Physics of Superconductivity and Magnetism

Advanced capabilities for materials modelling with Q <scp>uantum</scp> ESPRESSO

Quantum EXPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum EXPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.

Anyons in an exactly solved model and beyond

Doping a Mott insulator: Physics of high-temperature superconductivity

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

Exact Treatment of Bardeen's Theory of Superconductivity in the Strong Coupling Limit

Journal of the Physical Society of Japan 56 (1987) pp. 3421-3424 Estimate of Tc and Precursory Effects of Superfluidity of 3He in Dilute 3He-4He Solutions Toshio Soda Progress of Theoretical Physics Vol. 22 No. 6 (1959) pp. 775-806 On the Theory of Superconductivity Yasushi Wada and Nobuyuki Fukuda Progress of Theoretical Physics Vol. 22 No. 6 (1959) pp. 903-905 Inclusion of Hole Motions in the Brueckner Theory Fumiaki Iwamoto Progress of Theoretical Physics Vol. 23 No. 5 (1960) pp. 871-881 Inclusion of Hole Motions in Brueckner Theory Fumiaki Iwamoto Progress of Theoretical Physics Vol. 25 No. 4 (1961) pp. 653-666 On the Stability of the Hartree-Fock Solution in Many-Body Problem Katuro Sawada and Nobuyuki Fukuda Progress of Theoretical Physics Vol. 26 No. 3 (1961) pp. 321-336 Nuclear Matter at Low Density with Attractive and Singular Interactions Yasushi Wada Progress of Theoretical Physics Vol. 28 No. 5 (1962) pp. 809-819 The Asymptotic Behavior of Perturbation Expansions in Many-Body Problem and Superconducting State Kenji Fukushima and Nobuyuki Fukuda Progress of Theoretical Physics Vol. 29 No. 4 (1963) pp. 605-607 Theory of Many-Boson Systems V. H. Smith, Jr. and H. A. Gersch Progress of Theoretical Physics Vol. 34 No. 5 (1965) pp. 734-753 Spectrum of the BCS Reduced Hamiltonian in the Theory of Superconductivity Yusuke Kato Progress of Theoretical Physics Vol. 36 No. 2 (1966) pp. 296-312 Quasi-Spin Formalism and Matrix Elements in the Shell Model Akito Arima and Munetake Ichimura Progress of Theoretical Physics Vol. 36 No. 4 (1966) pp. 820-841 The Strong Coupling Theory of a Chiral Four Fermion Interaction Munetake Ichimura, Keiji Kikkawa and Koichi Yazaki Progress of Theoretical Physics Vol. 38 No. 4 (1967) pp. 813-831 Friedrichs-Berezin Transformation and Its Application to the Spectral Analysis of the BCS Reduced Hamiltonian Yusuke Kato and Nobumichi Mugibayashi Progress of Theoretical Physics Vol. 49 No. 1 (1973) pp. 181-205 A Microscopic Theory of the So-Called “Two-Phonon” States in Even-Even Nuclei. I Nobuo Kanesaki, Toshio Marumori, Fumihiko Sakata and Kenjiro Takada Progress of Theoretical Physics Vol. 49 No. 2 (1973) pp. 491-506 Theory of Pairing Vibration Mode Haruo Ui and Hiroyuki Sagawa Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1458-1474 Application of the 5-Dimensional Spin to the Theory of Superfluid 3He Yasumasa Hasegawa, Toshiyuki Usagawa and Fumiaki Iwamoto Progress of Theoretical Physics Vol. 93 No. 4 (1995) pp. 671-683 Ground State Energy, Spin Gap and Hole Superconductivity on Square Lattice Heisenberg Antiferromagnet by Majorana Fermion Toshio Soda Progress of Theoretical Physics Supplement No.71 (1981) pp. 48-70 Chapter 2. Outline of the Mode-Mode Coupling Theory Fumihiko Sakata, Toshio Marumori and Kenjiro Takada

Effect of the Coulomb Interaction between d Electrons and of the d-s Pairing Interaction on Superconductivity in Dilute Alloys

Journal of the Physical Society of Japan 69 (2000) pp. 1812-1823 Numerical Renormalization Group Studies on Single Impurity Anderson Model in Superconductivity: A Unified Treatment of Magnetic, Nonmagnetic Impurities, and Resonance Scattering Tomoki Yoshioka and Yoji Ohashi Progress of Theoretical Physics Vol. 36 No. 6 (1966) pp. 1299-1300 Effects of the d-Electron Correlation on the Transition Temperature of an Anisotropic Impure Superconductor with Resonance Scattering Tomitaro Nagashima and Toshio Soda Progress of Theoretical Physics Vol. 38 No. 2 (1967) pp. 291a-304 Thermodynamic and Electromagnetic Properties of Superconductors with Non-Magnetic Transition Element Impurities Kenji Takanaka and Tomitaro Nagashima Progress of Theoretical Physics Vol. 40 No. 6 (1968) pp. 1273-1286 Magnetic Properties of Superconductors with Resonance Scattering Kenji Takanaka and Fumihiko Takano Progress of Theoretical Physics Vol. 45 No. 2 (1971) pp. 651-652 Effect of Superconductivity on Localized Magnetic States Takashi Kusakabe Progress of Theoretical Physics Vol. 45 No. 5 (1971) pp. 1376-1381 Non-Magnetic Resonance Scattering in Two-Band Superconductors Takashi Kusakabe Progress of Theoretical Physics Vol. 47 No. 3 (1972) pp. 765-773 Effect of Spin Fluctuation in Superconductors Toyoyuki Kitamura Progress of Theoretical Physics Vol. 47 No. 6 (1972) pp. 1817-1823 Bound States Due to Resonance Scattering in Superconductor Kazushige Machida and Fumiaki Shibata Progress of Theoretical Physics Vol. 48 No. 4 (1972) pp. 1080-1089 Effect of Impurities on Superconductivity in Anderson Model Chuya Inoue and Fumihiko Takano Progress of Theoretical Physics Vol. 49 No. 4 (1973) pp. 1077-1095 Application of the Coherent Potential Approximation to Impurity Problems in Superconductor. I Fumihiko Takano, Kazushige Machida and Fumiaki Shibata Progress of Theoretical Physics Vol. 49 No. 4 (1973) pp. 1364-1365 Effect of Spin Fluctuation in Superconductors. II Toyoyuki Kitamura and Chuya Inoue Progress of Theoretical Physics Vol. 50 No. 1 (1973) pp. 50-73 A Hartree-Fock Theory of Transition-Metal Impurities in a Superconductor Hiroyuki Shiba Progress of Theoretical Physics Vol. 51 No. 6 (1974) pp. 1667-1677 Effect of Transition-Metal Impurities in Superconductors Kazushige Machida Progress of Theoretical Physics Vol. 55 No. 1 (1976) pp. 1-9 On Nuclear-Spin Lattice Relaxation Time in a Superconductor Containing Non-Magnetic Transition-Metal Impurities Kazushige Machida and Akira Nakanishi Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 713-733 Theory of Kondo Effect in Superconductors. I Tamifusa Matsuura, Shin'ichi Ichinose and Yosuke Nagaoka

Electronic structure and magnetism of the triple-layered ruthenate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Sr</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Ru</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>10</mml:mn></mml:msub></mml:math>

We report electronic band structure calculations for ${\mathrm{Sr}}_{4}{\mathrm{Ru}}_{3}{\mathrm{O}}_{10}$ which display both ferromagnetic and metamagnetic behavior. The density functional calculations find the ground state to be ferromagnetic in agreement with experiment and we show that the resulting spin polarization has dramatic consequences for the electronic properties. The minority-spin bands are mainly empty and disperse steeply upward at the Fermi energy, whereas the majority-spin bands are full or nearly fully occupied and form narrow bands near the Fermi energy, which could be the electronic origin of the metamagnetism. Inclusion of a Hubbard interaction $U$ applied to the Ru $4d$ states has major effects on the narrow bands, which reveal the role of Coulomb interactions and correlated many-body physics. The results are in qualitative agreement with recent angle-resolved photoemission spectroscopy (ARPES) experiments and show the need for a combined theoretical study and experimental ARPES investigation with better energy resolution to reveal the nature of the narrow bands close to the Fermi level, which is critical for understanding the exotic magnetic properties observed in this material.

Electronic States near Superconductive Transition Temperature

Journal of the Physical Society of Japan 56 (1987) pp. 4503-4509 Novel Aspect of the Critical Temperature of One-Dimensional Charge-Density-Wave Superconductors Yoshikazu Suzumura, Yutaka Okabe and A. D. S. Nagi Progress of Theoretical Physics Vol. 53 No. 5 (1975) pp. 1233-1242 Self-Consistent Theory of Peierls Transition in One-Dimensional Electron-Phonon Systems Yoshikazu Suzumura and Yasunari Kurihara Progress of Theoretical Physics Vol. 58 No. 1 (1977) pp. 28-43 Theory of Fluctuations in Quasi-One-Dimensional Electron-Phonon Systems Eijiro Sakai and Toyoyuki Kitamura