A framework for analytical studies of superconducting systems is presented and illustrated. The formalism, based on the conformal transformation of momentum space, allows one to study the effects of both the dispersio...A framework for analytical studies of superconducting systems is presented and illustrated. The formalism, based on the conformal transformation of momentum space, allows one to study the effects of both the dispersion relation and the structure of the pairing interaction in two-dimensional anisotropic high-T <sub>c</sub> superconductors. In this method, the number of employed degrees of freedom coincides with the dimension of the momentum space, which is different compared to that in the standard Van Hove scenario with a single degree of freedom. A new function, the kernel of the density of states, is defined and its relation to the standard density of states is explained. The versatility of the method is illustrated by analyzing coexistence and competition between spin-singlet and spin-triplet order parameters in superconducting systems with a tight-binding-type dispersion relation and an anisotropic pairing potential. Phase diagrams of stable superconducting states in the coordinates ?· (the ratio of hopping parameters) and n (the carrier concentration) are presented and discussed. Moreover, the role of attractive and repulsive on-site interactions for the stability of the s-wave order parameter is explained.展开更多
We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high- temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transfo...We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high- temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ≤ Tc are discussed using the method of successive approximations. The equation for the ratio R1, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R2, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low-To superconductors. The prospect of application of the presented model in studies of high-To superconductors and other superconducting systems of the new generation is also discussed.展开更多
文摘A framework for analytical studies of superconducting systems is presented and illustrated. The formalism, based on the conformal transformation of momentum space, allows one to study the effects of both the dispersion relation and the structure of the pairing interaction in two-dimensional anisotropic high-T <sub>c</sub> superconductors. In this method, the number of employed degrees of freedom coincides with the dimension of the momentum space, which is different compared to that in the standard Van Hove scenario with a single degree of freedom. A new function, the kernel of the density of states, is defined and its relation to the standard density of states is explained. The versatility of the method is illustrated by analyzing coexistence and competition between spin-singlet and spin-triplet order parameters in superconducting systems with a tight-binding-type dispersion relation and an anisotropic pairing potential. Phase diagrams of stable superconducting states in the coordinates ?· (the ratio of hopping parameters) and n (the carrier concentration) are presented and discussed. Moreover, the role of attractive and repulsive on-site interactions for the stability of the s-wave order parameter is explained.
文摘We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high- temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ≤ Tc are discussed using the method of successive approximations. The equation for the ratio R1, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R2, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low-To superconductors. The prospect of application of the presented model in studies of high-To superconductors and other superconducting systems of the new generation is also discussed.
