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Research Interests: Condensed Matter Theory of Real Solids

Our goal is to understand and predict properties of matter.  To meet the challenges of today’s world, growing out of the fields of biotechnology, computer technology, quantum mechanics, environmental protection, it is critically important to both understand the fundamental properties of matter and to be able to predict how these properties manifest themselves under varying conditions. We are engaged in characterizing the functional implications of such properties under the headings of optical, magnetic, topological and mechanical – as they emerge from the defining attributes of materials: Atomic identities, Composition and Structure (ACS).

Systems of interest include semiconductors, insulators, metals, nanostructures, surfaces, quasi-2D materials, alloys, and superlattices. In the “direct approach” we use ACS as input and predict as output properties of the said compound defined by this ACS. In our recently developed “inverse approach” (see figure) we use as input the target property we would like to discover, and predict as output the type of compound (ACS) that would have this property.The predictive power of our atomistic first principles approaches and their close reliance on realistic attributes of matter (encapsulated in ACS) form a strong basis for our close collaboration with various experimental groups that test our predictions.

Key words: Semiconductors; Transitional-metal compounds; Oxides; Density functional theory; Nanostructures.

Three historic approaches to the discovery of novel properties of solids

(a) General fundamental technique/tools in the theory of matter: These include the development of quantum mechanics, relativity, various algebras, group theory and their illustration for prototypical ‘ text book’ models. These generic tools transcend specific materials, (although they can be naturally applied to specific models of solids) and form the common heritage that all approaches discussed below build upon.

(b) ‘Model Hamiltonian’ theories of physical phenomena: This approach involves setting up a model Hamiltonian that accepts as ‘input’ some basic pre-selected interactions (such as spin-spin or electron-phonon) and provides as ‘output’ the physical effects induced by the assumed interactions (such as magnetism or superconductivity). Because such interactions are generally not mapped directly to specific solids, the Model Hamiltonian approach is not material specific but rather generic. For example, it will be difficult to tell whether the effect predicted by such an approach will ‘live’ in an oxide or nitride, or what do we need to do to the material to raise the predicted critical temperature by a given amount. The material-agnostic model Hamiltonian approach is nevertheless the ideal platform to teach physical effects as emerging from well-posed (assumed) interactions.

(c) Material-specific theory of physical phenomena: These approaches predict properties of materials –-optical, magnetic, transport, topological and mechanical-- as they emerge from the defining attributes of materials, being Atomic identities, Composition and Structure (ACS). The Hamiltonian must therefore have the ability to accept ACS as ‘input’, providing as ‘output’ those physical effects that are set up by ACS through the specific Hamiltonian description. Atomistic Hamiltonians with ability to recognize the chemical identity of the solid or molecule, (and their corresponding method of solution) range from mean-field Density Functional Theory (DFT) to atomically-resolved correlated methods such as many-body configuration interaction (CI); “G-W”, DFT-Dynamic mean field (DMFT) to DFT- Quantum Monte Carlo (QMC). We use this general approach © here. This approach comes in three flavors:

Our preference lies in the last two items. A specific approach to discovery and design-class theory is:                   

The concept of “Matter by Design" 

• The need to find materials with specified functionalities is key to modern technology: Society’s goals to deliver a material that is 30% more efficient at converting sunlight to electricity, or a battery with 5 times higher energy density, or a flat-panel display with a ten-fold increase in the conductivity of the transparent window rely on our ability to both discover and synthesize the next generation of functional semiconductor materials. Such modern technologies are increasingly based on specialized functionalities, which "live" in specific materials and no others. Yet, actual materials with such specific technology-enabling functionalities are often unknown: We understand the functionality needed for a given technology, but often we do not have the materials that provide those functionalities. 
• Many atomic configurations of matter can be realized in the laboratory, but there are way to many combinations to try via Edisonian experimentations of all possibilities: one can now realize almost arbitrary atomic configurations in the laboratory. Examples include the innumerably large number of possible ‘superlattice’ configurations-- a sequence of A’s and B’s deposited with some prescribed order-- that can be grown layer-by-layer from semiconductor, metallic or insulator ‘building blocks’. (The number of combinations 2N that can be made by different arrangement of two building blocks onto N sites can quickly reach astronomical proportions). In principle, each of the innumerably many superlattice configurations would have distinct physical property such as band gap or optical response. But which one should one make to achieve a given property or functionality?
• Material discovery has traditionally occurred by accidental discovery. Can this philosophy be used to discover all the critical materials given the enormous space of possibilities?  A few historic examples of lucky successful discoveries of important functionalities include Penicillin, the semi conductivity of silicon and compound semiconductors, the hardness of diamond, and the high-temperature superconductivity of cuprate oxides. The shortcoming of accidental discovery is that a target property may be missed, and that the R&D period tends to be rather long given that we are not really sure what we have. Furthermore, an enormous number of chemically plausible element combinations remain unreported (‘Missing Materials’). How can we be sure that a critically needed material functionality does not ‘live’ in one of these missing compounds?
• The idea underlies Inverse Design: Given that the atomic configuration controls the material property, and that many atomic configurations can be realized in the laboratory suggests that perhaps one might first articulate the needed functionality/property, and then look for the material that has this property .The target property could be a given band gap, or Curie temperature, or impurity level, or inverted order of bands akin to topological insulators, etc. Then, one would search quantum mechanically for the magic compound and the arrangement of atoms, which has the desired “target property”. The approach driving a structure or material from the desired property is inverted relative to the time-honored approach of starting with a given structure (or symmetry) and then calculating or measuring the properties.
• This “inverse Design” approach combining quantum theory of matter with chemical synthesis and material characterization --a set of sub-disciplines in which the University of Colorado has substantial strength.  Furthermore, proof of concept was already demonstrated.

Please also see: Inverse Design