Kapcia Konrad Jerzy
Faculty of Physics, Adam Mickiewicz University in Poznań, ulica Uniwersytetu Poznańskiego 2, PL-61614 Poznań, Poland.
Nanomaterials (Basel). 2021 Apr 30;11(5):1181. doi: 10.3390/nano11051181.
The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to S=1/2 fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite and intersite W1 and W2 (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive W1>0, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state (T=0) diagram for W2≤0 as well as finite temperature (T>0) phase diagrams for W2=0 are presented. Two different types of charge order within 3×3 unit cell can occur. At T=0, for W2=0 phase separated states are degenerated with homogeneous phases (but T>0 removes this degeneration), whereas attractive W2<0 stabilizes phase separation at incommensurate fillings. For U/W1<0 and U/W1>1/2 only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive 0<U/W1<1/2 the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.
吸附原子倾向于占据由底层晶体表面的周期性势形成的三角晶格。例如，这样的晶格由单层石墨烷或石墨表面以及面心立方晶体的(111)表面形成。在本工作中，分析了晶格气体模型向二维三角（六角）晶格上的S = 1/2费米子粒子的扩展。在这样一个模型中，每个晶格位置不仅可以被一个粒子占据，还可以被两个粒子占据，这两个粒子通过在位和近邻及次近邻（分别为W1和W2）密度-密度相互作用相互作用。所研究的哈密顿量具有原子极限（即零带宽极限）下的扩展哈伯德模型的形式。在分析具有排斥性W1>0的该模型的相图和热力学性质时，使用了变分方法，该方法精确处理在位相互作用项，并在平均场近似内处理近邻相互作用。给出了W2≤0时的基态（T = 0）图以及W2 = 0时的有限温度（T>0）相图。在3×3晶胞内可以出现两种不同类型的电荷序。在T = 0时，对于W2 = 0，相分离态与均匀相简并（但T>0消除了这种简并），而吸引性的W2<0在非 commensurate填充时稳定相分离。对于U/W1<0和U/W1>1/2，仅出现具有两种不同浓度的相（同时出现两种不同的相分离态），而对于小的排斥性0<U/W1<1/2，还会出现另一种有序相（子晶格中有三种不同浓度）。还讨论了与在超立方晶格上考虑的模型的定性差异。
