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Register a new userFundamental Principles for Calculating Charged Defect Ionization Energies in Ultrathin Two-Dimensional Materials
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Defects in 2D materials are becoming prominent candidates for quantum emitters and scalable optoelectronic applications. However, several physical properties that characterize their behavior, such as charged defect ionization energies, are difficult to simulate with conventional first-principles methods, mainly because of the weak and anisotropic dielectric screening caused by the reduced dimensionality. We establish fundamental principles for accurate and efficient calculations of charged defect ionization energies and electronic structure in ultrathin 2D materials. We propose to use the vacuum level as the reference for defect charge transition levels (CTLs) because it gives robust results insensitive to the level of theory, unlike commonly used band edge positions. Furthermore, we determine the fraction of Fock exchange in hybrid functionals for accurate band gaps and band edge positions of 2D materials by enforcing the generalized Koopmans condition of localized defect states. We found the obtained fractions of Fock exchange vary significantly from 0.2 for bulk $h$-BN to 0.4 for monolayer $h$-BN, whose band gaps are also in good agreement with experimental results and calculated GW results. The combination of these methods allows for reliable and efficient prediction of defect ionization energies (difference between CTLs and band edge positions). We motivate and generalize these findings with several examples including different defects in monolayer to few-layer hexagonal boron nitride ($h$-BN), monolayer MoS$_2$ and graphane. Finally, we show that increasing the number of layers of $h$-BN systematically lowers defect ionization energies, mainly through CTLs shifting towards vacuum, with conduction band minima kept almost unchanged.
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Formation energies of charged point defects in semiconductors are calculated using periodic supercells, which entail a divergence arising from long-range Coulombic interactions. The divergence is typically removed by the so-called jellium approach. Recently, Wu, Zhang and Pantelides [WZP, Phys. Rev. Lett. 119, 105501 (2017)] traced the origin of the divergence to the assumption that charged defects are formed by physically removing electrons from or adding electrons to the crystal, violating charge neutrality, a key principle of statistical mechanics that determines the Fermi level. An alternative theory was constructed by recognizing that charged defects form by trading carriers with the energy bands, whereby supercells are always charge-neutral so that no divergence is present and no ad-hoc procedures need to be adopted for calculations. Here we give a more detailed exposition of the foundations of both methods and show that the jellium approach can be derived from the statistical-mechanics-backed WZP definition by steps whose validity cannot be assessed a priori. In particular, the divergence appears when the charge density of band carriers is dropped, leaving a supercharged crystal. In the case of charged defects in two-dimensional (2D) materials, unphysical fields appear in vacuum regions. None of these pathological features are present in the reformulated theory. Finally, we report new calculations in both bulk and 2D materials. The WZP approach yields formation energies that differ from jellium values by up to ~1 eV. By analyzing the spatial distribution of wave functions and defect potentials, we provide insights into the inner workings of both methods and demonstrate that the failure of the jellium approach to include the neutralizing electron density of band carriers, as is the case in the physical system, is responsible for the numerical differences between the two methods.
The discovery of graphene makes it highly desirable to seek new two-dimensional materials. Through first-principles investigation, we predict two-dimensional materials of ReN$_{2}$: honeycomb and tetragonal structures. The phonon spectra establish the dynamical stability for both of the two structures, and the calculated in-plane stiffness constants proves their mechanical stability. The energy bands near the Fermi level consist of N-p and Re-d orbitals for the honeycomb structure, and are mainly from Re d orbitals for the tetragonal structure. While the tetragonal structure is non-magnetic, the honeycomb structure has N-based ferromagnetism, which will transit to anti-ferromagnetism under 14$%$ biaxial strain. The calculated electron localization function and spin density indicate that direct N-N bond can occur only in the honeycomb structure. The ferromagnetism allows us to distinguish the two 2D phases easily. The tetragonal phase has lower energy than the honeycomb one, which means that the tetragonal phase is more stable, but the hexagonal phase has much larger bulk, shear, and Youngs muduli than the tetragonal phase. The tetragonal phase is a three-bands metal, and the hexagonal phase is a ferromagnetic semi-metal. The special structural, electronic, magnetic, and optical properties in the honeycomb and tetragonal structures make them promising for novel applications.
Two-dimensional (2D) materials are strongly affected by the dielectric environment including substrates, making it an important factor in designing materials for quantum and electronic technologies. Yet, first-principles evaluation of charged defect energetics in 2D materials typically do not include substrates due to the high computational cost. We present a general continuum model approach to incorporate substrate effects directly in density-functional theory calculations of charged defects in the 2D material alone. We show that this technique accurately predicts charge defect energies compared to much more expensive explicit substrate calculations, but with the computational expediency of calculating defects in free-standing 2D materials. Using this technique, we rapidly predict the substantial modification of charge transition levels of two defects in MoS$_2$ and ten defects promising for quantum technologies in hBN, due to SiO$_2$ and diamond substrates. This establishes a foundation for high-throughput computational screening of new quantum defects in 2D materials that critically accounts for substrate effects.
Charged defects in 2D materials have emerging applications in quantum technologies such as quantum emitters and quantum computation. Advancement of these technologies requires rational design of ideal defect centers, demanding reliable computation methods for quantitatively accurate prediction of defect properties. We present an accurate, parameter-free and efficient procedure to evaluate quasiparticle defect states and thermodynamic charge transition levels of defects in 2D materials. Importantly, we solve critical issues that stem from the strongly anisotropic screening in 2D materials, that have so far precluded accurate prediction of charge transition levels in these materials. Using this procedure, we investigate various defects in monolayer hexagonal boron nitride (h-BN) for their charge transition levels, stable spin states and optical excitations. We identify $C_BN_V$ (nitrogen vacancy adjacent to carbon substitution of boron) to be the most promising defect candidate for scalable quantum bit and emitter applications.
The exfoliation energy, the energy required to peel off an atomic layer from the surface of a bulk material, is of fundamental importance in the science and engineering of two-dimensional materials. Traditionally, the exfoliation energy of a material has been obtained from first principles by calculating the difference in the ground-state energy between (i) a slab of $N$ atomic layers ($N gg 1$) and (ii) a slab of $N-1$ atomic layers plus an atomic layer separated from the slab. In this paper, we prove that the exfoliation energy can be obtained exactly as the difference in the ground-state energy between a bulk material (per atomic layer) and a single isolated layer. The proposed method is (i) tremendously lower in computational cost than the traditional approach since it does not require calculations on thick slabs, (ii) still valid even if there is a surface reconstruction of any kind, (iii) capable of taking into account the relaxation of the single exfoliated layer (both in-plane lattice parameters and atomic positions), and (iv) easily combined with all kinds of many-body computational methods. As a proof of principles, we calculated exfoliation energies of graphene, hexagonal boron nitride, MoS$_2$ and phosphorene using density-functional theory. In addition, we found that the in-plane relaxation of an exfoliated layer accounts for 5% of one-layer exfoliation energy of phosphorene while it is negligible (< 0.4%) in the other cases.
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