Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems

We review various connections between condensed matter systems with the Nambu-Jona Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Resent findings of a duality between the Nambu-Jona Lasinio model and the nonlinear sigma model enables us to investigate various properties underlying both theories. In this review we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in the nonlinear sigma model owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.Comment: 24pages, 10 figures, Invited review paper commissioned by Symmetry. Comments warmly welcom

Ultrarelativistic electron-hole pairing in graphene bilayer

We consider ground state of electron-hole graphene bilayer composed of two independently doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only conduction band of electron-doped layer and valence band of hole-doped layer, thus the ground state is similar to ordinary BCS condensate. At strong coupling, an ultrarelativistic character of electron dynamics reveals and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. The analysis of instability of unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. A relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of separable potential. It is shown that, if characteristic width of the pairing region is of the order of magnitude of chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However, if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.Comment: 13 pages with 8 figures; accepted to Eur. Phys. J.

Atomic structure, energetics, and dynamics of topological solitons in Indium chains on Si(111) surfaces

Based on scanning tunneling microscopy and first-principles theoretical studies, we characterize the precise atomic structure of a topological soliton in In chains grown on Si(111) surfaces. Variable-temperature measurements of the soliton population allow us to determine the soliton formation energy to be ~60 meV, smaller than one half of the band gap of ~200 meV. Once created, these solitons have very low mobility, even though the activation energy is only about 20 meV; the sluggish nature is attributed to the exceptionally low attempt frequency for soliton migration. We further demonstrate local electric field-enhanced soliton dynamics.Comment: 5 pages, 3 figure

Aspects of 3{}^3He and the Standard Electroweak Model

We describe certain aspects of ${}^3He$ and compare them to related aspects of the standard electroweak model of particle physics. We note various similarities in the order parameter structure, defect structure, interactions with fermions and anomalies in the two systems. Many issues in the condensed matter literature that are often confusing to the particle physics reader and vice versa are clarified.Comment: 60 pages + 15 figures; LaTe