Application of generalized Bloch method: Strain engineering of low dimensional materials through inhomogeneous strains

Abstract

Due to their special structural morphologies, low dimensional materials are in nanometer scale in zero, one or two dimensions. This feature offers them superior structural flexibility. This characteristic, together with their excellent electronic property response to mechanical deformation, makes strain engineering an important way to optimize the physical properties of materials. Because in low dimension, structural deformations are usually inhomogeneous, the standard electronic and phonon calculation methods formulated via translation under the periodic boundary conditions encounter fundamental difficulties. A fresh approach in this aspect is called for rapidly. In this paper, the essential idea of the generalized Bloch method is introduced, in the context of a tight-binding treatment of electrons. This special method makes use of the helical symmetry and rotational symmetry to deal with the two fundamental non-uniform structural deformations, i.e., torsion and bending. In this way, the atomistic simulation of the deformed structures can still be carried out through a relatively small repeating cell. Such treatment enables the realistic atomistic quantum mechanical simulations in a viable manner. In practice, this new method is implemented into the so-called density-functional tight-binding (DFTB) calculation, an approach widely used in the material computation today. We note that the utility of DFTB brings us several benefits. First of all, the self-consistent field improves the calculation accuracy to be compatible with first-principles calculations. Next, the capability to deal with spin freedoms of DFTB enables us to study the strain tunable properties of spin-polarized electronic states. We illustrate the application of the generalized Bloch method with several examples that can be categorized into “strain tunable electronic properties”, “spatial manipulation of dopants in semiconductor nanowires”, and “strain engineering of phonon properties”. We also have a vision that the generalized Bloch method shall have important application in more areas. Studies of twist bilayers of two-dimensional materials are one of the focuses of the current condensed matter physics research. However, due to the twist induced lattice mismatch, a twisted bilayer is often of a unit cell containing a huge number of atoms. This makes direct realistic atomistic simulations difficult. We indicate that the calculation can be simplified by using the generalized Bloch method where the helical symmetry and possible rotational symmetry of the twisted bilayer would be used. Exploring giant flexoelectricity is a growing area of materials science. Different from piezoelectricity, flexoelectricity is by definition the linear response of polarization to the strain gradient. Usually, in the actual experimental studies, the strain gradient of materials is generated by applying the bending deformation to the slab. This fact indicates that the generalized Bloch method can be used to simulate such systems. In today’s semiconductor technology, the design of flexible electronic devices is an important development field. The low dimensional materials are natural candidates of flexible systems. Obviously, the generalized Bloch method will also play an important role in this aspect. Our recent work has realized the phonon calculation for low-dimensional structures of helical and rotational symmetries based on the electronic structure calculation with the generalized Bloch method. This functionality will expand the application scope of the generalized Bloch method, making it possible to study the strain modulation of thermal properties in low-dimensional systems with inhomogeneous strain patterns.