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Physical review. B, Condensed matter

Bose-Einstein condensation of charged bosons in a magnetic field

A. S. Alexandrov

Published Oct 1, 1993• 108 citations
Publisher

Abstract

A critical magnetic field in which charged bosons are condensed is derived, taking into account their localization in a random potential. Positive curvature (${\mathit{T}}_{\mathit{c}}$-T${)}^{3/2}$ near ${\mathit{T}}_{\mathit{c}}$ and a divergence or reentry effect, depending on the impurity concentration at low temperatures, are found.

DOI
10.1103/physrevb.48.10571

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Physical Review•Aug 1, 1949•13 citations
A critical magnetic field in which charged bosons are condensed is derived, taking into account their localization in a random potential. Positive curvature (Tc{\mathit{T}}_{\mathit{c}}Tc​-T)3/2{)}^{3/2})3/2 near Tc{\mathit{T}}_{\mathit{c}}Tc​ and a divergence or reentry effect, depending on the impurity concentration at low temperatures, are found.
The magnetic properties of charged vector boson gas are studied in the very weak, and very strong (near critical value) external magnetic field limits. When the density of the vector boson gas is low, or when the external field is strong, no true Bose–Einstein condensation occurs, though significant amount of bosons will accumulate in the ground state. The gas is ferromagnetic in nature at low temperature. However, Bose–Einstein condensation of vector bosons (scalar bosons as well) is likely to occur in the presence of a uniform weak magnetic field when the gas density is sufficiently high. A transitional density depending on the magnetic field seems to exist below which the vector boson gas changes its property with respect to the Bose–Einstein condensation in a uniform magnetic field.
The Bogoliubov-de Gennes equations and the Ginzburg-Landau-Abrikosov-Gor'kov-type theory are formulated for the charged Bose gas (CBG). The theory of the Bose-Einstein condensation of the CBG in a magnetic field is extended to ultralow temperatures and ultrahigh magnetic fields. A low-temperature dependence of the upper critical field Hc2(T){H}_{c2}(T)Hc2​(T) is obtained both for the particle-impurity and particle-particle scattering. The normal-state collective plasmon mode in ultrahigh magnetic fields is studied.
Abstract We study the effects of a uniform and constant magnetic field on the Bose–Einstein condensation (BEC) of relativistic charged scalar bosons. The condensation of magnetized charged bosons is usually discussed in the weak or strong field regimes separately, and in each case, the properties predicted for the condensate are different. Here, we develop a low‐temperature analysis suitable for any field that allows us to observe how the gas behaves for intermediate values of the magnetic field. We find that BEC may occur at finite magnetic fields, despite the gas becoming effectively one‐dimensional due to Landau quantization of the momentum perpendicular to the magnetic axis.
Since the experimental realization of Bose–Einstein condensation of ultra cold atoms, extensive studies have been conducted on boson systems. One of recent epochmaking technologies is the synthesis of a fictitious gauge field acting on neutral atoms, which opened another wide field of studies on bosons and/or fermions in a synthetic magnetic field. Charged bosons were studied more than half a century ago by Schafroth. Charged bosons in a magnetic field were then studied in some respects and a rigorous proof was given by Angelescu and Corviovei, who showed absence of Bose– Einstein condensation of free charged bosons in a uniform magnetic field. This is due to the divergence of the density of states at the lowest band energy, i.e., the lowest Landau level. However the situation changes in the presence of a periodic potential. Namely some external periodic potentials are able to restore the Bose–Einstein condensation of the free charge bosons in a magnetic field in threedimensions (3D), although there has been no actual calculation of the condensation temperature of bosons in a typical lattice structure under a magnetic field. According to these previous studies, it is expected that free cold bosonic atoms under a synthetic magnetic field, if realized experimentally, would not condensate in a continuum space but would have a finite Bose–Einstein condensation temperature in the presence of an optical lattice potential. The aim of this short note is to demonstrate the restoration of the Bose–Einstein condensation under a magnetic field by the introduction of a periodic potential, taking typical lattice structures as examples and calculating the condensation temperature analytically. In what follows, with focus on bosons in a 3D lattice under a uniform magnetic field, we calculate the condensation temperature for different lattices and different magnitude of the magnetic field. In particular we consider a layered structure of two dimensional lattices such as square, triangular and honeycomb ones, with a magnetic field applied in the direction normal to the two-dimensional (2D) lattices. The energy spectrum of a particle on a two dimensional lattice, which we assume to be a square lattice for a moment, under a uniform magnetic field shows a characteristic pattern, so-called Hofstadter’s diagram. The one-particle energy of this system is described by the following Hamiltonian in the tight-binding approximation.
Bose-Einstein condensation of charged scalar and vector particles may actually occur in presence of a constant homogeneous magnetic field, but there is no critical temperature at which condensation starts. The condensate is described by the statistical distribution. The Meissner effect is possible in the scalar, but not in the vector field case, which exhibits a ferromagnetic behavior. Permanent address: Grupo de Fisica Teórica, ICIMAF, Academia de Ciencias de Cuba, Calle E No. 309,Vedado, La Habana 4, Cuba. It was pointed out long ago by Schafroth [1] that for a non-relativistic boson gas, Bose-Einstein condensation (BEC) does not take place in the presence of a constant magnetic field. The problem was studied afterwards by May [2], who investigated the condensation in the non-relativistic case for an arbitrary dimension d and showed that it occurs for d ≥ 5, and later by Daicic et al [3], [4], who extended the considerations made by [2] to the relativistic high temperature case and found new magnetization properties. More recently Toms [5] has proved that BEC in presence of a constant magnetic field does not occur in any number of spatial dimensions, and Elmfors et al [6] consider that a in the 3d
The condensation and accumulation phenomena of charged Bose-Einstein particles in a magnetic field are examined, neglecting electrostatic interactions. For weak fields a single condensation occurs at the same temperature as that for uncharged particles; for strong fields there is a separate lower accumulation temperature, indicating the accumulation of particles in the lowest translational state. The total energy, free energy, and polarization are calculated, and applied to the properties of a gas of electron pairs, and a solution of deuterons in a metal, these being systems whose low temperature behavior might show a Bose-Einstein condensation. It is shown that the Bose-Einstein condensation of free electron pairs cannot provide a theory of superconductivity.