Antiferromagnetism, Superconductivity, Pseudogap and Their Interplay with the Mott Transition

Research output: ThesisDoctoral Thesis

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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 short-range order correlations.
By the use of Cellular Dynamical Mean-Field Theory with the Hybridisation Expansion Continuous-Time Quantum Monte Carlo as the impurity solver, we begin examining the two-dimensional Hubbard model. The comparative analysis at half-filling 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 high-temperature 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 potential-energy driven to kinetic-energy driven upon a reduction in doping.
The first-order 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 charge-transfer 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 languageEnglish
Awarding Institution
  • Royal Holloway, University of London
  • Sordi, Giovanni, Supervisor
  • Eschrig, Matthias, Advisor
Award date1 Dec 2017
Publication statusUnpublished - 2017


  • Cellular dynamical mean field theory
  • high temperature superconductivity
  • strongly correlated fermions
  • Mott transition
  • d-wave superconductivity

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