Abstract The Snyder-de Sitter (SdS) model which is invariant under the action of the de Sitter group, is an example of a noncommutative space-time with three fundamental scales. In this paper, we considered the massless Dirac fermions in graphene layer in a curved Snyder space-time which are subjected to an external magnetic field. We employed representation in the momentum space to derive the energy eigenvalues and the eigenfunctions of the system. Then, we used the deduced energy function obtaining the internal energy, heat capacity, and entropy functions. We investigated the role of the fundamental scales on these thermal quantities of the graphene layer. We found that the effect of the SdS model on the thermodynamic properties is significant.

中文翻译：

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弯曲 Snyder 空间中的石墨烯

摘要 Snyder-de Sitter (SdS)模型在de Sitter群作用下保持不变，是具有三个基本尺度的非对易时空的一个例子。在本文中，我们考虑了弯曲的 Snyder 时空中石墨烯层中的无质量狄拉克费米子，这些费米子受到外部磁场的影响。我们在动量空间中使用表示来推导系统的能量特征值和特征函数。然后，我们使用推导的能量函数获得内能、热容和熵函数。我们研究了基本尺度对石墨烯层的这些热量的作用。我们发现 SdS 模型对热力学性质的影响是显着的。