Thermodynamical Cross‐Relations for Superconductors at the Critical Point

Abstract

We investigate superconducting systems with the use of the phenomenological Landau's theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantites (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross-relations between different quantities at the critical point. The derived formulae can practically be used in many cases to find such thermodynamical quantities at the critical point which are extremely difficult to measure under the assumption that the other ones are already known. We additionally perform a test of the two derived relations by using two-band microscopic model, describing superconducting systems. We calculate the specific heat, order parameter and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.

Extended Hubbard Model in the Dimer Representation. I. Dimer Hamiltonian in the Large U Limit

“…The appl i cati on o f the m etho d presented i n thi s pap er to the crysta l as a who l e, descri bed by the Ha mi l to nia n (2 ) i s gi ven i n the next pap er (see Ref. [40]). …”

Extended Hubbard Model in the Dimer Representation. II. Lattice Hamiltonian in the Large U Limit

“…[12] we ha ve presented the exact decom p ositi on of the ori gi na l extended Hubba rd m odel for the sc latti ce (i t can b e general i zed to any l atti ce, to o) i nto a set of i ntera cti ng di mers where each di mer pro bl em has b een exactl y sol ved (see (1 2) in R ef. [12]). The m etho d ha s b een tested i n R ef.…”

“…The m etho d ha s b een tested i n R ef. [12] for a di mer (the sma ll est compl ex of i ntera cti ng ato m s), descri bed by the extended Hubba rd mo del (see (3 ) in R ef. [12]).…”

“…[12] for a di mer (the sma ll est compl ex of i ntera cti ng ato m s), descri bed by the extended Hubba rd mo del (see (3 ) in R ef. [12]). The di m er energy spectrum consists of 16 energi es, 6 of them i n the l arg e U l i m it ta ke on larg e, p ositi ve val ues (see (1 2) i n R ef.…”

“…The di m er energy spectrum consists of 16 energi es, 6 of them i n the l arg e U l i m it ta ke on larg e, p ositi ve val ues (see (1 2) i n R ef. [12]), m uch l arg er tha n the other. It m eans tha t the mentio ned 6 l evels, pro duci ng negl i gi bl e sm al l term s i n the pa rti ti on functi on canno t be o ccupi ed by electro ns and theref ore we can rej ect them fro m the considera ti ons i n the l arg e U l i mi t. T aki ng thi s i nto a ccount we coul d rewri te the di m er Ha mi l to nia n i n the l arg e U l i mi t (see (2 2) i n Ref.…”