Abstract
Thanks to the ultrahigh flexibility of 2D materials and to their extreme sensitivity to applied strain, there is currently a strong interest in studying and understanding how their electronic properties can be modulated by applying a uniform or nonuniform strain. In this work, using density functional theory (DFT) calculations, we discuss how uniform biaxial strain affects the electronic properties, such as ionization potential, electron affinity, electronic gap, and work function, of different classes of 2D materials from X-enes to nitrides and transition metal dichalcogenides. The analysis of the states in terms of atomic orbitals allows to explain the observed trends and to highlight similarities and differences among the various materials. Moreover, the role of many-body effects on the predicted electronic properties is discussed in one of the studied systems. We show that the trends with strain, calculated at the GW level of approximation, are qualitatively similar to the DFT ones solely when there is no change in the character of the valence and conduction states near the gap.
Highlights
Much of the emphases on 2D materials[1,2,3] was born with the discovery of graphene, for which the Nobel Prize in physics was awarded to Novoselov and Geim in 2010.4 Graphene is a 2D crystal made up of carbon atoms arranged in a hexagonal honeycomb form; it is one million times thinner than paper, almost transparent, and, at the same time, is the strongest material in the world.[5,6] Its electronic structure can be derived from a simple tight-binding model, which explains the presence of bands with conical dispersion intersecting at the Fermi level, making graphene a semimetal.[7]
For 2D semiconductors, we report the electronic band structures and bandgap values at several biaxial uniform compressive and tensile strains, the ionization potential (IP) ( IP 1⁄4 E vac À E valence band maximum (VBM)) and the electron affinity (EA) ( EA 1⁄4 E vac À E conduction band minimum (CBM)) to show their specific dependence on strain and to understand which are the different effects leading to the peculiar behaviors observed
For nitrides (TMD ML and their homobilayers), the density functional theory (DFT) band structures have been calculated for applied strains ranging from À10% to 10% (À7% to 7% for MoS2,À10% to 10% for MoTe2) but, here, we report only those at zero strain and À4%, 4% (À5%, 5% for MoS2 and MoTe2)
Summary
Much of the emphases on 2D materials[1,2,3] was born with the discovery of graphene, for which the Nobel Prize in physics was awarded to Novoselov and Geim in 2010.4 Graphene is a 2D crystal made up of carbon atoms arranged in a hexagonal honeycomb form; it is one million times thinner than paper, almost transparent, and, at the same time, is the strongest material in the world.[5,6] Its electronic structure can be derived from a simple tight-binding model, which explains the presence of bands with conical dispersion intersecting at the Fermi level, making graphene a semimetal.[7] Massless Dirac fermions move in graphene as fast as vF1⁄4 106 m=s at the Fermi level, and twisted bilayers of graphene have even been shown to be superconductors for very small twisting angles.[8] This peculiar linear dispersion of low-energy carriers, which can be mapped to an effective 2D Dirac Hamiltonian, is very different from the usual parabolic dispersion of bulk semiconductors. Despite the enormous interest both at the fundamental and applicative level, the lack of an electronic gap limits graphene use in applications like digital electronics, Rome, Italy 3 Istituto di Struttura della Materia-CNR (ISM-CNR), Rome, Italy 4 Dipartimento di Scienza dei Materiali, Universita Milano Bicocca, Milano, Italy
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