Magnetization of planar four-fermion systems

Abstract

We consider a planar system of fermions, at finite temperature and density, under a static magnetic field parallel to the two-dimensional plane. This magnetic field generates a Zeeman effect and, then, a spin polarization of the system. The critical properties are studied from the Landau's free energy. The possible observable consequences of the magnetization of planar systems such as polymer films and graphene are discussed.Published: Phys. Rev. B 80, 115428 (2009)

Superconductivity Phenomenon Induced by External in-Plane Magnetic Field in (2 + 1)-Dimensional Gross–neveu Type Model

“…Indeed, twenty years ago, it was found that at G 2 = 0 and G 1 > 0 an arbitrary weak perpendicular external magnetic field B ⊥ can not only enhance the chiral symmetry breaking (if G 1 > G c ) but also induce spontaneous breaking of the chiral symmetry at G 1 < G c (see, e.g., [6,[20][21][22][23]). In contrast, recently it was found [35] that an application of an external parallel to the system plane (in-plane) magnetic field B results in the restoration of chiral symmetry (recall, in this case G 2 = 0). For an explanation of such a different reaction of the chiral symmetry on perpendicular and parallel magnetic fields one should remember that B ⊥ acts on the orbital angular momentum of electrons, whereas the in-plane field B couples only to their spin.…”

“…Among these systems are the high-T c cuprate and iron superconductors [27,28], the one-atom thick layer of carbon atoms, or graphene, [29,30] etc. Thus, many properties of such condensed matter systems can be explained in the framework of various (2+1)-dimensional QFT, including the GN-type models (see, e.g., [31][32][33][34][35][36][37][38][39][40][41][42][43][44] and references therein).…”

Phase structure of Gross-Neveu model with compactification in the presence of external magnetic field

“…Consider the limit L → ∞ (this case has been considered in [6]). One can see that in the expression for first derivative of the thermodynamic potential (34) the last term tends to zero as O(…”

The Zeeman effect in a modified Gross—Neveu model in (2 + 1)-dimensional space—time with compactification

“…On the other hand, it is known that many results that are obtained using the Gross-Neveu model can be used in the physics of the condensed state of matter. Thus, a Lagrangian similar to the (1 + 1) dimensional Gross-Neveu model occurs in the study of one dimensional polymers, such as polyacet ylene [3,4], and a Lagrangian similar to the (2 + 1) dimensional Gross-Neveu model occurs in the study of two dimensional polymers (such as graphene, see, for example, [5]). Thus, the Gross-Neveu model that is used for the description of such systems with account for the influences of such parameters as tem perature, chemical potential, and external fields [5][6][7][8][9] is of special interest.…”

“…It should be noted that in theories that are connected with graphene, in spite of the intro duction of the Dirac equation for four component fermions (see the definitions below), their compo nents are not connected with the real spin [11]. For this reason, if the Zeeman effect is introduced, the real spin is represented as an additional quantum number (see Section 4), similar to the approach that was applied in [5] for a planar space.…”