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arXiv 1509.08093cond-mat.mes-hallhep-th
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外部条件影响下六方、类石墨烯晶格片和纳米管的相变

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

D. Ebert, K. G. Klimenko, P. B. Kolmakov, V. Ch. Zhukovsky

摘要:

在本文中,我们考虑了一类(2+1)D示意模型与四费米子相互作用,有效地用于研究凝聚态系统的平面晶体结构,特别是石墨烯。在这些模型中,对称性破缺是由于可能出现的凝聚体。特别注意的是在离散的手征和$\mathcal C$,$\mathcal P$和$\mathcal T$转换的框架中出现的凝聚物的对称性。此外,相应的碳纳米管的边界条件被认为是和它们的关系与外加磁场的影响进行了研究。为此,我们计算的有效潜力的纳米管模型,包括有限的温度,密度和外部磁场的影响。作为例子,我们在一个简单的Gross-Neveu模型中,只考虑一种凝聚体,对手征对称性进行了数值计算。我们还研究了在Aharonov-Bohm效应影响下的纳米管模型的相结构,并证明了Aharonov-Bohm相的大小、空间维度的紧致化和最初破坏的手征对称性的热恢复之间存在非平凡的关系。

英文摘要:

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.

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