivity is a resistanceless state of matter first discovered in mercury by Onnes [1]. is paradoxical state of matter was described microscopically by Bardeen et al [2] in 1957. E interest in the field was further increased by the possibility that the disorder-driven or magnetic field-driven suppression of superconductivity in the limit of zero temperature might be a quantum phase transition [10] Investigations in this field revealed that the pairbreaking and decoherence effects of disorder on superconductivity of materials depend on their physical dimension and superconducting pairing symmetry. According to Anderson, weak nonmagnetic disorders (impurities, dislocations, etc.) which could not affect the time-reversal symmetry have no significant effect on thermodynamic properties of three-dimensional (3D) s-wave superconductors. The scaling theory of localization developed in 1979 by Abrahams et al [14] revolutionized the study of dirty superconductors According to this theory, two-dimensional (2D) systems are supposed to exist in only one of the two states at zero temperature, superconductor or insulator. Based on the bosonic scenario of Mathew Fisher [18, 19], we have developed a Hamiltonian which describes our system and derived analytically the relationship between superconducting order parameter and disorder strength
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