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Register a new userA Practical Introduction to Density Functional Theory
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Louk Rademaker
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These lecture notes contain a brief practical introduction to doing density functional theory calculations for crystals using the open source Quantum Espresso software. The level is aimed at graduate students who are studying condensed matter or solid state physics, either theoretical or experimental.
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Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is know about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single particle calculations tend to overestimate spin gaps while they underestimate charge gaps.
In this article, we will give a brief introduction to the topological insulators. We will briefly review some of the recent progresses, from both theoretical and experimental sides. In particular, we will emphasize the recent progresses achieved in China.
We systematically calculate the structure, formation enthalpy, formation free energy, elastic constants and electronic structure of Ti$_{0.98}$X$_{0.02}$ system by density functional theory (DFT) simulations to explore the effect of transition metal X (X=Ag, Cd, Co, Cr, Cu, Fe, Mn, Mo, Nb, Ni, Pd, Rh, Ru, Tc, and Zn) on the stability mechanism of $beta$-titanium. Based on our calculations, the results of formation enthalpy and free energy show that adding trace X is beneficial to the thermodynamic stability of $beta$-titanium. This behavior is well explained by the density of state (DOS). However, the tetragonal shear moduli of Ti$_{0.98}$X$_{0.02}$ systems are negative, indicating that $beta$-titanium doping with a low concentration of X is still elastically unstable at 0 K. Therefore, we theoretically explain that $beta$-titanium doping with trace transition metal X is unstable in the ground state.
Recent experiments demonstrate the synthesis of 2D black arsenic exhibits excellent electronic and transport properties for nanoscale device applications. Herein, we study by first principle calculations density functional theory together with non equilibrium Greens function methods, the structural, electronic, adsorption strength, charge transfer, and transport properties of five gas molecules CO, CO2, NO, NO2, and NH3 on a monolayer of black arsenic. Our findings suggest optimum sensing performance of black arsenic that can even surpass that of other 2D material such as graphene. Further, we note the optimum adsorption sites for all the five gas molecules on the black arsenic and significant charge transfer between the gas molecules and black arsenic are responsible for optimum adsorption strength. Particularly, the significant charger transfer is a sign that the interaction between the target gas molecule and nanoscale device is sufficient to yield noticeable changes in the electronic transport properties. As a proof of principle, we have examined the sensitivity of a modeled nano-scale device towards CO, CO2, NO, NO2, and NH3 gas molecules, indicating that it is indeed possible to reliably detect all the five gas molecules. Thus, based on all these findings, such as sensitivity and selectivity to all the five gas molecules adsorption make black arsenic a promising material as an optimum gas sensor nano-scale device.
We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose, we derive the nonlinear (third-order) TDDFT equation for the excitonic polarization. In this equation, the nonlinear time-dependent effects are described by the time-dependent (non-adiabatic) part of the effective exciton-exciton interaction, which depends on the exchange-correlation (XC) kernel. We apply the approach to study the nonlinear optical response of a GaAs quantum well. In particular, we calculate the 2D Fourier spectra of the system and compare it with experimental data. We find that it is necessary to use a non-adiabatic XC kernel to describe excitonic bound states - biexcitons, which are formed due to the retarded TDDFT exciton-exciton interaction.
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