Theoretical Solid State Physics Research Articles

Berry: A code for the differentiation of Bloch wavefunctions from DFT calculations

Density functional calculation of electronic structures of materials is one of the most used techniques in theoretical solid state physics. These calculations retrieve single electron wavefunctions and their eigenenergies.The berry suite of programs amplifies the usefulness of DFT by ordering the eigenstates in analytic bands, allowing the differentiation of the wavefunctions in reciprocal space. It can then calculate Berry connections and curvatures and the second harmonic generation conductivity.The berry software is implemented for two dimensional materials and was tested in hBN and InSe. In the near future, more properties and functionalities are expected to be added. Program summaryProgram Title: berryCPC Library link to program files:https://doi.org/10.17632/mpbbksz2t7.1Developer's repository link:https://github.com/ricardoribeiro-2020/berryLicensing provisions: MITProgramming language: Python3Nature of problem: Differentiation of Bloch wavefunctions in reciprocal space, numerically obtained from a DFT software, applied to two dimensional materials. This enables the numeric calculation of material's properties such as Berry geometries and Second Harmonic conductivity.Solution method: Extracts Kohn-Sham functions from a DFT calculation, orders them by analytic bands using graph and AI methods and calculates the gradient of the wavefunctions along an electronic band.Additional comments including restrictions and unusual features: Applies only to two dimensional materials, and only imports Kohn-Sham functions from Quantum Espresso package.

Inverse design in search of materials with target functionalities

Solid-state chemists have been consistently successful in envisioning and making new compounds, often enlisting the tools of theoretical solid-state physics to explain some of the observed properties of the new materials. Here, a new style of collaboration between theory and experiment is discussed, whereby the desired functionality of the new material is declared first and theoretical calculations are then used to predict which stable and synthesizable compounds exhibit the required functionality. Subsequent iterative feedback cycles of prediction–synthesis–characterization result in improved predictions and promise not only to accelerate the discovery of new materials but also to enable the targeted design of materials with desired functionalities via such inverse design. The conventional theoretical approach to the study of materials typically involves explaining the properties of known materials. This approach is compared with the inverse design of materials, in which the desired properties are set as inputs and the material that exhibits them as the output.

Periodic and fragment models based on the local correlation approach

A rigorous treatment of dynamical electron correlation in crystalline solids is one of the main challenges in today's materials quantum chemistry and theoretical solid state physics. In this study, we address this problem by using the local correlation approach and exploring a variety of methods, ranging from the full periodic treatment through embedded fragments to finite clusters. Apart from the computational advantages, the direct‐space local representation for the occupied space allows one to partition the system into fragments and thus forms a natural basis for a hierarchy of embedding models. Furthermore, a subset of localized orbitals in a cluster or a fragment can be chosen to mimic the unit cell of the reference periodic system. Introduction of such subsets allows one to define a formal quantity “the correlation energy per unit cell”, which is directly related to the correlation energy per unit cell in the crystal. The orbital pairs, where neither of the two localized orbital indices belongs to the “unit cell” do not explicitly contribute to the “energy per cell”: Their role is to provide correlated embedding via the couplings in the amplitude equations. The periodic, fragment and finite‐cluster approaches can be combined in a form of high precision computational protocols, where progressively higher‐level corrections are evaluated using lower‐level embedding models. We apply these techniques to investigate the importance of Coulomb screening in dispersively interacting systems on the examples of the phosphorene bilayer and the adsorption of water on 2D silica.This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

A tryst with density

WalterKohn transformed theoretical chemistry and solid state physics with his development of density functional theory, for which he was awarded the Nobel Prize. This article tries to explain, in simple terms, why this was an important advance in the field, and to describe precisely what it was that he (together with his collaborators Pierre Hohenberg and Lu Jeu Sham) achieved.

Semilocal density functional theory with correct surface asymptotics

Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the non-locality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the image-like surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to the ones at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.

The education of Walter Kohn and the creation of density functional theory

The theoretical solid-state physicist Walter Kohn was awarded one-half of the 1998 Nobel Prize in Chemistry for his mid-1960s creation of an approach to the many-particle problem in quantum mechanics called density functional theory (DFT). In its exact form, DFT establishes that the total charge density of any system of electrons and nuclei provides all the information needed for a complete description of that system. This was a breakthrough for the study of atoms, molecules, gases, liquids, and solids. Before DFT, it was thought that knowledge of the vastly more complicated many-electron wave function was essential for a complete description of such systems. Today, 50 years after its introduction, DFT (in one of its approximate forms) is the method of choice used by most scientists to calculate the physical properties of materials of all kinds. In this paper, I present a biographical essay of Kohn’s educational experiences and professional career up to and including the creation of DFT. My account begins with Kohn’s student years in Austria, England, and Canada during World War II and continues with his graduate and postgraduate training at Harvard University and Niels Bohr’s Institute for Theoretical Physics in Copenhagen. I then study the research choices he made during the first 10 years of his career (when he was a faculty member at the Carnegie Institute of Technology and a frequent visitor to the Bell Telephone Laboratories) in the context of the theoretical solid-state physics agenda of the late 1950s and early 1960s. Subsequent sections discuss his move to the University of California, San Diego, identify the research issue which led directly to DFT, and analyze the two foundational papers of the theory. The paper concludes with an explanation of how the chemists came to award “their” Nobel Prize to the physicist Kohn and a discussion of why he was unusually well suited to create the theory in the first place.

Relation between the interband dipole and momentum matrix elements in semiconductors

It is shown that a frequently used relation between the interband momentum and dipole matrix elements (shortened to the ``p-r relation'') in semiconductors acquires an additional correction term if applied to finite-volume crystals treated with periodic boundary conditions. The correction term, which is a generalization of the one obtained by Yafet [Phys. Rev. 106, 679 (1957)] for infinite crystals, does not vanish in the limit of infinite volume. We illustrate this with numerical examples for bulk GaAs and GaAs superlattices. The persistence of the correction term is traced to the subtle nature of the dipole matrix element with spatially extended wave functions. In contrast, a straightforward application of the findings by Blount [Solid State Phys. 13, 305 (1962)] and Haug [Theoretical Solid State Physics (Pergamon, Oxford, 1972)] yields the usual p-r relation in the distribution sense, without any corrections, when Bloch wave functions normalized to delta functions in crystal momentum space are used. Our findings therefore show that, for the interband dipole matrix element, using Bloch wave functions under periodic boundary conditions is not the proper way to approach the infinite-volume limit. From our numerical evaluations, we find that the correction term is large in the case of interband transitions in bulk GaAs, and that it can be chosen to be small in the case of intersubband transitions in superlattices, which are important in the context of terahertz (THz) radiation. We also show that one can interpret the infinite-volume p-r relation in terms of a limiting procedure using progressively broadened wave packet states that approach delta-normalized Bloch wave functions. Finally, we discuss the p-r relation for nanostructures in the envelope function approximation and show that the cell-envelope factorization of the nanostructure dipole matrix element into a cell-matrix element and an envelope overlap integral involves the cell gradient-$k$ rather than the cell dipole matrix element.

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

The optimized-effective-potential (OEP) method is a special technique to construct local Kohn-Sham potentials from general orbital-dependent energy functionals. In a recent publication [M. Betzinger, C. Friedrich, S. Bl\"ugel, A. G\"orling, Phys. Rev. B 83, 045105 (2011)] we showed that uneconomically large basis sets were required to obtain a smooth local potential without spurious oscillations within the full-potential linearized augmented-plane-wave method (FLAPW). This could be attributed to the slow convergence behavior of the density response function. In this paper, we derive an incomplete-basis-set correction for the response, which consists of two terms: (1) a correction that is formally similar to the Pulay correction in atomic-force calculations and (2) a numerically more important basis response term originating from the potential dependence of the basis functions. The basis response term is constructed from the solutions of radial Sternheimer equations in the muffin-tin spheres. With these corrections the local potential converges at much smaller basis sets, at much fewer states, and its construction becomes numerically very stable. We analyze the improvements for rock-salt ScN and report results for BN, AlN, and GaN, as well as the perovskites CaTiO3, SrTiO3, and BaTiO3. The incomplete-basis-set correction can be applied to other electronic-structure methods with potential-dependent basis sets and opens the perspective to investigate a broad spectrum of problems in theoretical solid-state physics that involve response functions.

Preface: Phys. Status Solidi B 246/5

AbstractEvery second year the Department of Theoretical Physics at the University of Silesia, Katowice, Poland, organizes the International Conference on Theoretical Physics. The XXXII meeting “Coherence and Correlations in Nanosystems” took place in September 2008 in Ustroń, Poland. The conference focused on current and important topics related to coherence and correlations in small systems. Special emphasis was given to the areas of physics at the border between theoretical solid state physics and nanophysics. The broad spectrum of topics covered during the six days of the conference can be summarized into the following five points:1. Quantum information and computation,2. Transport phenomena in nanosystems,3. Superconductivity and magnetism at the nanometer scale,4. Inhomogeneous systems,5. Ultracold atoms in optical lattices.The careful selection of the topics allowed the organizers of the conference to bring together distinguished scientists from different areas of physics. This in turn resulted in an effective cooperation between specialists and gave an excellent opportunity to exchange ideas. Thanks to the speakers and participants the 2008 conference maintained its international character and highest scientific quality. Both invited and contributed presentations were followed by fruitful formal and informal discussions.We would like to express our gratitude to all authors and referees whose effort allowed us to prepare this excellent issue. We also thank the editorial staff of physica status solidi for their kind assistance (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Kenneth Charles Hass

Kenneth Charles Hass, a theoretical condensed matter physicist, died on 1 June 2005 in Ann Arbor, Michigan, after a long, courageous, and graceful bout with cancer. At the time of his death, he led 60 physicists, chemists, and engineers as manager of the physical and environmental sciences department at the Ford Motor Co.Ken was born in Flushing, New York, on 7 May 1958 and attended Queens College, where he earned a BA, summa cum laude, in physics and mathematics in 1979. He attended graduate school at Harvard University under an NSF graduate fellowship and received an AM in 1980 in physics and a PhD in theoretical solid-state physics in 1984. His thesis adviser, Henry Ehrenreich, remembers Ken as one of his “most broadly interested and imaginative graduate students, whose friendliness, helpfulness, and modesty were inspiring to anyone who had the privilege of working with him.” Ken held joint appointments as a postdoctoral fellow at Harvard and a visiting scientist at MIT before joining Ford’s Scientific Research Laboratory in 1987.Initially Ken’s research focused on the effects of disorder in semiconductor alloys, the electronic structure and magnetic properties of diluted magnetic semiconductors, the electronic properties of copper oxide-based high-T c. superconductors, and the vibrational and thermal-transport properties of isotopically modified diamond. Among the dozens of papers he wrote on these subjects, his 1989 chapter “Electronic Structure of Copper-Oxide Superconductors” in Solid State Physics certainly stands out as a seminal publication.Ken made theoretical contributions to many Ford projects. The most significant work from a scientific and societal perspective was his groundbreaking density functional theory studies of the adsorption and catalysis of nitrogen oxides (NO x ) on metals, zeolites, and oxides and of the bulk and surface structures and hydration of aluminas. Those issues are central to air-quality improvement technologies, including automotive emission controls.In 2001, Ken became the manager of the chemical and environmental sciences department, and beginning in 2002, he led the organization formed by its merger with the physics department. Ken responded to the challenging times in the automotive industry by arguing successfully that critical research areas such as environment, energy, safety, and new materials demanded long-term support from Ford.Ken was equally at home in the academic and corporate worlds. He had a lifelong interest in science education. While leading a strong materials-modeling effort at Ford, he simultaneously served on the American Physical Society’s committee on education (1998-2000), including one year as its chair. Ken worked tirelessly to promote and expand the activities of the APS forum on industrial and applied physics during his tenure as vice chair, chair, and past chair (2001-04). He wrote and spoke eloquently of the need for new approaches and attitudes in industrial research and academia. Ken was elected an APS fellow in 2004 in recognition of his significant applications of atomic-level modeling to technological materials and his outstanding leadership in the promotion of industrially relevant research and education. A yearlong sabbatical (1999-2000) in the physics department at the University of Michigan, Ann Arbor, enabled Ken to explore ideas from the emerging field of complexity. On returning to Ford, he applied the new ideas to technical management and other complex problems. Working closely with the Center for Complex Systems at Michigan, he encouraged applications of this discipline to practical problems such as sustainable mobility.An avid reader, Ken appreciated the complementary approaches of scientific reductionism and the view that fundamental laws exist at all levels of the physical world. He thought seriously about the roles of science and religion. His personal interests included travel, food and wine, chess, tennis, and music.Those in the physics community who read Ken’s papers or heard him speak will remember him as a first-rate scientist. Those at Ford can also attest that he was a leader who possessed outstanding vision and integrity. He was a terrific colleague and friend, and we all miss him. Kenneth Charles Hass JIM BRETZ, FORD MOTOR COPPT|High resolution© 2005 American Institute of Physics.

Sir Alan Herries Wilson. 2 July 1906 — 30 September 1995

Alan Wilson was one of the founders of modern theoretical solid-state physics. In two fundamental papers in 1931 he applied band theory to explain the distinction between metals, insulators and semiconductors and to elucidate the mechanism of conduction in semiconductors. These ideas underlie the later invention of the transistor and many of the developments in microelectronics that are revolutionizing today's technology. After World War II, Wilson left academic life to pursue a second, highly distinguished, career in industry.

Strained-Layer Semiconductor Research and Development at Sandia

Sandia National Laboratories pioneered work in strained-layer superlattice systems for electronics and optoelectronics. Based on that work, it now conducts research and development in compound semiconductor and optoelectronics physics, materials science, and device technology. Although Sandia's research relies heavily on theoretical and experimental solid state physics, this paper will emphasize applications that exploit the properties of strained-layer systems. This research allows the microelectronics and photonics community to use the special properties of strained-layer systems in an engineering, rather than an empirical, manner. The number of electronic and optoelectronic devices that depend on strained-layer systems for their highest performance with device applications indicates their importance. Selected strained-layer structures and devices developed at Sandia will be discussed.

A model for dynamic relaxations in amorphous polymers. I. Conceptual framework, formal implementation of simplest version, and application to poly(ester carbonates)

AbstractA new model for the dynamic relaxations occurring below the glass transition temperature in amorphous polymers is introduced. This model combines ideas from theoretical solidstate physics, thermodynamics, and statistical mechanics. Formal analogies are made between the dynamic relaxations and phase transitions. The concepts of percolation theory are briefly discussed. The molecular level motions which might be giving rise to each dynamic relaxation are incorporated within this framework. The simplest version of the model is then formally implemented within the context of bisphenol‐A polycarbonate (BPAPC) and its poly (ester carbonates) (PEC). The following results are calculated: (1) Characteristic temperatures (Tc) for BPAPC, similar to γ1, and γ2 relaxation temperatures observed by dynamic mechanical spectroscopy (DMS) at commonly used measurement frequencies. (2) Tc for the β2 relaxation in tetrabromo‐BPAPC much higher than the Tc in BPAPC. (3) A slow and monotonic increase in both the intensity and the Tcof the γ2 relaxation with an increasing fraction of terephthalate comonomer in PEC copolymers. It is hoped that this model, which is admittedly tentative at this time, will be useful as a working hypothesis. The next paper of this series will provide extensions and generalizations of the model, and its application to the poly (alkyl methacrylates).

Up Close: Science of Materials at Trinity College, University of Dublin

Materials Science at Trinity College, University of Dublin, Ireland, has a distinguished past as well as a promising future. Trinity College published the first book on optics in English by Molyneux (1692). The work of Hamilton, Lloyd, Fitzgerald and others in the 19th century are impressive antecedents for today's research as well, which now enjoys broader horizons and new research opportunities due to major funding by the European Community (EC) and other agencies.In the Departments of Chemistry and Pure and Applied Physics, internationally recognized research groups are pursuing materials-oriented research in laser physics and nonlinear optics, surfaces and interfaces, magnetic materials, polymers, and theoretical solid-state physics and chemistry.The current research, described in the following two sections, has for many years resulted from close collaboration in the materials area among researchers in both departments. Common interests have led the departments to establish an honors degree course in the science of materials. The final section discusses the aims of this course.

Formation of a research school: Theoretical solid state physics at Bristol 1930–54

In June 1930 the Department of Scientific and Industrial Research (DSIR) of the British Government awarded a modest research grant to J. E. (later Sir John) Lennard-Jones, Professor of Theoretical Physics at the University of Bristol, in response to a proposal submitted under the title of ‘A theoretical investigation of the physical properties of the solid state of matter’. This initiative marked the first notable recognition by public funding bodies in Great Britain of the potential contribution to be made by the new theoretical ideas in physics to a deeper understanding of the properties of industrially important materials, particularly metals and their alloys. The possible technological relevance of such a study was, indeed, a central factor in the decision to support it. The research arising out of this initial award provided the impetus for the first stage of Bristol theoretical research on the solid state of matter, an enterprise initially associated with the name of Lennard-Jones, and later with Nevili Mott who succeeded him as Professor of Theoretical Physics in 1933.

Structural phase transitions in crystals: Broken-symmetry (isotropy) groups

A systematic procedure ensuring the determination of all isotropy groups of a given representation of a space group is presented for the first time. Isotropy groups play an important role in various areas of theoretical solid state physics. For example, only isotropy groups may occur in a structural phase transition driven by an order parameter belonging to a given representation. The method uses the chain criterion directly on the image of the representation, employing a labeling of the matrices by space group elements. A notion of a substar of a wave vector associated with the representation is central to the method. Finally, as a detailed illustration the method is applied to a structural phase transition in A15 systems driven by an X-point order parameter. The result agrees with previously reported ones.

Philip W Anderson

Professor Philip W Anderson's contributions to theoretical solid state physics have been so varied that one's first reaction on hearing of the Nobel prize was to wonder which piece of work it had been awarded for: Anderson localisation in disordered materials, the Anderson model for magnetic impurities, the theory of superexchange interaction, seminal ideas in various fields. It is not surprising that in 1967 Cambridge decided (in spite of thin-end-of-wedge arguments about residential university and several changes of statutes) that it wanted Anderson as a professor on a half-time basis shared with Bell Telephone Laboratories

Theoretical Solid State Physics Vols 1 and 2 (Vol 1: Perfect Lattices in Equilibrium, Vol 2: Nonequilibrium and Disorder)

William Jones and Norman H March Chichester: J Wiley 1973 pp (Vol 1) xvi + 680, (Vol 2) xv + 681–1301 price $39.5O each Solid state physics has grown to such a degree that it takes both courage and perseverance to write a book covering a large part of the subject; but such books are necessary, for only a systematic presentation by one or two authors can hope to bring out the relations between different areas and to give the proper survey of the subject which is missed in even the best specialist reviews. The authors have chosen a pedagogical approach, including problems and relatively few references to research papers, and preferring to prove results rather than to merely indicate them.

Book reviews

Book reviews

Solid State Theory

Theoretical Solid State Physics. By Albert Haug. Vol. 1. Pp. xiv + 497. (Pergamon: Oxford and New York, May 1972.) £7. Theoretical Solid State Physics. By Albert Haug. Translated by H. S. H. Massey. Edited by D. ter Haar. Vol. 2. Pp. xiii + 355. (Pergamon: Oxford and New York, August 1972.) £6.