
Superfluidity in Strongly Correlated Systems A dissertation presented by Eun Gook Moon to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts May 2011 c 2011 - Eun Gook Moon All rights reserved. Thesis advisor Author Subir Sachdev Eun Gook Moon Superfluidity in Strongly Correlated Systems Abstract We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order ∆ , where ∆ is pairing amplitude, so that the region of SDW order is smaller j j in the superconductor than in the metal. This shift is larger than the ∆ 2 shift j j predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by cop- per based high temperature superconductors. Based on spin and charge fraction- alization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductiv- ity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractional- ization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as \nodal-antinodal dichotomy" at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such uni- versal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. iii Contents Title Page....................................i Abstract..................................... iii Table of Contents................................ iv Citations to Previously Published Work................... vi Acknowledgments................................ vii Dedication.................................... ix 1 Introduction1 1.1 Phase diagrams of cuprates and pnictides................4 1.2 Spin and charge fractionalization....................7 1.3 Superfluidity near the Feshbach resonance............... 10 1.4 Organization of this thesis........................ 14 2 Quantum critical point shifts under superconductivity: the pnictides and the cuprates 16 2.1 Introduction................................ 16 2.2 The spin-fermion model......................... 20 2.3 Pairing instabilities............................ 24 2.4 Microscopic symmetry and effective theory............... 26 2.5 Critical point shifts............................ 29 2.6 Conclusions................................ 36 3 Competition between spin density wave order and superconductivity in the underdoped cuprates 40 3.1 Introduction................................ 40 3.2 Eliashberg theory of pairing....................... 49 3.3 Shift of SDW ordering by superconductivity.............. 61 3.4 Conclusions................................ 66 4 Quantum-critical pairing with varying exponents 70 4.1 Introduction................................ 70 4.2 Review of the models........................... 74 iv Contents v 4.3 the MS model as the γ model with varying exponent γ ........ 80 4.4 the MS model at the SDW QCP { the equivalence with color super- conductivity................................ 88 4.5 Conclusions................................ 91 5 The underdoped cuprates as fractionalized Fermi liquids: transition to superconductivity 93 5.1 Introduction................................ 93 5.2 Effective Hamiltonian........................... 100 5.3 Invariant pairings and instability.................... 104 5.4 Spectral Gap............................... 108 5.5 Conclusions................................ 115 6 Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential 119 6.1 Introduction................................ 119 6.2 Model Hamiltonian............................ 121 6.3 Discussion................................. 126 Citations to Previously Published Work Chapter2 has been previously published as \Quantum critical point shifts under superconductivity: the pnictides and the cuprates", E. G. Moon and S. Sachdev, Phys. Rev. B, 82, 104516 (2010), arXiv:1005.3312. Chapter3 has been recently published as \Competition between spin density wave order and superconductivity in the underdoped cuprates", E. G. Moon and Subir Sachdev, Phys. Rev. B, 80, 035117 (2009), arXiv:0905.2608. Chapter4 has been previously published as \Quantum-critical pairing with varying exponents", E. G. Moon and A. V. Chubukov, JLTP , 161, 263(2010), arXiv:1005.0356. Chapter5 has been recently submitted and accepted as \The underdoped cuprates as fractionalized fermi liquids : transition to superconductivity", E. G. Moon and Subir Sachdev, arXiv:1010.4567. Chapter6 has been previously published as \Superfluid-insulator transitions of the Fermi gas with near-unitary inter- actions in a periodic potential", E. G. Moon, P. Nikolic, and S. Sachdev, Phys. Rev. Lett., 99, 230403 (2007), arXiv:0707.2383. Electronic preprints (shown in typewriter font) are available on the Internet at the following URL: http://arXiv.org vi Acknowledgments It would have been impossible to complete this thesis without help from many people. I wish to thank them from my heart. Most of all, I would like to thank my advisor, Professor Subir Sachdev. I vividly remember the first moment of graduate years at Harvard when I got author's signature on his book. Since then it was a great experience to work with him. His deep understanding and intuition of physics guided me well. Discussions with him always made my understanding deeper. Writing papers together gave me great opportunities to learn his perspective and knowledge which I desire to reach. Without his help, I could not imagine finishing this thesis. Also, I would like to thank Professor Eugene Demler and Professor Markus Greiner for being on my thesis committee. I am grateful to them for providing me presentation opportunities though I have changed my subfield from the ultracold atoms. Discussions with many talented postdocs was one of the most effective ways to learn physics. I am especially grateful to Cenke Xu, Erez Berg, and Liang Fu. Cenke's theoretical viewpoint inspired me and motivated me to study topological objects in field theories. Erez not only taught me a number of phenomenologies but also showed me how one could understands physics in one's own way. Discussions with Liang always gave me chances to think different perspectives. I was impressed by his tendency to find easier ways to explain phenomena. I am indebted to my fellow students in the condensed matter group at Harvard: Yang Qi, Rudro Biswas, Max Metlitski, Yejin Huh, and Susanne Piewala, Takuya Kitagawa. I learned a lot of physics from discussions with them, and I appreciate their friendship. Particularly, Yang taught me useful numerics and his previous work on which I studied superconductivity in an exotic ground state based. Discussions with Max always became good motivations and helped me to understand physics more, and I would like to thank him. I wish to thank Yejin for being a wonderful office-mate and correcting my numerous English mistakes. I wish to thank all my friends I met during my Ph.D program. I am especially grateful to my Korean physics friends at Harvard and MIT: Eunmi Chae, Junhyun Lee, Jaehoon Lee, Jung Ook Hong, Sungkun Hong and Eunju Lee. I deeply appreciate their care, support, and friendship. Their preparation of my defense party was one vii Acknowledgments viii of the most moving events in my time at Harvard. I would like to thank Professors Yong-Baek Kim, Hae-Young Kee, and Eunah Kim for their advices, supports, and encouragements. I would also like to offer my thanks to Professors Junghun Han, Jun-Sung Kim, Jisoon Ihm, Gun-Sang Jeon, Kee-hoon Kim, Tae-won Noh, and Kwon Park and their group members for their hospitality, giving me chances to present my work during my visits to Korea. And I thank Sungwan, Changhyun, Daesu, Jaehyung, Youngkuk, Hosung, Seungeun, Hongki for their unchanging friendship. I deeply appreciate help from all secretaries. Sheila Ferguson helped a clueless international student and made him get through all hurdles to graduate. I would also like to thank William Walker and Heidi Kaye, who made it possible for me to travel. Lastly and most importantly, I would like to thank my parents, Byeong-Kil Moon and Geum-Hee Park. They bore me, raised me, taught me, and loved me. And I wish to thank my brother, Eun-Oh Moon, who always supported me, being the best friend in my life. To them I dedicate this thesis. Dedicated to my father Byeong-Kil Moon, my mother Geum-Hee Park, and my brother Eun-Oh Moon. ix Chapter 1 Introduction This thesis studies theory of superfluidity
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