Chiral symmetry breaking in high-temperature superconductors and birefringent cold atoms, helicity modulus in layered bosons and phase diagram...
Kamran Kaveh Maryan
CHIRAL SYMMETRY BREAKING IN HIGH-TEMPERATURE SUPERCONDUCTORS AND BIREFRINGENT COLD ATOMS, HELICITY MODULUS IN LAYERED BOSONS AND PHASE DIAGRAM OF SUPERCONDUCTOR-INSULATOR TRANSITION
This work is a compilation of different research projects which has been done during the years. The main theme of this thesis, however, is the high-temperature superconductivity.
In Chapter 1 we carefully proceed to construct the field theory of underdoped cuprates beginning with a well-defined d-wave superconductor and adding the vortex degree of freedom using a singular gauge transformation. The symmetries of the theory both in the presence and absence of a quasiparticle mass are a main focus of this Chapter. Nodal quasi-particles is known to obey relativistic Lorentz symmetry while their massless nature represent another symmetry which we will identify as a chiral SU(2) symmetry. It is shown that 2+1 quantum electrodynamics is the effective theory the describes underdoped cuprates in the zero-temperature pseudogap regime.
In Chapter 2, we focus on the mechanism of the dynamical mass generation in three dimensional quantum electrodynamics and theories with four-fermion interactions. This is a field that has been subject of extensive research in last two decades. However, our momentum-shell renormalization group approach is new to the field and through that we are able to estimate the conditions for the mass generation mechanism and also work out the phase diagram of the theory for charge and interaction strength. We devote the rest of Chapter 2 to discuss the applications of momentum-shell renormalization group to other four-fermionic theories in the absence of a gauge field. The justification for this is the fact that in the superconducting regime the system can be described by a massive gauge field theory coupled to relativistic quasi-particles which effectively represent a four-fermionic theory.
Inspired by the field theory constructed in Chapter 1, in Chapters 3 and 4 we discuss the superfluid response of the underdoped materials using an anisotropic bosonic model and compare it to the experiment. The original idea is to see how the c-axis superfluid density measurements can help one to set the parameters in our original field theory for underdoped cuprates. The behaviours of the superfluid responses in both out-of-plane and in-plane has been detailed as a function of temperature and density (doping) and is shown there is disagreement for measured c-axis response using bosonic-only Hamiltonian conjectured. Discussions on the limitations of the layered bosonic model to explain the superfluid response of a underdoped cuprate is detailed at the end of Chapter 4.
The next two Chapters, Chapters 5 and 6 are somewhat diversions of the subject of high-temperature superconductivity. Chapter 5 which is based on a paper I collaborated with M. Kennett and N. Komeilizadeh, discusses similar features of broken chiral symmetry in context of fermions in optical lattices. The particular model which is constructed in Chapter 5 represents broken chiral symmetry for relativistic quasi-particles. However, the mechanism of symmetry breaking is different from dynamical mass generation. Effect of different staggered potentials and Hubbard interaction on this model is briefly discussed.
Chapter 6 is an original work of the author with I.F. Herbut on Superconductor- Insulator transition (SI) in the context of low-dimensional disordered systems. We construct a bosonic theory for a conventional BCS superconductor in the presence of quenched disorder and show that in the