Low Energy Electrodynamics in Solids June 28 - July 8, 2021 Table of Contents
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Lecture 3: Fermi-Liquid Theory 1 General Considerations Concerning Condensed Matter
Phys 769 Selected Topics in Condensed Matter Physics Summer 2010 Lecture 3: Fermi-liquid theory Lecturer: Anthony J. Leggett TA: Bill Coish 1 General considerations concerning condensed matter (NB: Ultracold atomic gasses need separate discussion) Assume for simplicity a single atomic species. Then we have a collection of N (typically 1023) nuclei (denoted α,β,...) and (usually) ZN electrons (denoted i,j,...) interacting ∼ via a Hamiltonian Hˆ . To a first approximation, Hˆ is the nonrelativistic limit of the full Dirac Hamiltonian, namely1 ~2 ~2 1 e2 1 Hˆ = 2 2 + NR −2m ∇i − 2M ∇α 2 4πǫ r r α 0 i j Xi X Xij | − | 1 (Ze)2 1 1 Ze2 1 + . (1) 2 4πǫ0 Rα Rβ − 2 4πǫ0 ri Rα Xαβ | − | Xiα | − | For an isolated atom, the relevant energy scale is the Rydberg (R) – Z2R. In addition, there are some relativistic effects which may need to be considered. Most important is the spin-orbit interaction: µ Hˆ = B σ (v V (r )) (2) SO − c2 i · i × ∇ i Xi (µB is the Bohr magneton, vi is the velocity, and V (ri) is the electrostatic potential at 2 3 2 ri as obtained from HˆNR). In an isolated atom this term is o(α R) for H and o(Z α R) for a heavy atom (inner-shell electrons) (produces fine structure). The (electron-electron) magnetic dipole interaction is of the same order as HˆSO. The (electron-nucleus) hyperfine interaction is down relative to Hˆ by a factor µ /µ 10−3, and the nuclear dipole-dipole SO n B ∼ interaction by a factor (µ /µ )2 10−6. -
Quantum Fluctuations Across the Superconductor-Insulator Transition
Quantum Fluctuations Across the Superconductor-Insulator Transition Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Hasan Khan, B.S. Graduate Program in Physics The Ohio State University 2019 Dissertation Committee: Nandini Trivedi, Advisor Yuan-Ming Lu Rolando Vald´esAguilar Richard J. Furnstahl c Copyright by Hasan Khan 2019 Abstract Superconductivity has been at the heart of research into quantum phenomena since its discovery over a century ago. More recently efforts have been made to un- derstand the nature of the quantum phase transition (QPT) that separates the super- conducting and insulating phases in certain 2D materials at zero temperature. This superconductor-insulator transition (SIT) has been theoretically and experimentally proven to be driven by quantum fluctuations of the superconducting phase instead of the breakup of Cooper pairs. In this thesis we present a study of quantum fluctua- tions across the SIT and how they can be imaged in both theoretical simulations and experimental measurements. We begin with an overview of the field from a historical perspective, describing the development of the theory of SITs driven by experiments on thin films. We present the Josephson junction array (JJA) model as a paradigm to investigate the quantum phase fluctuation-driven SIT using quantum Monte Carlo (QMC) techniques. We explore the manifestation of quantum fluctuations across the SIT in three different local measurements: the diamagnetic susceptibility χ(r), two-particle den- sity of states P (r;!), and compressibility κ(r), revealed through their local maps and calculated via QMC. -
Bose-Einstein Condensation in Bacusi2o6
Institute of Physics Publishing Journal of Physics: Conference Series 51 (2006) 9–14 doi:10.1088/1742-6596/51/1/002 Yamada Conference LX on Research in High Magnetic Fields Bose-Einstein condensation in BaCuSi2O6 1N Harrison, 2,3S E Sebastian, 1C D Batista, 1MJaime,4L Balicas, 1P A Sharma, 5N Kawashima and 2IRFisher 1MST-NHMFL, Los Alamos National Laboratory, Los Alamos, NM 87545 2Department of Applied Physics, Geballe Laboratory for Advanced Materials, Stanford University, California 94305-4045 4National High Magnetic Field Laboratory, Tallahassee, FL 32310 5Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan Abstract. BaCuSi2O6 is a model spin dimer system in which a BEC QCP is realised. Universal BEC power law scaling is experimentally observed, with 3d critical behaviour above 0.5 K, but a crossover to 2d BEC critical scaling down to 30 mK. Here we briefly review and expand on the results presented in the recent Nature paper [8]. 1. Spin dimer systems Spin dimer materials have attracted considerable attention recently due to the realisation of Bose-Einstein condensate (BEC) physics in these systems [1, 2, 3, 4, 5, 6, 7, 8, 9]. The ground state of these systems comprises singlets with gapped triplet excitations. In an applied magnetic field, Zeeman splitting of the triplet levels lowers the energy of the lowest triplet, such that above critical field Hc1, a finite concentration of triplets is populated in the ground state. The ground state above Hc1 is an ordered XY antiferromagnet, separated from the disordered quantum paramagnet below Hc1 by a BEC quantum critical point (QCP) at 0 K. -
Unconventional Hund Metal in a Weak Itinerant Ferromagnet
ARTICLE https://doi.org/10.1038/s41467-020-16868-4 OPEN Unconventional Hund metal in a weak itinerant ferromagnet Xiang Chen1, Igor Krivenko 2, Matthew B. Stone 3, Alexander I. Kolesnikov 3, Thomas Wolf4, ✉ ✉ Dmitry Reznik 5, Kevin S. Bedell6, Frank Lechermann7 & Stephen D. Wilson 1 The physics of weak itinerant ferromagnets is challenging due to their small magnetic moments and the ambiguous role of local interactions governing their electronic properties, 1234567890():,; many of which violate Fermi-liquid theory. While magnetic fluctuations play an important role in the materials’ unusual electronic states, the nature of these fluctuations and the paradigms through which they arise remain debated. Here we use inelastic neutron scattering to study magnetic fluctuations in the canonical weak itinerant ferromagnet MnSi. Data reveal that short-wavelength magnons continue to propagate until a mode crossing predicted for strongly interacting quasiparticles is reached, and the local susceptibility peaks at a coher- ence energy predicted for a correlated Hund metal by first-principles many-body theory. Scattering between electrons and orbital and spin fluctuations in MnSi can be understood at the local level to generate its non-Fermi liquid character. These results provide crucial insight into the role of interorbital Hund’s exchange within the broader class of enigmatic multiband itinerant, weak ferromagnets. 1 Materials Department, University of California, Santa Barbara, CA 93106, USA. 2 Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA. 3 Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 4 Institute for Solid State Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany. -
Landau Effective Interaction Between Quasiparticles in a Bose-Einstein Condensate
PHYSICAL REVIEW X 8, 031042 (2018) Landau Effective Interaction between Quasiparticles in a Bose-Einstein Condensate A. Camacho-Guardian* and Georg M. Bruun Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark (Received 19 December 2017; revised manuscript received 28 February 2018; published 15 August 2018) Landau’s description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction. They show that it can be strong even for a weak impurity-boson interaction, if the transferred momentum- energy between the quasiparticles is resonant with a sound mode in the BEC. We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak-coupling results. Using this scheme, we show that the Landau effective interaction, in general, is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas. The interaction is particularly large near the unitarity limit of the impurity-boson scattering or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC. -
Attractive Fermi Polarons at Nonzero Temperatures with a Finite Impurity
PHYSICAL REVIEW A 98, 013626 (2018) Attractive Fermi polarons at nonzero temperatures with a finite impurity concentration Hui Hu, Brendan C. Mulkerin, Jia Wang, and Xia-Ji Liu Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia (Received 29 June 2018; published 25 July 2018) We theoretically investigate how quasiparticle properties of an attractive Fermi polaron are affected by nonzero temperature and finite impurity concentration in three dimensions and in free space. By applying both non- self-consistent and self-consistent many-body T -matrix theories, we calculate the polaron energy (including decay rate), effective mass, and residue, as functions of temperature and impurity concentration. The temperature and concentration dependencies are weak on the BCS side with a negative impurity-medium scattering length. Toward the strong attraction regime across the unitary limit, we find sizable dependencies. In particular, with increasing temperature the effective mass quickly approaches the bare mass and the residue is significantly enhanced. At temperature T ∼ 0.1TF ,whereTF is the Fermi temperature of the background Fermi sea, the residual polaron-polaron interaction seems to become attractive. This leads to a notable down-shift in the polaron energy. We show that, by taking into account the temperature and impurity concentration effects, the measured polaron energy in the first Fermi polaron experiment [Schirotzek et al., Phys.Rev.Lett.102, 230402 (2009)] could be better theoretically explained. DOI: 10.1103/PhysRevA.98.013626 I. INTRODUCTION Experimentally, the first experiment on attractive Fermi polarons was carried out by the Zwierlein group at Mas- Over the past two decades, ultracold atomic gases have pro- sachusetts Institute of Technology (MIT) in 2009 using 6Li vided an ideal platform to understand the intriguing quantum many-body systems [1]. -
Electron-Electron Interactions(Pdf)
Contents 2 Electron-electron interactions 1 2.1 Mean field theory (Hartree-Fock) ................ 3 2.1.1 Validity of Hartree-Fock theory .................. 6 2.1.2 Problem with Hartree-Fock theory ................ 9 2.2 Screening ..................................... 10 2.2.1 Elementary treatment ......................... 10 2.2.2 Kubo formula ............................... 15 2.2.3 Correlation functions .......................... 18 2.2.4 Dielectric constant ............................ 19 2.2.5 Lindhard function ............................ 21 2.2.6 Thomas-Fermi theory ......................... 24 2.2.7 Friedel oscillations ............................ 25 2.2.8 Plasmons ................................... 27 2.3 Fermi liquid theory ............................ 30 2.3.1 Particles and holes ............................ 31 2.3.2 Energy of quasiparticles. ....................... 36 2.3.3 Residual quasiparticle interactions ................ 38 2.3.4 Local energy of a quasiparticle ................... 42 2.3.5 Thermodynamic properties ..................... 44 2.3.6 Quasiparticle relaxation time and transport properties. 46 2.3.7 Effective mass m∗ of quasiparticles ................ 50 0 Reading: 1. Ch. 17, Ashcroft & Mermin 2. Chs. 5& 6, Kittel 3. For a more detailed discussion of Fermi liquid theory, see G. Baym and C. Pethick, Landau Fermi-Liquid Theory : Concepts and Ap- plications, Wiley 1991 2 Electron-electron interactions The electronic structure theory of metals, developed in the 1930’s by Bloch, Bethe, Wilson and others, assumes that electron-electron interac- tions can be neglected, and that solid-state physics consists of computing and filling the electronic bands based on knowldege of crystal symmetry and atomic valence. To a remarkably large extent, this works. In simple compounds, whether a system is an insulator or a metal can be deter- mined reliably by determining the band filling in a noninteracting cal- culation. -
Matthias Vojta Subir Sachdev Quantum Phase Transitions in D
Quantum phase transitions in d-wave superconductors •C. Buragohain Matthias Vojta •Y. Zhang •A. Polkovnikov Subir Sachdev Transparencies on-line at http://pantheon.yale.edu/~subir Phys. Rev Lett. 83, 3916 (1999) Science 286, 2479 (1999) Phys. Rev. B 61, 15152 (2000) Phys. Rev. B 62, Sep 1 (2000) cond-mat/0005250 (review article) cond-mat/0007170 Yale University Quantum Phase Transitions Cambridge University Press Elementary excitations of a d-wave superconductor (A) S=0 Cooper pairs, phase fluctuations Negligible below Tc except near a T=0 superconductor-insulator transition. (B) S=1/2 Fermionic quasiparticles Ψ π π h : strongly paired fermions near ( ,0), (0, ) ∆ have an energy gap h ~ 30-40 meV Ψ 1,2 : gapless fermions near the nodes of the superconducting gap at (±±KK , ) with K =0.391π (C) S=1 Bosonic, resonant collective mode Represented by φ α , a vector Γ field measuring the strength of pure antiferromagnetic spin S(Q,ω) fluctuations near Q ≈ (,)ππ Damping is small at T=0 Γ≈ = pure 0 at T 0 (Theory generalizes to the cases with Γ≠ incommensurate Q and pure 0 ) ∆ ω res Constraints from momentum conservation π Ψ h Ψ 2 Ψ 1 φ Ψ α Ψ 0 h h Q φα Ψ 1 Ψ Q 2 Ψ −π h −π 0 π Ψ φ φ h : strongly coupled to α , but do not damp α ∆ ∆ as long as res < 2 h Ψ φ 1,2 : decoupled from α I. Zero temperature broadening of resonant collective mode φ α by impurities: comparison with neutron scattering experiments of Fong et al Phys. -
Non-Fermi Liquids in Oxide Heterostructures
UC Santa Barbara UC Santa Barbara Previously Published Works Title Non-Fermi liquids in oxide heterostructures Permalink https://escholarship.org/uc/item/1cn238xw Journal Reports on Progress in Physics, 81(6) ISSN 0034-4885 1361-6633 Authors Stemmer, Susanne Allen, S James Publication Date 2018-06-01 DOI 10.1088/1361-6633/aabdfa Peer reviewed eScholarship.org Powered by the California Digital Library University of California Reports on Progress in Physics KEY ISSUES REVIEW Non-Fermi liquids in oxide heterostructures To cite this article: Susanne Stemmer and S James Allen 2018 Rep. Prog. Phys. 81 062502 View the article online for updates and enhancements. This content was downloaded from IP address 128.111.119.159 on 08/05/2018 at 17:09 IOP Reports on Progress in Physics Reports on Progress in Physics Rep. Prog. Phys. Rep. Prog. Phys. 81 (2018) 062502 (12pp) https://doi.org/10.1088/1361-6633/aabdfa 81 Key Issues Review 2018 Non-Fermi liquids in oxide heterostructures © 2018 IOP Publishing Ltd Susanne Stemmer1 and S James Allen2 RPPHAG 1 Materials Department, University of California, Santa Barbara, CA 93106-5050, United States of America 062502 2 Department of Physics, University of California, Santa Barbara, CA 93106-9530, United States of America S Stemmer and S J Allen E-mail: [email protected] Received 18 July 2017, revised 25 January 2018 Accepted for publication 13 April 2018 Published 8 May 2018 Printed in the UK Corresponding Editor Professor Piers Coleman ROP Abstract Understanding the anomalous transport properties of strongly correlated materials is one of the most formidable challenges in condensed matter physics. -
Magnetic Field Enhanced Superconductivity in Epitaxial Thin Film Wte2
Lawrence Berkeley National Laboratory Recent Work Title Magnetic Field Enhanced Superconductivity in Epitaxial Thin Film WTe2. Permalink https://escholarship.org/uc/item/1642v6qf Journal Scientific reports, 8(1) ISSN 2045-2322 Authors Asaba, Tomoya Wang, Yongjie Li, Gang et al. Publication Date 2018-04-25 DOI 10.1038/s41598-018-24736-x Peer reviewed eScholarship.org Powered by the California Digital Library University of California www.nature.com/scientificreports OPEN Magnetic Field Enhanced Superconductivity in Epitaxial Thin Film WTe2 Received: 13 December 2017 Tomoya Asaba1, Yongjie Wang 2, Gang Li 1, Ziji Xiang1, Colin Tinsman1, Lu Chen1, Accepted: 5 April 2018 Shangnan Zhou1, Songrui Zhao2, David Laleyan2, Yi Li3, Zetian Mi2 & Lu Li 1 Published: xx xx xxxx In conventional superconductors an external magnetic feld generally suppresses superconductivity. This results from a simple thermodynamic competition of the superconducting and magnetic free energies. In this study, we report the unconventional features in the superconducting epitaxial thin flm tungsten telluride (WTe2). Measuring the electrical transport properties of Molecular Beam Epitaxy (MBE) grown WTe2 thin flms with a high precision rotation stage, we map the upper critical feld Hc2 at diferent temperatures T. We observe the superconducting transition temperature Tc is enhanced by in-plane magnetic felds. The upper critical feld Hc2 is observed to establish an unconventional non- monotonic dependence on temperature. We suggest that this unconventional feature is due to the lifting of inversion symmetry, which leads to the enhancement of Hc2 in Ising superconductors. Superconductivity generally competes with magnetic felds. Based on thermodynamics, an applied magnetic feld usually suppresses superconductivity by destroying the underlying electron pairing in the superconducting state1. -
Wte2): an Atomic Layered Semimetal
The Pennsylvania State University The Graduate School Department of Materials Science and Engineering TUNGSTEN DITELLURIDE (WTE2): AN ATOMIC LAYERED SEMIMETAL A Thesis in Materials Science and Engineering by Chia-Hui Lee 2015 Chia-Hui Lee Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 2015 ii The thesis of Chia-Hui Lee was reviewed and approved* by the following: Joshua A. Robinson Professor of Materials Science and Engineering Thesis Advisor Thomas E. Mallouk Head of the Chemistry Department Evan Pugh University Professor of Chemistry, Physics, Biochemistry and Molecular Biology Mauricio Terrones Professor of Physics, Chemistry and Materials Science & Engineering Suzanne Mohney Professor of Materials Science and Engineering and Electrical Engineering Chair, Intercollege Graduate Degree Program in Materials Science and Engineering *Signatures are on file in the Graduate School iii ABSTRACT Tungsten ditelluride (WTe2) is a transition metal dichalcogenide (TMD) with physical and electronic properties that make it attractive for a variety of electronic applications. Although WTe2 has been studied for decades, its structure and electronic properties have only recently been correctly described. We explored WTe2 synthesis via chemical vapor transport (CVT) method for bulk crystal, and chemical vapor deposition (CVD) routes for thin film material. We employed both experimental and theoretical techniques to investigate its structural, physical and electronic properties of WTe2, and verify that WTe2 has its minimum energy configuration in a distorted 1T structure (Td structure), which results in metallic-like behavior. Our findings confirmed the metallic nature of WTe2, introduce new information about the Raman modes of Td-WTe2, and demonstrate that Td- WTe2 is readily oxidized via environmental exposure. -
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Nanoscale Advances View Article Online REVIEW View Journal | View Issue In-plane anisotropic electronics based on low- symmetry 2D materials: progress and prospects Cite this: Nanoscale Adv., 2020, 2,109 Siwen Zhao, a Baojuan Dong,bc Huide Wang,a Hanwen Wang,bc Yupeng Zhang, a Zheng Vitto Han*bc and Han Zhang *a Low-symmetry layered materials such as black phosphorus (BP) have been revived recently due to their high intrinsic mobility and in-plane anisotropic properties, which can be used in anisotropic electronic and optoelectronic devices. Since the anisotropic properties have a close relationship with their anisotropic structural characters, especially for materials with low-symmetry, exploring new low- symmetry layered materials and investigating their anisotropic properties have inspired numerous research efforts. In this paper, we review the recent experimental progresses on low-symmetry layered Received 4th October 2019 materials and their corresponding anisotropic electrical transport, magneto-transport, optoelectronic, Accepted 30th October 2019 thermoelectric, ferroelectric, and piezoelectric properties. The boom of new low-symmetry layered DOI: 10.1039/c9na00623k materials with high anisotropy could open up considerable possibilities for next-generation anisotropic Creative Commons Attribution 3.0 Unported Licence. rsc.li/nanoscale-advances multifunctional electronic devices. 1. Introduction energy band structure and can be regarded as a process of lowering the dimensionality of the carrier transport. Therefore, Two dimensional (2D) layered materials with strong in-plane the electrical, optical, thermal, and phonon properties of these covalent bonds and weak out-of-plane van der Waals interac- anisotropic materials are diverse along the different in-plane tions span a very broad range of solids and exhibit extraordinary crystal directions.