Distributed Latent Heat of Phase Transitions in Low-Dimensional Conductors
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ELECTRONICS
Distributed Latent Heat of Phase Transitions in Low-Dimensional Conductors V. Ya. Pokrovskii* Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow, 125009 Russia *e-mail: [email protected] Received December 10, 2019; revised December 10, 2019; accepted December 13, 2019
Abstract—It is shown that if the temperature of the second-order phase transition is lowered due to fluctuations, then the dominant singularity at the transition is the maximum, and not the jump in specific heat. A certain value of latent heat corresponds to this transition, and an estimate is proposed for it. The result is compared with the singularities of the specific heat and coefficient of thermal expansion in the region of Peierls and superconducting transitions. DOI: 10.1134/S1064226920090089
INTRODUCTION The classical second-order phase transition is characterized by a jump δcp in specific heat [1], as well as in the coefficient of thermal expansion (CTE) α, which behaves in a similar manner near phase transitions [2, 3]. This jump distinguishes second-order from first-order transitions, which are accompanied by latent heat equal to the change in enthalpy, Q = δH, and a jumpwise change in dimensions Lx, y, z. A different pattern arises when the reduced dimension of the system leads to strong fluctuations. Transition temperature Tc is much lower than TMF obtained from minimization of enthalpy H in the mean (selfconsistent) field (MF) approximation. In particular, this is clearly seen from the large value of the relation 2Δ/Tc (Δ is the energy gap, either Peierls or superconducting) compared to the value 3.52 obtained in the Bardin–Cooper–Schriffer theory. For example, in the theory of quasi-one-dimensional conductors [4], it was shown that Tc (here, the Peierls transition temperature) can be four times lower than TMF due to fluctuations, but the transition remains quite sharp. There is much evidence of fluctuations in a wide temperature range, Tc < T < TMF [5–7]. For a superconducting transition, a decrease in the transition temperature was considered, for example, in [8]. Usually, phase transitions in the presence of strong fluctuations, for example, the λ transition in He-4 [2], the superconducting transition in layered compounds [3], and the Peierls transition [9, 10], are well described by the 3D-XY (scaling) model [11]. In addition, a Gaussian approach was applied to fluctuations in the region of the superconducting [12] and Peierls [13] transitions. Both approaches predict peculiarities
in the behavior of cP and α when T approaches the critical temperature Tc both from above and below. However, the physical meaning of the peaks cp and α in these approaches has not been discussed. The following question arises: from intuitive considerations, one might think that fluctuations simply shift the “classical” transition to lower temperatures. In this case, one can expect steps (possibly smeared) in the temperature dependences cp and α, but not the maximum. Meanwhile, in some cases, it is preci
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