Effects of strain in α − T3 lattice and its nanoribbons

Abstract

The α − T3 lattice, commonly regarded as a model system with a hexagonal structure containing an additional atom at the center of each hexagon, whose couplings to the surrounding sublattices are modulated by an intrinsic parameter α that continuously interpolates between the honeycomb lattice (α = 0) and the dice lattice (α = 1)—has attracted considerable interest within the condensed matter physics community owing to its unusual electronic and transport properties. Along this interpolation, the nature of the low-energy charge carriers in the α − T3 lattice evolves from spin-S = 1/2 Dirac fermions, as in graphene, to spin-S = 1 Dirac fermions characteristic of the dice lattice. Beyond the interpolation parameter α, additional mechanisms can be employed to tailor the physical properties of the α − T3 lattice, including geometric confinement in narrow nanoribbons, structural deformations of the lattice, and the application of external electric or magnetic fields. Motivated by this tunable morphological character and the associated quantum finite-size effects, this master’s thesis investigates how the electronic properties of the α − T3 lattice and its nanoribbons are modified under different types of uniform strain, specifically uniaxial, biaxial, and shear deformations. We systematically examine the influence of edge terminations (zigzag and armchair boundaries), the connectivity of the central atom in the hexagon to its neighboring sites, the ribbon width, and the magnitude and nature of the applied deformation. Our theoretical analysis, formulated in both first- and second-quantized forms, is based on a tight-binding Hamiltonian that captures, in the appropriate limits, the electronic structures of graphene and the dice lattice, including the coexistence of flat and conical bands. The resulting band structures reveal how the electronic properties evolve as functions of lattice morphology, orbital overlap, quantum confinement, and strain amplitude. We demonstrate that five out of the six considered types of in-plane uniform deformations (uniaxial strain, simple shear in the x and y directions, and pure shear) induce a finite energy gap in the band structure. Furthermore, we obtain analytical expressions that describe the monotonic increase of this gap with strain amplitude and its dependence on the underlying model parameters. For nanoribbons, we classify the systems as metallic or semiconducting and show how this classification can be altered by varying the lattice morphology, edge termination, and ribbon width. In addition, we demonstrate that the band gap can be effectively tuned by applying shear strain along the periodicity direction.