Condensed Matter Seminars
2005 – 2006

Quantum systems with periodic potentials play an important role when it comes about our understanding of the condensed matter. In a seminal paper, Bloch showed that the solutions of the Schrodinger equation for electrons in periodic potentials are still waves and, ever since, these solutions were labeled Bloch waves. In 1959, Walter Kohn published a 1D study on these functions, in which he revealed the analytic structure of Bloch waves as a function of the k vector. Understanding this structure, for real as well as for complex k vectors, turned out to be the key for understanding, besides many other  things, the exponential localization of different correlation functions in periodic insulators. In this talk I will discuss recent and first extensions  of these results to higher dimensions. I will present the analytic structure of the Bloch functions for linear molecular chains and cubic crystals and discuss several applications which include: estimating the changes of the particle density and local density of states in periodic crystals due to impurities, surfaces and interfaces

By recognizing the vital importance of two-hole Cooper pairs in addition to the standard two-fermion ones in a many-fermion system such as a superconductor or neutral-fermion superfluid, the concept of pairing has been re-examined with striking conclusions. Based on this, Bose-Einstein condensation (BEC) theory is generalized to include not boson-boson interactions (also neglected in BCS theory) but rather boson-fermion interactions. The new formalism reduces to all the old known statistical theories as special cases---including the so-called BCS-Bose crossover picture which in turn generalizes BCS theory. With no adjustable parameters, it yields substantially higher superconducting transition temperatures without invoking non-phonon dynamics. The implications of all this in neutral-fermion superfluids like trapped ultracold Fermi atomic clouds, is still to be explored.

Quantum Dots and Single-Electron Transistors have been used over the past decade to model Fermi liquid or Kondo states in and near
equilibrium. The universal features of the Kondo effect and its significance in describing strongly correlated electron materials have led to a strong interest both from a technological as well as scientific point of view.
Here, we introduce what we believe to be the first realistic system - a quantum dot attached to ferromagnetic leads - that models non-Fermi liquid states near a quantum phase transition. We theoretically demonstrate a gate-voltage induced quantum phase transition. At the transition the Kondo effect becomes quantum critical, leading to distinct, universal properties. We find a fractional-power-law dependence of the conductance on temperature (T). The AC conductance and thermal noise spectrum have related power-law dependences on frequency (omega) and, in addition, show an (omega/T) scaling. Our results imply that the ferromagnetic nanostructure constitutes a robust and realistic model system to elucidate magnetic quantum criticality that is central to the heavy fermions and other strongly correlated electron systems with non-Fermi liquid behavior.