Faculté des sciences

## Amplitude and phase fluctuations in high temperature superconductors

### Thèse de doctorat : Université de Neuchâtel, 2003 ; 1784.

Depuis la découverte en 1986 des cuprates, céramiques supraconductrices à haute température, les expérimentateurs ont mis en évidence que l'état non-supraconducteur des céramiques présente un comportement très différent des métaux classiques. Certains ont avancé l'hypothèse que ce régime, dit de pseudogap, est lié à des causes extérieures à la supraconductivité comme... Plus

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Résumé
Depuis la découverte en 1986 des cuprates, céramiques supraconductrices à haute température, les expérimentateurs ont mis en évidence que l'état non-supraconducteur des céramiques présente un comportement très différent des métaux classiques. Certains ont avancé l'hypothèse que ce régime, dit de pseudogap, est lié à des causes extérieures à la supraconductivité comme l'antiferromagnétisme ou un point critique quantique, alors que d'autres pensent que le pseudogap est lié directement à la supraconductivité. L'approche théorique présentée dans cette thèse a pour but de tester si la supraconductivité est liée aux propriétés non conventionnelles du pseudogap. Les résultats des calculs et les comparaisons avec les expériences confirment cette hypothèse, et permettent de comprendre les apparentes contradictions de certains résultats expérimentaux.
Summary
We begin this work by an overview of selected topics of phase transitions and condensed matter physics, then we have the following chapters: Chapter \ref{variational} is devoted to the study the reciprocal influence between the phase $\phi$ and the amplitude $|\psi|$ of the complex field $\psi$ in the Ginzburg-Landau (GL) functional. This functional contains two parts: the amplitude part, involving only the amplitude \index{amplitude} $|\psi|$ and a coupling constant coming from the phase part, and the phase part, XY like, with a coupling constant coming from the amplitude part. The essential result of this chapter is a new approach for solving the GL functional integral by separating amplitude and phase. One important consequence is the possibility of a first order transition (that is a jump of the order parameter) at the transition temperature. The aim of the chapter \ref{pseudogap} is to focus on the problem of the pseudogap phase of underdoped high temperature superconductors. The starting point will be a pairing hamiltonian for fermions like in BCS theory. Using the Hubbard-Stratonovich transformation with a complex pairing field, the main goal will be to take into account both amplitude and phase influence on the electronic properties. One of the results is that the mean amplitude of the pairing field remains large at high temperature: it is never zero because of fluctuations especially in the underdoped regime where the charge carrier density is low. Phase fluctuations are still correlated above $T_c$ until some crossover temperature $T_\phi$ which is typically 30 \% above $T_c$. Comparison with measured specific heat on underdoped YBCO reproduces the double peak structure: a sharp peak at $T_c$ coming from phase fluctuations and a wide hump above $T_c$ rounded by amplitude fluctuations. The spin susceptibility, related to the amplitude, recovers its normal behaviour near the temperature $T^*$ whereas the orbital magnetic susceptibility, related to the phases, disappears near $T_{\phi}$. All these findings provide additional evidence for the fact that superconductivity and pseudogap have the same origin. The former is primarily related to phases of the pairing field, which order below the transition temperature and whose correlations survive over a limited temperature region above $T_c$ until $T_{\phi}$. The pseudogap regime of underdoped materials then extends to much higher temperatures thanks to the persisting amplitude fluctuations of the pairing field. Chapter 5 is devoted to the study of the high temperature domain of the pseudogap phase where phases are completely uncorrelated, i.e. above $T_\phi$. A method suitable to disordered systems known as CPA (Coherent Potential Approximation) is used to compute the Green function. CPA is extended to $d$-wave symmetry, and the role of amplitude fluctuations is discussed in a simplified approach. A comparison is made to DMFT results on the attractive Hubbard model showing similar results provided that amplitude fluctuations are included in the CPA approach. In chapter 6, the CPA calculations is extended below $T_c$ in the presence of a superconducting order parameter. In chapter 7, the Green function and the self-energy are computed in the Hubbard-Stratonovich transformation below and above the critical temperature $T_c$ by introducing phase correlations.