Abstract
After more than thirty years since the discovery of high temperature superconductivity in the cuprates, their properties still lack a complete theoretical understanding.
In this work, we will argue that the key role to decipher the phase diagram of these compounds lies in the physics of the Mott transition, combined with the effect of shortrange order correlations.
By the use of Cellular Dynamical MeanField Theory with the Hybridisation Expansion ContinuousTime Quantum Monte Carlo as the impurity solver, we begin examining the twodimensional Hubbard model. The comparative analysis at halffilling of the properties of the antiferromagnetic and normal state reveals a detectable, sharp crossover in the condensation energy linked to the underlying Mott transition.
Upon doping the system, the study of several parametric regimes in the presence of $d$wave superconductivity reveals the role of the pseudogap to correlated metal transition, hidden under the superconducting dome.
The Widom line is a line of crossovers that emerges at hightemperature from this transition.
This supercritical behaviour not only determines the shape of this dome but also the maxima of $T_c$ at optimal doping as well as the driving mechanism that allows the superconductivity to occur. Furthermore, it explains how
the condensation energy can change from potentialenergy driven to kineticenergy driven upon a reduction in doping.
The firstorder transition affects the superconducting properties, providing an organising principle for the whole phase diagram.
Additionally, we investigate a more realistic model for the cuprates that includes three orbitals per unit cell, the Emery model. We compute the finite temperature behaviour of the metal to chargetransfer insulator transition driven by the interaction and of the pseudogap to correlated metal transition driven by increasing the hole carrier concentration. The features of the superconducting and normal states confirm the Hubbard model scenario, despite the large differences in microscopic details, such as the presence of oxygen and the different band structure.
In this work, we will argue that the key role to decipher the phase diagram of these compounds lies in the physics of the Mott transition, combined with the effect of shortrange order correlations.
By the use of Cellular Dynamical MeanField Theory with the Hybridisation Expansion ContinuousTime Quantum Monte Carlo as the impurity solver, we begin examining the twodimensional Hubbard model. The comparative analysis at halffilling of the properties of the antiferromagnetic and normal state reveals a detectable, sharp crossover in the condensation energy linked to the underlying Mott transition.
Upon doping the system, the study of several parametric regimes in the presence of $d$wave superconductivity reveals the role of the pseudogap to correlated metal transition, hidden under the superconducting dome.
The Widom line is a line of crossovers that emerges at hightemperature from this transition.
This supercritical behaviour not only determines the shape of this dome but also the maxima of $T_c$ at optimal doping as well as the driving mechanism that allows the superconductivity to occur. Furthermore, it explains how
the condensation energy can change from potentialenergy driven to kineticenergy driven upon a reduction in doping.
The firstorder transition affects the superconducting properties, providing an organising principle for the whole phase diagram.
Additionally, we investigate a more realistic model for the cuprates that includes three orbitals per unit cell, the Emery model. We compute the finite temperature behaviour of the metal to chargetransfer insulator transition driven by the interaction and of the pseudogap to correlated metal transition driven by increasing the hole carrier concentration. The features of the superconducting and normal states confirm the Hubbard model scenario, despite the large differences in microscopic details, such as the presence of oxygen and the different band structure.
Original language  English 

Qualification  Ph.D. 
Awarding Institution 

Supervisors/Advisors 

Award date  1 Dec 2017 
Publication status  Unpublished  2017 
Keywords
 Cellular dynamical mean field theory
 CUPRATES SUPERCONDUCTORS
 high temperature superconductivity
 strongly correlated fermions
 Mott transition
 dwave superconductivity