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Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and

Superconductivity and Superfluidity heat at the point of this transition is discontinuous (see below). These findings clearly indicate that the superconducting transition is associated with a change order. The complete absence of changes of the crystal lattice structure, proven by X-ray measurements, suggests that this transition occurs as an ordering in the electron subsystem. 4.3.2 The Energy Gap and Specific Heat of a Superconductor The energy gap of a superconductor. Along with the X-ray studies that show no structural changes at the superconducting transition, no changes can be seen in the optical range. When viewing with the naked eye here, nothing happens. However, the reflection of radio waves undergoes a significant change in the transition. Detailed measurements show that there is a sharp boundary in the wavelength range 1 1011 5 1011 Hz, which is different for different superconductors. This phenomenon clearly indicates on the existence of a threshold energy, which is needed for the transition of a superconducting carrier to normal state, i.e., there is an energy gap between these two states. The specific heat of a superconductor. The laws of thermodynamics provide possibility for an idea of the nature of the phenomena by means of general reasoning. We show that the simple application of thermodynamic relations leads to the conclusion that the transition of a normal metal-superconductor transition is the transition of second order, i.e., it is due to the ordering of the electronic system. In order to convert the superconductor into a normal state, we can do this via a critical magnetic field, H c . This transition means that the difference between the free energy of a bulk sample (per unit of volume) in normal and superconducting states complements the energy density of the critical magnetic field: F n − F s = H2 c 8π . (4.22) By definition, the free energy is the difference of the internal energy, U, and thermal energy T S (where S is the entropy of a state): F = U − T S. (4.23) 36 Science Publishing Group

Chapter 4 Basic Milestones in the Study of Superconductivity Therefore, the increment of free energy is δF = δU − T δS − SδT. (4.24) According to the first law of thermodynamics, the increment of the density of thermal energy δQ is the sum of the work made by a sample on external bodies δR, and the increment of its internal energy δU: δQ = δR + δF (4.25) as a reversible process heat increment of δQ = T δS, then δF = −δR − SδT (4.26) thus the entropy ( ) ∂F S = − . (4.27) ∂T R In accordance with this equation, superconducting states (4.22) can be written as: S s − S n = H c 4π the difference of entropy in normal and ( ∂Hc ∂T ) . (4.28) R Since critical field at any temperature decreases with rising temperature: ( ) ∂Hc < 0, (4.29) ∂T then we can conclude (from equation (4.28)), that the superconducting state is more ordered and therefore its entropy is lower. Besides this, since at T = 0, the derivative of the critical field is also zero, then the entropy of the normal and superconducting state, at this point, are equal. Any abrupt changes of the first derivatives of the thermodynamic potential must also be absent, i.e., this transition is a transition of the order-disorder in electron system. Since, by definition, the specific heat C = T ( ) ∂S ∂T , then the difference of specific heats of superconducting and normal states: [ C s − C n = T (∂Hc ) ] 2 ∂ 2 H c + H c 4π ∂T ∂T 2 . (4.30) Science Publishing Group 37

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