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Numerical Studies of Iron Based Superconductors Using Spin- Fermion Models

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Numerical Studies of Iron Based Superconductors Using Spin- Fermion Models University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2017 Numerical Studies of Iron Based Superconductors using Spin- Fermion Models Christopher Brian Bishop University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Condensed Matter Physics Commons Recommended Citation Bishop, Christopher Brian, "Numerical Studies of Iron Based Superconductors using Spin-Fermion Models. " PhD diss., University of Tennessee, 2017. https://trace.tennessee.edu/utk_graddiss/4735 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Christopher Brian Bishop entitled "Numerical Studies of Iron Based Superconductors using Spin-Fermion Models." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Physics. Adriana Moreo, Major Professor We have read this dissertation and recommend its acceptance: Elbio Dagotto, Steve Johnston, Takeshi Egami Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Numerical Studies of Iron Based Superconductors using Spin-Fermion Models A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Christopher Brian Bishop December 2017 c by Christopher Brian Bishop, 2017 All Rights Reserved. ii Acknowledgements I would like to thank Shuhua Liang for all of his help during my early stages of graduate research. For all of the opportunities and guidance that she has given me throughout my graduate years, I would like to thank my advisor Dr. Adriana Moreo. I would also like to thank my brothers for all of their support. Lastly, I would like to thank my parents Leonard and Carol Bishop. Without their support and sacrifices this Dissertation would not have been possible. iii Abstract The iron pnictide and iron chalchogenide superconductors are studied numerically using classical Monte Carlo techniques to reproduce experimental data and make predictions about the nature of the relevant interactions. The focus will be using Spin-Fermion models in a classical approximation to explore the phase diagram and calculate important physical properties of these materials over a wide range of temperatures. iv Table of Contents 1 Introduction1 1.1 High Temperature Superconductors.......................1 1.2 Properties of the Iron Pnictides.........................2 1.3 Properties of Iron Chalcogenides......................... 10 1.4 Relevant Degrees of Freedom in the Fe-Based Superconductors........ 11 1.5 Spin Fermion Model............................... 15 2 Study and Explanation of the Features of the Magnetic Susceptibility Under Uniaxial Pressure in BaFe2As2 17 2.1 Introduction.................................... 17 2.2 Models....................................... 19 2.3 Many-body techniques and main results.................... 21 2.4 Nematic Susceptibility.............................. 25 2.4.1 Analysis of χs results........................... 25 2.4.2 Analysis of χo results........................... 27 2.5 TS vs. λ~66 ..................................... 30 2.6 Spin structure factors and pseudogaps..................... 30 2.7 Conclusions.................................... 32 3 Disorder Induced Nemacity 33 3.1 Introduction.................................... 33 3.2 Model....................................... 36 3.2.1 Hamiltonian................................ 36 v 3.2.2 Quenched Disorder and Dilution..................... 39 3.3 Methods...................................... 39 3.4 Results....................................... 41 3.4.1 Clean limit................................ 41 3.4.2 Co doping................................. 42 3.4.3 Cu doping................................. 45 3.4.4 Dependence on impurity characteristics................. 47 3.5 Properties of the Nematic Phase......................... 50 3.5.1 Neutron scattering............................ 50 3.5.2 Scanning Tunneling Microscopy..................... 54 3.6 Discussion and Conclusions........................... 55 4 Bicollinear Magnetic order and Monoclinic Lattice Distortion in Iron Telluride 58 4.1 Introduction.................................... 58 4.2 Model....................................... 61 4.3 Results....................................... 64 4.4 Discussion.................................... 68 5 Possible Bicollinear Nematic State with Monoclinic Lattice Distortions in Iron Telluride Compounds 69 5.1 Introduction.................................... 69 5.2 Model....................................... 73 5.3 Methods: the Parallel Traveling Cluster Approximation........... 76 5.4 Results....................................... 79 5.4.1 Special case λ~12 = 1............................ 79 5.4.2 Special case λ~12 = 0:85.......................... 82 5.4.3 Phase Diagram.............................. 82 5.5 Discussion and Possible Physical Realizations................. 84 5.6 Conclusions.................................... 86 vi 6 Summary 88 Bibliography 89 Appendices 114 A Full Spin-Fermion Hamiltonian with B1g Lattice Couplings 115 B Ginzburg-Landau Phenomenological Approach 120 C Partial and Total Derivatives at TS 126 D Spin-nematic Susceptibility at Large λ~66 128 E Definition and Calculations of Lattice Displacement and Magnetic and Structural Order Parameters 130 F Resistivity Calculation 134 G Additional Phase Diagrams for the Hamiltonian Studied in Ch.4 137 H Unexpected Intermediate Temperature Range of Finite JNNN /JNN for the Hamiltonian Studied in Ch.4 142 I Reversed Resistivity in FeTe with Details on the Results Presented in Ch.4 144 Vita 147 vii List of Tables A.1 Values of the parameters that appear in the tight-binding portion of the three- orbital model Eqs.(A.3) to (A.5). The overall energy unit is electron volts.. 118 viii List of Figures 1.1 (Top) The lattice structure and chemical formula for three common cop- per based superconductors characterized by CuO2 layers. This figure is reproduced from Ref. [6].(Bottom) The lattice structure for the iron based superconductors and their superconducting transition temperatures Tc. The left three materials exemplify the 1111, 122 and 111 members of the pnictide family. The green circles are As atoms (pnictides) and the blue are Fe atoms. These form the FeAs layers that characterize these materials. The compound on the far right does not contain As and is a representative of the chalcogenides where here the green circles are Se/Te. This figure is reproduced from Ref. [7]3 1.2 (Left) A schematic phase diagram for the cuprates. The blue areas denote the checkerboard AFM phase while the red areas indicate the superconducting phase. This figure is reproduced from Ref. [10]. (Right) Schematic phase diagram for 122 pnictides. Ort/AFM denotes the phase with collinear magnetic order and orthorhombic lattice distortion, SC the superconducting phase,and PM/Tet the paramagnetic and tetragonal phase. In addition, a nematic phase appears upon doping. Tetragonal symmetry is only broken below the nematic/orthorhombic transition line, but nematic fluctuations remain at higher temperatures. This figure is reproduced from Ref. [11]....4 ix 1.3 (a) The copper oxide plane in the cuprate superconductors showing the Q~ =(π,π), checkerboard AFM order in the Cu spins. The red circles are oxygen ions and are co-planar with the blue Cu ions. (b) The pnictide FeAs plane. The blue circles are Fe ions and the red circles are As ions where the darker (lighter) red circles are the As ions above (below) the Fe plane. The collinear (π,0) AFM order is indicated in the Fe spins. This figure is reproduced from Ref. [12]......................................5 1.4 An illustration of the five d orbitals where the valence electrons in Fe and Cu reside. The orbitals can be separated into two groups: t2g and eg. For Cu the eg orbitals, particularly dx2 y2 , contain the most weight at the FS while for − Fe the t2g orbitals are the ones that form the FS. This figure is reproduced from Ref. [14]...................................5 1.5 (Left) The La2CuO4 band structure from LDA calculations. The band that crosses the Fermi surface has mostly Cu 3dx2 y2 character. This figure is − reproduced from Ref. [15]. (Right) Band structure of LaFeAsO from First Principles calculations. The red and green bands have mainly Fe 3d and pnictogen/oxygen p characters, respectively. This figure is reproduced from Ref. [16]......................................6 1.6 (Left) Fermi Surface for the cuprates calculated in a one band Hubbard model. This figure is reproduced from Ref. [17]. (Right) Fermi Surface for the pnictides calculated in a five orbital tight-binding model. This figure is reproduced from Ref. [18]. The blue, red, and green represents the dxy , dxz, and dyz orbitals respectively............................7 1.7 (Left) An illustration of four examples of proposed pairing symmetries for the iron pnictides. The colors (green/orange) represent the sign
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