Related papers: Hopf Term for a Two-Dimensional Electron Gas
The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We…
In this paper we deduce transport properties in the presence of a pseudogap associated with precursor superconductivity. Our theoretical analysis is based on the widely adopted self energy expression reflecting this normal state gap, which…
The thermodynamic potential of an ideal nonrelativistic gas of two-dimensional electrons in crossed uniform magnetic and electric fields is constructed. For low temperatures and very weak electric fields, it is shown that the Hall…
In this paper we study generalized Poincar\'e-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in n-dimensional manifolds satisfying some suitable conditions. This result allows us to obtain…
An alternative multipole expansion of the correlation term is derived. Modified spherical Bessel type functions which simplify as a summation of multiple orders of basic trigonometric functions are generated from this new method. We use…
We introduce a family of periods of mixed Tate motives called dissection polylogarithms, that are indexed by combinatorial objects called dissection diagrams. The motivic coproduct on the former is encoded by a combinatorial Hopf algebra…
We revisit our recent contribution (SIAM J. Math. Analysis, 42 (2010) 2499--2538) and give two simpler proofs of the so-called Haff's law for granular gases (with non-necessarily constant restitution coefficient). The first proof is based…
We theoretically investigate the electric transport in the pseudogap state of High-Tc cuprates. Starting from the repulsive Hubbard model, we perform the microscopic calculation to describe the pseudogap phenomena which are induced by the…
We discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the $\phi$-mapping topological current theory. The main purpose in this paper is to present a new theoretical framework which can directly give the…
The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum,…
Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce…
I briefly review several key issues in understanding the cuprate superconductors from the point of view of doped-Mott-insulator. Then I present an effective low-energy theory and show that the phase diagram of such a model includes an…
We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…
We have considered the conductivity properties of a two dimensional electron gas (2DEG) in two different kinds of inhomogeneous magnetic fields, i.e. a disordered distribution of magnetic flux vortices, and a periodic array of magnetic flux…
We establish the consistency of the Fermi liquid description and find a relation between Fermi liquid constants for the two dimensional electron system near the point of full polarization due to a parallel magnetic field $H$. Our results…
A new quantization of groupoids under the name of \times-Hopf coalgebras is introduced. We develop a Hopf cyclic theory with coefficients in stable-anti-Yetter-Drinfeld modules for \times-Hopf coalgebras. We use \times-Hopf coalgebras to…
Let $X$ be a two-cell complex with attaching map $\alpha\colon S^q\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\to X\times X$. It is shown that the topological complexity (${\rm TC}$) of $X$ agrees with the…
Combining the complementary capabilities of two of the most powerful modern computational methods, we find superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model (with next nearest neighbor…
Following our earlier work we argue in detail for the equivalence of the nonlinear $\sigma$ model with Hopf term at~$\theta=\pi/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $\sigma$ model and show the…
The chemical potential of the electron gas on a two-dimensional recttangular lattice is determined.An approximate expression for exp(-mu/T) is obtained,and its second order approximation is discussed to some extent.This result will find…