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Engineering of the Properties of Low Dimensional Materials via Inhomogeneous Strain

low dimensional materials represent a special organization of matters. Exploring their novel properties stands for an important frontier in the fundamental research of condensed matter physics and material science. Due to their small length scale in one or two dimensions, low dimensional materials are usually structural flexible. This feature together with the electronic response to structural deformations enable us to modulate the material properties via a strain way. The main purpose of this paper is to introduce the recent research progress of obtaining novel physical properties by inhomogeneous strain in two-dimensional materials, with focus on two effects, i.e., pseudomagnetic field effect and the flexoelectric effect. Of course, the influence of inhomogeneous strains on electrons is not limited to these two effects. Fundamentally, an inhomogeneous deformation breaks the symmetry of crystalline structure. This serves as a start point to delineate the structural-properties relation. First, the symmetry breaking can left the degeneracy of energy levels. Secondly, the symmetry breaking will also cause the heterogeneity of electronic and phonon properties in different parts of the material.

The paper also introduces a special method named as the generalized Bloch theorem that is suitable to deal with the inhomogeneous strain patterns at the atomistic level. From the perspective of atomistic simulation, due to the breaking of translational symmetry, standard quantum mechanical calculations encounter fundamental difficulties in dealing with an inhomogeneous strain, e.g., bending and torsion. The generalized Bloch method overcomes such obstacle by considering rotational and/or screw symmetries given by bending and/or torsion in solving the eigenvalue problem. As such, quantum mechanical calculations can be still conducted with a relatively small number of atoms.