Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions

TL;DR

This study explores phase transitions and symmetry breaking in graphene-like lattice models, including nanotubes, under external conditions such as magnetic fields, temperature, and density, revealing complex relations between these factors and chiral symmetry.

Contribution

It introduces a detailed analysis of symmetry properties and phase structure in (2+1)D fermionic models with boundary conditions relevant to nanotubes, incorporating external magnetic and thermal effects.

Findings

Chiral symmetry can be restored thermally in nanotube models.

External magnetic fields influence the phase structure and symmetry breaking.

A nontrivial relation exists between Aharonov--Bohm phase and chiral symmetry restoration.

Abstract

In this paper we consider a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene. Symmetry breaking in these models occurs due to a possible appearance of condensates. Special attention is paid to the symmetry properties of the appearing condensates in the framework of discrete chiral and $\mathcal C$, $\mathcal P$ and $\mathcal T$ transformations. Moreover, boundary conditions corresponding to carbon nanotubes are considered and their relations with the effect of an applied external magnetic field are studied. To this end we calculated the effective potential for the nanotube model including effects of finite temperature, density and an external magnetic field. As an illustration we made numerical calculations of the chiral symmetry properties in a simpler Gross--Neveu model with only one condensate taken into account. We also investigated the phase structure of the nanotube model under the influence of the Aharonov--Bohm effect and demonstrated that there is a nontrivial relation between the magnitude of the Aharonov--Bohm phase, compactification of the spatial dimension and thermal restoration of the originally broken chiral symmetry.