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Title:  Pair density wave superconducting states and statistical mechanics of dimers 
Author(s):  Soto Garrido, Rodrigo Andres 
Director of Research:  Fradkin, Eduardo H. 
Doctoral Committee Chair(s):  Stone, Michael 
Doctoral Committee Member(s):  Cooper, S. Lance; Di Francesco, Philippe 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  High temperature superconductivity
Pair density wave Arctic curves Aztec diamond Topological superconductors 
Abstract:  The following thesis is divided in two main parts. Chapters 2, 3 and 4 are devoted to the study of the so called pairdensitywave (PDW) superconducting state and some of its connections to electronic liquid crystal (ELC) phases, its topological aspects in a one dimensional model and its appearance in a quasione dimensional system. On the other hand, chapter 5 is focused on the investigation of the classical statistical mechanics properties of dimers, in particular, the dimer model on the Aztec diamond graph and its relation with the octahedron equation. In chapter 2 we present a theory of superconducting states where the Cooper pairs have a nonzero centerofmass momentum, inhomogeneous superconducting states known as a pairdensitywaves (PDWs) states. We show that in a system of spin1/2 fermions in two dimensions in an electronic nematic spintriplet phase where rotational symmetry is broken in both real and spin space PDW phases arise naturally in a theory that can be analysed using controlled approximations. We show that several superfluid phases that may arise in this phase can be treated within a controlled BCS mean field theory, with the strength of the spintriplet nematic order parameter playing the role of the small parameter of this theory. We find that in a spintriplet nematic phase, in addition to a triplet pwave and spinsinglet dwave (or s depending on the nematic phase) uniform superconducting states, it is also possible to have a dwave (or s) PDW superconductor. The PDW phases found here can be either unidirectional, bidirectional, or tridirectional depending on the spintriplet nematic phase and which superconducting channel is dominant. In addition, a triplehelix state is found in a particular channel. We show that these PDW phases are present in the weakcoupling limit, in contrast to the usual FuldeFerrellLarkinOvchinnikov phases, which require strong coupling physics in addition to a large magnetic field (and often both). In chapter 3 we show that the pairdensitywave (PDW) superconducting state emergent in extended HeisenbergHubbard models in twoleg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform dwave onedimensional superconductor. Similarly to a conventional finitemomentum paired state, the order parameter of the PDW state is a charge2e field with finite momentum. However, the order parameter here is a quartic electron operator and conventional meanfield theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finitemomentum pairing fields and charge4e superconductivity. In chapter 4 we provide a quasionedimensional model which can support a PDW state. The model consists of an array of stronglyinteracting onedimensional systems, where the onedimensional systems are coupled to each other by local interactions.Within the interchain meanfield theory (MFT), we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coexisting phase of the uniform SC and PDW states. In this quasi1D regime we can treat the strong correlation physics essentially exactly using bosonization methods and the crossover to the 2D system by means of interchain MFT. The resulting critical temperatures of the SC phases generically exhibit a powerlaw scaling with the coupling constants of the array, instead of the essential singularity found in weakcoupling BCStype theories. Electronic excitations with an open Fermi surface, which emerge from the electronic Luttinger liquid systems below their crossover temperature to the Fermi liquid, are then coupled to the SC order parameters via the proximity effect. From the Fermi surface thus coupled to the SC order parameters, we calculate the quasiparticle spectrum in detail. We show that the quasiparticle spectrum can be fully gapped or nodal in the uniform SC phase and also in the coexisting phase of the uniform SC and PDW parameters. In the pure PDW state, the excitation spectrum has a reconstructed Fermi surface in the form of Fermi pockets of Bogoliubov quasiparticles. In chapter 5 we study the octahedron relation (also known as the A∞ Tsystem), obeyed in particular by the partition function for dimer coverings of the Aztec Diamond graph. For a suitable class of doubly periodic initial conditions, we find exact solutions with a particularly simple factorized form. For these, we show that the density function that measures the average dimer occupation of a face of the Aztec graph, obeys a system of linear recursion relations with periodic coefficients. This allows us to explore the thermodynamic limit of the corresponding dimer models and to derive exact “arctic” curves separating the various phases of the system. 
Issue Date:  20150630 
Type:  Thesis 
URI:  http://hdl.handle.net/2142/87983 
Rights Information:  Copyright 2015 Rodrigo Andres Soto Garrido 
Date Available in IDEALS:  20150929 
Date Deposited:  August 201 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois