相关论文: Critical magnetic field for 2d magnetic Dirac-Coul…
Magnetic properties under the external field are investigated in low-carrier two-band systems, which may explain the nontrivial phase boundary found in temperature vs. magnetic field diagram discovered in some materials, such as…
We consider the Ginzburg-Landau functional defined over a bounded and smooth three dimensional domain. Supposing that the magnetic field is comparable with the second critical field and that the Ginzburg-Landau parameter is large, we…
Classical Maxwell and Maxwell-Chern-Simons (MCS) Electrodynamics in (2+1)D are studied in some details. General expressions for the potential and fields are obtained for both models, and some particular cases are explicitly solved.…
Ferromagnetism is typically discussed in terms of the exchange interaction and magnetic anisotropies. Yet real samples are inevitably affected by the magnetostatic dipole-dipole interaction. Because of this interaction, a theorem (R.B.…
An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight $r^{-b}$ for functions in $\R^n$. The exact Hardy constant $c_b=c_b(n)$ is found and generalized minimizers are given. The constant $c_b$…
We develop a theory of Coulomb drag due to momentum transfer between graphene layers in a strong magnetic field. The theory is intended to apply in systems with disorder that is weak compared to Landau level separation, so that Landau level…
Recent thermodynamic measurements on two-dimensional (2D) electron systems have found diverging behavior in the magnetic susceptibility and appearance of ferromagnetism with decreasing electron density. The critical densities for these…
We study the two dimensional massless Coulomb-Dirac operator restricted to its positive spectral subspace and prove estimates on the negative eigenvalues created by electromagnetic perturbations.
We consider the motion of electrons confined to a two dimensional plane with an externally applied perpendicular inhomogeneous magnetic field, both with and without a Coulomb potential. We find that as long as the magnetic field is…
We consider the heat equation in the presence of compactly supported magnetic field in the plane. We show that the magnetic field leads to an improvement of the decay rate of the heat semigroup by a polynomial factor with power proportional…
In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface $M^2 \hookrightarrow {\Bbb R}^3$ as well as intrinsic bounds for 2-dimensional compact manifolds of genus…
Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the…
We continue the analysis started in [Noris,Terracini,Indiana Univ Math J,2010] and [Bonnaillie-No\"el,Noris,Nys,Terracini,Analysis & PDE,2014], concerning the behavior of the eigenvalues of a magnetic Schr\"odinger operator of Aharonov-Bohm…
We study the Fermi level structure of (2+1)-dimensional strongly interacting electron systems in external magnetic field using the AdS/CFT correspondence. The gravity dual of a finite density fermion system is a Dirac field in the…
The effect of an in-plane magnetic field upon open quasi-two-dimensional electron and hole systems is investigated in terms of the carrier ground-state spectrum. The magnetic field, classified as weak from the viewpoint of correlation…
We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schr\"odinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly…
We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the Kre{\u\i}n-Vi\v{s}ik-Birman extension scheme, or…
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$-polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized…
The upper critical field, the lower critical field and the critical magnetic field ratio of anisotropic magnetic superconductors are calculated by Ginzburg-Landau theory analytically. The effect of the Ginzburg-Landau parameter(\kappa_0),…
Strong spin fluctuations are expected near the thermodynamic critical point of a continuous magnetic phase transition. Such critical spin fluctuations are highly correlated and in principle can occur at any time- and length-scales; they…