Nearest Neighbour Particle-Particle Interaction in Fermionic Quasi One-Dimensional Flat Band Lattices

In this paper, we have studied spinless fermions in four specific quasi one-dimensional systems that are known to host flat bands in the noninteracting limit: the triangle lattice, the stub lattice, the diamond lattice, and the diamond lattice with transverse hopping. The influence of the nearest neighbour interaction on the flat bands was investigated. We used exact diagonalization of finite size lattices employing the Lanczos technique and determine the single particle spectral functions of the interacting system. Our results are compared with mean field calculations. In the cases of the triangle lattice and the stub lattice we found that the flat bands become dispersive in the presence of a finite interaction. For the diamond lattice and the diamond lattice with transverse hopping, we demonstrated that the flat bands are robust under the influence of the interaction in certain parameter ranges. Such systems could be realised experimentally with cold atoms in optical lattices.

Bi-Material Re-Entrant Triangle Cellular Structures Incorporating Tailorable Thermal Expansion and Tunable Poisson's Ratio1

Based on the bi-material triangle lattice cell, a new cellular structure, bi-material re-entrant triangle (BRT) cellular structure, is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson's ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. A general thermoelasticity equation to systematically build the relationship among the external force, the temperature load, and the deformation for planar lattice structures with bounded joints is derived and then embedded into a theoretical model for the devised BRT structure. Using assembled thermoelasticity equation, effective PR, Young's modulus, as well as CTE are computed. In order to guide designers to construct initial concepts, the design domain for coupling negative CTE and negative PR properties is plotted. The material-property-combination region that can be achieved by this cellular structure is determined within an Ashby material selection chart of CTE versus PR. Nine available combinations of CTE and PR properties are extracted and demonstrated with abaqus simulation.

Bi-Material Re-Entrant Triangle Structures Incorporating Tailorable Thermal Expansion and Tunable Poisson’s Ratio

Based on the bi-material triangle lattice material, a new cellular structure: bi-material re-entrant triangle (BRT) is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson’s ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. An equation to systematically build the relationship among the external force, the temperature increment and the deformation for the planar lattice material with bounded joints is derived and then embedded into a theoretical model for devised BRT structure. Using master stiffness equation, effective PR, effective Young’s modulus as well as effective CTE are computed. In order to guide designers to construct an initial concept quickly, the design domain for coupling negative CTE and negative PR properties is proposed. Nine available paired characteristics for coupling effect are extracted and demonstrated with ABAQUS simulation.