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Title:  Quantum Liquid Crystal Phases in Strongly Correlated Fermionic Systems 
Author(s):  Sun, Kai 
Doctoral Committee Chair(s):  Phillips, Philip W. 
Doctoral Committee Member(s):  Fradkin, Eduardo H.; Cooper, S. Lance; Stack, John D. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Quantum liquid crystal phases
fermionic systems 
Abstract:  This thesis is devoted to the investigation of the quantum liquid crystal phases in strongly correlated electronic systems. Such phases are characterized by their partially broken spatial symmetries and are observed in various strongly correlated systems as being summarized in Chapter 1. In quantum liquid crystal phases formed by fermions, behaviors beyond Landau's theory of the Fermi liquids appear naturally, signed by the absence of welldefined quasiparticle excitations. Although quantum liquid crystal phases often involve strongcoupling physics, the associated symmetry analysis can often be carried out also in a relatively weak coupling regime and this is the main approach taken in this thesis. Two different quantum liquid crystal phases, the nematic state and the smectic state, are studied in Chapters 2 and 3 respectively, by investigating various instabilities of a Landau Fermi liquid. A nematic phase is a state that breaks the rotational symmetry spontaneously but preserves the translational symmetries. It can be reached by the Pomeranchuk instability of a Landau Fermi liquid. The Pomeranchuk instability in the charge (spinsinglet) sector of a Fermi liquid was studied previously within a random phase approximation and by a highdimensional bosonization method. In Chapter 2, we concentrate on the Pomeranchuk instability in the spintriplet sector, and two different classes of ordered phases are discovered, dubbed the a and ,8phases by analogy to the superfluid 3HeA and Bphases. The Fermi surfaces in the aphases exhibit spontaneous anisotropic distortions, while in the ,8phases the Fermi surfaces remain circular or spherical with topologically nontrivial spin configurations in momentum space. The behaviors of the low energy bosonic excitations are studied both in the order phases (a and .B) and at the quantum critical point separating the ordered phases from the Fermi liquid phase. In Chapter 3, the smectic phase and the quantum phase transition between a metallic nematic state and a metallic smectic phase are investigated using the random phase approximation, by considering the formation of a unidirectional charge density wave in an electronic nematic state. The associated quantum critical point is investigated within the HertzMillis approach. NonFermi liquid behaviors are discovered both at the quantum phase transition and in the smectic ordered phase. The theory we studied here provides a simple description for the socalled "fluctuating stripe" phase in cuprates. Similar to its classical counterpart, the phase transition between the nematic and smectic phases are described by a "gaugelike" theory as required by the rotational invariance in close analogy with the McMillandeGennes theory of the smecticnematic phase transition in classical liquid crystals. However, unlike the classical McMillandeGennes theory, in which the coupling between the "gaugelike" nematic fluctuations and the "matterlike" smectic fields is relevant, in the sense of renormalization group, this coupling is irrelevant at the quantum phase transition. This property enables the study of low energy fluctuations and the fate of fermions near this quantum critical point. In Chapter 4, quantum liquid crystal phases with a broken timereversal symmetry are investigated. We start by studying the general scenario of timereversal symmetry breaking phases in the absence of magnetic ordering in systems with longlived lowenergy fermionic quasiparticle excitations in two dimensions. Using a Berry phase approach, we classified possible timereversal symmetry breaking phases by the accompanying spatial symmetry breaking patterns. Two of the simplest situations are referred to as the type I state, which breaks simultaneously the spaceinversion symmetry and the timereversal symmetry, and the type I I state, in which the chiral symmetry is broken in addition to the breaking of the timereversal symmetry. Although the starting point is general and has little relation with the quantum liquid crystal phases, both type I and type II states defined above are realized by (generalized) Pomeranchuk instabilities. In fact , a type I I state is usually a nematic state which also breaks the timereversal symmetry. Interestingly, the type II states also shows spontaneously generated Hall effect even in the absence of a magnetic field, which is known as the spontaneous anomalous Hall effect. In Chapter 5, we investigate the stability of a quadratic bandcrossing point in twodimensional fermionic systems that provide an explicit example, within well controlled approximations, for the nematic ordering discussed in Chapter 2 and spontaneous anomalous Hall effect discussed in Chapter 4. At the noninteracting level, we show that a quadratic bandcrossing point exists and is topologically stable when the Berry flux of this crossing point is ±27r and the point symmetry group at this point has either fourfold or sixfold rotational symmetries. Strikingly, we find that this wouldbe topologically stable quadratic bandcrossing is marginally unstable against shortrange interactions: a quadratic bandcrossing point in two dimensions is unstable against shortrange repulsion, no matter how weak! Four ordered phases are found in this system, the quantum anomalous Hall state, the quantum spin Hall phase, the nematic phase, and the nematicspinnematic phase. 
Issue Date:  2009 
Genre:  Book Chapter Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/27739 
Rights Information:  © 2009 Kai Sun. 
Date Available in IDEALS:  20111106 
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