DISTRIBUTED LATENT HEAT OF THE PHASE TRANSITIONS IN LOW-DIMENSIONAL CONDUCTORS

1. DISTRIBUTED LATENT HEAT OF THE PHASE TRANSITIONS IN LOW-DIMENSIONAL CONDUCTORS • V.Ya. Pokrovskii, Institute of Radioengineering and Electronics, Russian Academy of Sciences, Mokhovaya 11-7, Moscow, 125009, Russia Plan • The main idea. • What follows from it. • Comparison with experiments.

2. A classical 2nd-order phase transition:step of cp (or )Equivalent: K.H. Mueller, F. Pobell and Guenter Ahlers, Phys. Rev. Lett. 34, 513 (1975); “Phase Transition and Critical Phenomena”, edited by C. Domb and M.S. Green (Academic, New York, 1976), V. 6.V. Pasler, P. Schweiss, C. Meingast, B. Obst, H. Wuhl, A.I. Rykov and S. Tajima, Phys. Rev. Lett. 81, 1094 (1998).A classical 1st-order phase transition:Q= Hand a step-like change of dimensions  Lx,y,z.Fluctuations:Tc < Tmf; Typically, Tmf – Tc ~ Tmf .

3. Usual description of the transitions: • 3D-XY model (scaling):L. Onsager, Phys. Rev. 65, 117 (1944). -transition in He:K.H. Mueller, F. Pobell and Guenter Ahlers, Phys. Rev. Lett. 34, 513 (1975); “Phase Transition and Critical Phenomena”, edited by C. Domb and M.S. Green (Academic, New York, 1976), V. 6. Superconducting transition in layered compounds:V. Pasler, P. Schweiss, C. Meingast, B. Obst, H. Wuhl, A.I. Rykov and S. Tajima, Phys. Rev. Lett. 81, 1094 (1998). Peierls Transition: M.R. Hauser, B.B. Plapp, and G. Mozurkevich, Phys. Rev. B 43, 8105 (1991); J.W. Brill, M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, and G. Mozurkewich, Phys. Rev. Lett 74, 1182 (1995); M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, J.W. Brill, and G. Mozurkewich, Synth. Metals 71, 1891 (1995). • Gaussian approach: Superconducting transition in layered compounds:C. Meingast, A. Junod, E. Walker, Physica C 272,106 (1996). Peierls Transition: M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, J.W. Brill and G. Mozurkewich, Synth. Metals 71, 1891 (1995). Discontinuity at Tc.

4. What is surprising: WHY not just shifting down?

5. What is surprising: WHY not just shifting down?

6. What is surprising: WHY not just shifting down? Suppose, at |T-Tc| > Tc/2 both cp and H follow MF, And for SOME reason Tc < Tmf-Tc.

7. What is surprising: WHY not just shifting down? Suppose, at |T-Tc| > Tc/2 both cp and H follow MF, And for SOME reason Tc < Tmf-Tc. The only way: a smeared out STEP of H and MAXIMUM of cp. If Tc << Tmf-Tc, the maximum should dominate over the step.

8. Estimates. From the condition of the conservation of the area under cp(T) curve [C. Meingast, V. Pasler, P. Nagel, A. Rykov, S. Tajima, and P. Olsson, Phys. Rev. Lett. 86, 1606 (2001) ]: Integrating the maximum of cp(T) we can attribute a certain distributed latent heat to the transition (implying that cp=const for Tc < T < Tmf).

9. How to check? • Tmf – only theoretically. • K0.3MoO3[J.W. Brill, M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, and G. Mozurkewich, Phys. Rev. Lett. 74, 1182 (1995); M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, J.W. Brill, and G. Mozurkewich, Synth. Metals 71, 1891 (1995)]: 1) Tmf- Tc = 16 Kfrom the CAS model [Z.Y. Chen, P.C. Albright, and J.V. Sengers, Phys. Rev. A 41, 3161 (1990).] • The width of the cp maximum is about 5 K . 3) The cp anomaly is about 2-3 times larger than the MF-step value (3 is not >>1, so both the step and the max. are seen)

10. The model of Gaussian fluctuations. The singular parts of cp above and below Tc: (t =|T-Tc|/Tc ) [G. Mozurkewich, M.B. Salamon, S.E. Inderhees, Phys. Rev. B 46, 11914 (1992).] To avoid the divergency integrating we can cut off the anomaly at t=1 for (Tmf- Tc)/Tc > 1 and at t=(Tmf- Tc)/Tc for (Tmf-Tc)/Tc < 1. - 1st case - 2nd case

11. The form of the cp(T) maximum? • Particular model. We do not see a universal reason for Tc < Tmf-Tc. Approach from below: the precursor effect is the cpgrowth. We can attribute it to the nucleation of normal phase. Once T<Tmf, Hn>Hc, and we can try to describe the whole transition region as thermal activation of the normal excitations: [V. Ya. Pokrovskii, A. V. Golovnya, and S. V. Zaitsev-Zotov, Phys. Rev. B 70, 113106 (2004).] Narrow transition: 1/W < 1/Tc-1/Tmf – collective excitations. No transition point?! No divergence – exponent.

12.  D. Starešinić et al., Eur. Phys. J. B 29, 71 (2002). G. Mozurkewich et al., Synth. Met. 60, 137 (1993).

13. Not always: critical behavior is observed, e.g., for YBa2Cu3Ox .  measurements demonstrate the tendency of evolution of a MF step into a wide maximum with the decrease of the doping (equivalent tothe growth of anisotropy, and, consequently, of the 2D fluctuations) [C. Meingast, V. Pasler, P. Nagel, A. Rykov, S. Tajima, and P. Olsson, Phys. Rev. Lett. 86, 1606 (2001) ] growth of Tmf- Tc. See also the tomorrow poster of A.V. Golovnya et al. • Conclusions: • The simple consideration shows that a maximum of cpand  should be the prevailing effect observed at Tc. • An estimate relating the distributed “latent heat” with the mean-field step of cp and the difference Tmf-Tc is given. • Agreement for cp(T) in K0.3MoO3. Particular forms of cp(T) require particular models. • I am grateful to S.N. Artemenko, A.V. Golovnya, S.V. Zaitsev-Zotov, …