Condensed Matter Theory

Faculty: M. Cohen (emeritus), A.B. Harris (emeritus), R.D. Kamien, C.L. Kane, A. Liu, T.C. Lubensky, E.J. Mele, P. Nelson, P. Soven
 

• Biophysics and Biomaterials ( Kamien, Liu, Lubensky, Nelson)
  There is a cultural gap between physics, which seeks to understand extremely simple systems, and biology, which is obliged to study the overall behavior of extremely complex systems. One area where simplicity and life intersect is the study of biomembranes, both in isolation and as active elements of cells. In recent years amazing new experimental techniques, including optical tweezers, have opened up the study of both the equilibrium conformations and dynamic response of membranes to quantitative analysis. Similarly the DNA molecule, while architecturally complex, has remarkably simple elastic behavior governed by just a few parameters. Apart from their potential relevance to biology, the study of these systems has revealed new physical phenomena characteristic of the highly-fluctuating micron world. At UPenn we currently have groups developing the theory of lipid bilayers, the physics of single DNA molecules, as well as the structure of condensed DNA in vitro and in vivo.

Photomicrograph of a shape transition induced in an artificial bilayer vesicle by laser tweezers, studied by Nelson

• Carbon Tubules and Fullerides ( Harris, Kamien, Kane, Mele)
  Over the last few years a spectrum of new solid phases of carbon have been discovered which are derived from the carbon molecule C60, and more recently from carbon nanotubules which are formed by wrapping graphitic sheets into compact cylindrical forms. These solids span an impressive range of electronic behavior: by moderately varying the degree of doping in the fullerides one finds phases with insulating, magnetic, and even superconducting ground states. New methods have been developed for controlling the growth of solid phases of single wall carbon nanotubes, and these structures hold great promise for new applications which exploit their unique electronic and elastic properties. We are actively investigating the electronic properties in these molecular solids, with a focus on understanding the phase equilibrium in these systems, and the effects of the underlying molecular symmetry, the orientational registry in the solid phase, and the quenched disorder in the condensed phases on their macroscopic electronic properties. The work is carried out in close collaboration with experimental work in the Department of Physics and Astronomy and the Department of Materials Science and Engineering on these systems.
  
  
• Liquid Crystals and Molecular Crystals (Harris, Kamien, Lubensky)
  The theory of liquid crystals and liquid crystalline polymers runs the gamut from the rheology of complex fluids to the esoterica of homotopy and topological defects. All aspects of theory are intimately influenced and connected with experiment. This places liquid crystal physics in an exciting position: it is driven by both theory and experiment and by both the abstract and the applied. Specifically, chiral molecules are ubiquitous in nature and exhibit many liquid crystal phases. They are extensively studied by biologists, chemists and biophysicists. There is still much theoretical work to be done on the wealth of experimental data. We are actively pursuing the theory and prediction of new liquid crystalline phases, in particular equilibrium defect phases such as the twist-grain-boundary (TGB) phase of smectic liquids crystals, the analog of the Abrikosov flux lattice phase of a superconductor. Many of these defected phases are chiral and we are also actively engaged in understanding the origin of chiral interactions in crystal and liquid crystal phases. The theory group actively collaborates with local experimentalists and is part of the UPenn soft condensed matter physics effort.
  
  
• Polymer Physics ( Kamien, Liu, Lubensky, Nelson)
  Polymers are an important component and fuel in the modern world and, as a result, are carefully studied. Typically, the theory of liquids treats the constituents as featureless. However, because of their large lengths, polymers can not be treated this way. Recent progress in experimental technique has allowed direct observation of and interaction with these macromolecules. We are pursuing the physics of both single polymer molecules as well as ensembles of many polymers, studying both the static, equilibrium behavior, as well as dynamical behavior. Because of their long lengths, the dynamics of polymers is topologically obstructed through the linking and entanglement of the polymers. Part of our program is to study this "topological dynamics". We work closely with groups at Penn and nearby at the National Institutes of Health.
  
  
• Strongly Correlated Electrons in Low Dimensions( Kane, Mele)
  There are broad classes of degenerate electronic systems to which the usual Fermi liquid theory of the interacting electron fluid is inapplicable. Remarkably, these are not at all rare situations and the consequences of its failure are often dramatic. The discovery in the late 1980's of high Tc superconductivity in a family of cuprates which are doped away from a strongly correlated insulating state is perhaps the most celebrated example, and this discovery has renewed theoretical interest in understanding this long standing problem. Unfortunately theoretical methods for analyzing the degenerate electron fluid in the presence of strong interactions remain poorly developed in three dimensions. The situation is much more amenable to careful study in low dimensional systems, and in particular a solvable theoretical model, the Luttinger model, exists and describes an interacting electron problem in one dimension. We are undertaking theoretical work to further understand the predictions of the Luttinger model for the measured transport coefficients as functions of temperature, frequency and applied fields. This theory has direct applications in recent experiments studying transport in semiconductor heterostructures which effectively confine the electron motion to one dimension, to edge state transport in the 2D electron gas in the quantum Hall regime, and potentially to new structures which are derived from carbon nanotubes.
   
  
• Strongly Fluctuating Systems ( Harris)
  Fluctuations can become dominant in several situations which we have studied recently. Near a continuous phase transition even weak randomness can lead to modifications both to critical exponents (as has been known for a long time) and to the nature of the distribution function describing observables in the limit of large system size. Another example is an insulating magnetic systems in which the magnetic structure is not stable at the level of mean field theory, but is stable when fluctuations are taken into account, an for an antiferromagnet on an fcc lattice, as typified by the insulator MnO. This phenomenon also occurs in lamellar copper oxide family of antiferromagnets (which, when doped, lead to high-temperature superconductors). Here the mean field at a spin at (or directly over) the center of a square plaquette of antiferromagnetic spins vanishes if isotropic interactions are assumed. The resulting structural degeneracy can be removed by either fluctuations (ignored in mean field theory) or by pseudo-dipolar interactions arisiong from the anisotropy of the exchange interaction. A proper treament of these interactions allowed us to understand the otherwise mysterious sequence of spin reorientation transitions in the noncollinear magnet Nd2CuO4 (as well as the absence of such transitions in isostrucural Pr2CuO4) and the complex spin-wave behavior of Nd2CuO4 and the antiferrmagnet Sr2Cu3O4Cl2 which also displays weak ferromagnetism. This work involves a collaboration with Tel Aviv University and MIT.
  
  
• Surfaces and Interfaces ( Mele)
  At the surface of a crystalline solid the symmetry of the ordered bulk phase is broken, and one frequently encounters new structural, elastic and electronic phenomena which are not possible in the perfectly ordered bulk environment. These are important for providing a microscopic understanding of the surface effects which determine growth modes for epitaxial thin films, the equilibrium height profile of a growing interface and the pathways by which surface chemical reactions can occur. We are studying electronic, structural and elastic effects at solid surfaces by using quantum mechanical first principles electronic structure methods to determine the interatomic forces, equilibrium relaxed structures, and microscopic elastic properties at the surface. These are incorporated into appropriate long wavelength elastic theories which are then used to study stress distributions, and to explore the spectra of elementary elastic waves at solid surfaces. Presently, we are applying these methods to study the dynamics of vicinal surfaces which are miscut slightly away from a low index direction; here one finds particularly large atomic relaxations and new physical effects. We are extending these methods to investigate the possibility of surface vibrational spectrosopy as a probe of elastic properties of buried interfaces 1-5 nm below the surface, and which are difficult to access using traditional surface sensitive spectroscopies. This work is carried out in collaboration with theorists in the Department of Chemistry, and with an experimental group in the Department of Materials Science and Engineering.
   

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