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Graphene is favorable to realize topological nontrivial state by introducing spin-orbit coupling and exchange field through the proximity effect. The recent discovery of van der Waals magnets allows great proximitized modulation on graphene by building atomically clean heterostructures. Here, we realize anomalous Hall effect in graphene coupling with a layered magnetic material, ${\mathrm{Fe}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{S}}_{2}$. The anomalous Hall resistance and the carrier density show a nonmonotonous dependence on the back-gate voltage, indicating emergence of band-structure transformation. Furthermore, low-field quantum interference measurement shows the enhancement of spin-orbit coupling (SOC) in the heterostructure. Our findings confirm that graphene coupling to ${\mathrm{Fe}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{S}}_{2}$ is an ideal platform that is likely to introduce a strong exchange field and SOC simultaneously, which has outstanding potential in realizing topological nontrivial states and spintronics.

Band gap engineering of graphene has been intensively studied, but it is still difficult to be realized effectively in practice, which limits its applications in optoelectronics. Here, by using first-principles methods, we predicate that the band gap of graphene can be obviously enlarged up to 0.83 eV and type-I band alignment is also realized in the $\text{graphene}/\mathrm{BN}/M{X}_{2}$ (M = Mo, W; X = S, Se) heterotrilayers when the interlayer distance is compressed. Moreover, the electrons and holes can be confined inside the gap opened graphene layer, and the staggered band alignment can be formed under the presence of electric field as well as the vertical pressure in the $\text{graphene}/\text{BN}/M{X}_{2}$ heterotrilayers. Our results may pay an effective route to tune the gap of graphene and broaden its applications in optoelectronic fields.

Due to mirror symmetry breaking, two-dimensional Janus transition metal dichalcogenides $MXY$ ($M=\text{Mo,W}$; $X,Y=\text{S,Se,Te}$) present charming electronic properties. However, there have not been many related studies as of yet, and the intrinsic physical pictures are unclear. Here, we use first-principles calculations to explore the universality of electronic characteristics and photocatalyst applications of Janus $MXY$, finding that the induced dipole moment, vibrational frequency, Rashba parameters, and direct-indirect band transition of monolayer $MXY$ are deeply associated with the atomic radius and electronegativity differences of chalcogen $X$ and $Y$ elements. The internal electric field renders Janus $MXY$ the ideal photocatalysts. Moreover, the stacking-dependent on/off switch of the dipole moment further confirms that asymmetric Janus $MXY$ serves as a promising candidate for highly efficient photocatalysts within a broad range from infrared, visible, to ultraviolet light.

Recently, constructing van der Waals (vdW) heterojunctions by stacking different two-dimensional (2D) materials has been considered to be effective strategy to obtain the desired properties. Here, through first-principles calculations, we find theoretically that the 2D $n$-InSe/$p$-GeSe(SnS) vdW heterojunctions are the direct-band-gap semiconductor with typical type-II band alignment, facilitating the effective separation of photogenerated electron and hole pairs. Moreover, they possess the high optical absorption strength ($\ensuremath{\sim}{10}^{5}$), broad spectrum width, and excellent carrier mobility ($\ensuremath{\sim}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$). Interestingly, under the influences of the interlayer coupling and external electric field, the characteristics of type-II band alignment is robust, while the band-gap values and band offset are tunable. These results indicate that 2D $n$-InSe/$p$-GeSe(SnS) heterojunctions possess excellent optoelectronic and transport properties, and thus can become good candidates for next-generation optoelectronic nanodevices.

Density functional theory calculations are performed to explore the nature of the contact between metal electrodes and defected monolayer ${\mathrm{MoSe}}_{2}$. Partial Fermi level pinning is observed at perfect ${\mathrm{MoSe}}_{2}$/metal interfaces. Both As- and Br-substituted ${\mathrm{MoSe}}_{2}$ will induce extra bands in valence band and conduction band, respectively, which exerts influence on the Schottky barrier height. An enhanced partial Fermi level pinning occurs when As- and Br-substituted ${\mathrm{MoSe}}_{2}$ make contacts with metal electrodes. Se vacancy in the ${\mathrm{MoSe}}_{2}$ layer can induce a large amount of interfacial states in the band gap of the ${\mathrm{MoSe}}_{2}$ layer. As a result, nearly complete Fermi level pinning is observed in Se-vacancy ${\mathrm{MoSe}}_{2}$/metal contacts. Our work offers insight into the Fermi level pinning at the interfaces between two-dimensional materials and metal electrodes, which is important for the applications of two-dimensional materials in nanoelectronic devices with good performance.

Ab initio atomic relaxations often take large numbers of steps and long times to converge, especially when the initial atomic configurations are far from the local minimum or there are curved and narrow valleys in the multidimensional potentials. An atomic relaxation method based on on-the-flight force learning and a corresponding curved-line search algorithm is presented to accelerate this process. Results demonstrate the superior performance of this method for metal and magnetic clusters when compared with the conventional conjugate-gradient method.

Searching for ferromagnetic (FM) van der Waals (vdW) heterostructures with high Curie temperature and multiple-band alignments is crucial to develop next-generation spintronic and optoelectronic nanodevices. Here, through first-principles methods, the FM vdW heterostructure is found for the first time in the Mg(${\mathrm{OH})}_{2}/{\mathrm{VS}}_{2}$ heterobilayer with high Curie temperature (385 K) and type-II alignment. The negative electric field induces the transition from type-II to type-III alignment in the spin-up channel. However, under the positive electric field, the type-II to type-I alignment transition occurs in the spin-up and spin-down channels. This work provides the possibilities of realizing the high-temperature FM vdW heterostructures and electrostatic gating dependent multiple-band alignments in practice.

We present a method to approximate the Hessian matrix of the Born-Oppenheimer energy landscape by using a simple force field model whose parameters are fitted to on-the-flight ab-initio results. The inversed Hessian matrix is used as the preconditioner of conjugate gradient algorithms to speed up the atomic structure relaxation, resulting in a speedup factor of 2 to 5 on systems of bulk, slab, sheets, and atomic clusters. Because the force field model employed is simple and general, the parameter fitting is straightforward; the method is applicable to a variety of complicated systems for minimum structure relaxation. In the metal cluster new structure search, the new method yields better structures than the one obtained before with conventional algorithms.

We have studied the hole levels and exciton states in CdS nanocrystals by using the hole effective-mass Hamiltonian for wurtzite structure. It is found that the optically passive P-x state will become the ground hole state for small CdS quantum dots of radius less than 69 Angstrom. It suggests that the "dark exciton" would be more easily observed in the CdS quantum dots than that in CdSe quantum dots. The size dependence of the resonant Stokes shift is predicted for CdS quantum dots. Including the Coulomb interaction, exciton energies as functions of the dot radius are calculated and compared with experimental data.

By using the hole effective-mass Hamiltonian for semiconductors with the wurtzite structure, we have studied the exciton states and optical spectra in CdSe nanocrystallite quantum dots. The intrinsic asymmetry of the hexagonal lattice structure and the effect of spin-orbital coupling (SOC) on the hole states are investigated. It is found that the strong SOC limit is a good approximation for hole states. The selection rules and oscillator strengths for optical transitions between the conduction- and valence-band states are obtained. The Coulomb interaction of exciton states is also taken into account. In order to identify the exciton states, we use the approximation of eliminating the coupling of Gamma(6)(X, Y) with Gamma(1)(Z) states. The results are found to account for most of the important features of the experimental photoluminescence excitation spectra of Norris ct nl. However, if the interaction between Gamma(6)(X, Y) and Gamma(1)(Z) states is ignored, the optically passive P-x state cannot become the ground hole state for small CdSe quantum dots of radius less than 30 Angstrom. It is suggested that the intrinsic asymmetry of the hexagonal lattice structure and the coupling of Gamma(6)(X,Y) with Gamma(1)(Z) states are important for understanding the "dark exciton" effect.

The hole effective-mass Hamiltonian for the semiconductors with wurtzite structure is given. The effective-mass parameters are determined by fitting the valence-band structure near the top with that calculated by the empirical pseudopotential method: The energies and corresponding wave functions are calculated with the obtained effective-mass Hamiltonian for the CdSe quantum spheres, and the energies as functions of sphere radius R are given for the zero spin-orbital coupling (SOC) and finite SOC cases. The energies do not vary as 1/R-2 as the general cases, which is caused by the crystal-field splitting energy and the linear terms in the Hamiltonian. It is found that the ground state is not the optically active S state for the R smaller than 30 Angstrom, in agreement with the experimental results and the "dark exciton'' theory. [S0163-1829(99)01040-1].

Using the tight-binding model, we have studied the resonant-transport properties of the multiply connected ring systems threaded by magnetic flux F , and coupled to two electron reservoirs. For different flux F the electronic-energy spectrum and their corresponding total transmission probabilities of multiring systems have been calculated and compared. Some novel resonant-transport properties which display the Aharonov-Bohm effect have been found. We have also studied the same problem of a single ring with two barriers. It is found that for the high barriers the distribution of resonant states is coincident with the energy spectrum of the isolated ring, but the energies of resonant states have deviated from the eigenenergies of the system. @S0163-1829~97!11607-1#

Amorphous semiconductors are known to give rise to greatly reduced conductivity relative to their crystalline counterparts, which makes the recent development of amorphous oxide semiconductors with high electron mobility unexpected. Using first-principles molecular dynamics and electronic structure simulations, we have analyzed the electronic and optical properties of covalent and ionic oxide amorphous semiconductors. We observe that in covalent systems, amorphization introduces deep defect states inside the gap, resulting in a substantial deterioration of electrical conductivity. In contrast, in ionic systems, such as the transparent conducting oxide ZnO, amorphization does not create deep carrier-recombination centers, so the oxides still exhibit good conductivity and visible transparency relative to the crystalline phases. The origin of the conductivity imbalance between covalent and ionic amorphous semiconductors can be explained using a band coupling mechanism.

First-principles calculations are performed to investigate the transport properties of zigzag $\ensuremath{\alpha}$-graphyne nanoribbons (Z$\ensuremath{\alpha}$GNRs). It is found that asymmetric Z$\ensuremath{\alpha}$GNRs behave as conductors with linear current-voltage relationships, whereas symmetric Z$\ensuremath{\alpha}$GNRs have very small currents under finite bias voltages, similar to those of zigzag graphene nanoribbons. The symmetry-dependent transport properties arise from different coupling rules between the $\ensuremath{\pi}$ and ${\ensuremath{\pi}}^{*}$ subbands around the Fermi level, which are dependent on the wave-function symmetry of the two subbands. Based on the coupling rules, we further demonstrate the bipolar spin-filtering effect in the symmetric Z$\ensuremath{\alpha}$GNRs. It is shown that nearly 100$%$ spin-polarized current can be produced and modulated by the direction of bias voltage and/or magnetization configuration of the electrodes. Moreover, the magnetoresistance effect with the order larger than $500\phantom{\rule{0.16em}{0ex}}000%$ is also predicted. Our calculations suggest Z$\ensuremath{\alpha}$GNRs as a promising candidate material for spintronics.

In theoretical studies of thin film and nanostructured semiconductors, pseudohydrogen (PH) is widely used to passivate the surface dangling bonds. Based on these calculations, it is often believed that nanostructured semiconductors, due to quantum confinement, have a larger band gap than their bulk counterparts. Using first-principles band structure theory calculation and comparing systematically the differences between PH-passivated and real-hydrogen--passivated (RH-passivated) semiconductor surfaces and nanocrystals, we show that, unlike PH passivation that always increases the band gap with respect to the bulk value, RH passivation of the nanostructured semiconductors can either increase or decrease the band gap, depending on the ionicity of the nanocompounds. The differences between PH and RH passivations decreases when the covalency of the semiconductor increases and can be explained using a band coupling model. This observation greatly increases the tunability of nanostructured semiconductor properties, especially for wide-gap ionic semiconductors.

For large size- and chemical-mismatched isovalent semiconductor alloys, such as N and Bi substitution on As sites in GaAs, isovalent defect levels or defect bands are introduced. The evolution of the defect states as a function of the alloy concentration is usually described by the popular phenomenological band anticrossing (BAC) model. Using first-principles band-structure calculations we show that at the impurity limit the N- (Bi)-induced impurity level is above (below) the conduction- (valence-) band edge of GaAs. These trends reverse at high concentration, i.e., the conduction-band edge of ${\text{GaAs}}_{1\ensuremath{-}x}{\text{N}}_{x}$ becomes an N-derived state and the valence-band edge of ${\text{GaAs}}_{1\ensuremath{-}x}{\text{Bi}}_{x}$ becomes a Bi-derived state, as expected from their band characters. We show that this band crossing phenomenon cannot be described by the popular BAC model but can be naturally explained by a simple band broadening picture.

It is revealed from first-principles calculations that polarization-induced asymmetric distribution of oxygen vacancies plays an important role in the insulating behavior at p-type LaAlO3/SrTiO3 interface. The formation energy of the oxygen vacancy (V-O) is much smaller than that at the surface of the LaAlO3 overlayer, causing all the carriers to be compensated by the spontaneously formed V-O's at the interface. In contrast, at an n-type interface, the formation energy of V-O is much higher than that at the surface, and the V-O's formed at the surface enhance the carrier density at the interface. This explains the puzzling behavior of why the p-type interface is always insulating but the n-type interface can be conducting.

The intrinsic large electronegativity of O 2p character of the valence-band maximum (VBM) of ZnO renders it extremely difficult to be doped p type. We show from density functional calculation that such VBM characteristic can be altered by compensated donor-acceptor pairs, thus improve the p-type dopability. By incorporating (Ti+C) or (Zr+C) into ZnO simultaneously, a fully occupied impurity band that has the C 2p character is created above the VBM of host ZnO. Subsequent doping by N in ZnO: (Ti+C) and ZnO: (Zr+C) lead to the acceptor ionization energies of 0.18 and 0.13 eV, respectively, which is about 200 meV lower than it is in pure ZnO.

Using first-principles electronic structure calculations we find that the titanium vacancy and divacancy may be responsible for the unexpected ferromagnetism in undoped anatase TiO2. An isolated titanium vacancy produces a magnetic moment of 3.5 mu(B), and an isolated titanium divacancy produces a magnetic moment of 2.0 mu(B). The origin of the collective magnetic moments is the holes introduced by the titanium vacancy or divacancy in the narrow nonbonding oxygen 2p(pi) band. At the center of the divacancy, an O-2 dimer forms during the relaxation, which lowers the total energy of the system and leads to the decrease in the total magnetic moment due to a hole compensation mechanism. For both the two native defects, the ferromagnetic state is more stable than the antiferromagnetic state.

The alloy formation enthalpy and band structure of InGaN nanowires were studied by a combined approach of the valence-force field model, Monte Carlo simulation, and density-functional theory (DFT). For both random and ground-state structures of the coherent InGaN alloy, the nanowire configuration was found to be more favorable for the strain relaxation than the bulk alloy. We proposed an analytical formula for computing the band gap of any InGaN nanowires based on the results from the screened exchange hybrid DFT calculations, which in turn reveals a better band-gap tunability in ternary InGaN nanowires than the bulk alloy.

The Mg-Ga acceptor energy levels in GaN and random Al8In4Ga20N32 quaternary alloys are calculated using the first-principles band-structure method. We show that due to wave function localization, the MgGa acceptor energy level in the alloy is significantly lower than that of GaN, although the two materials have nearly identical band gaps. Our study demonstrates that forming AlxInyGa1-x-yN quaternary alloys can be a useful approach to lower acceptor ionization energy in the nitrides and thus provides an approach to overcome the p-type doping difficulty in the nitride system.

Doping difficulty in semiconductor nanocrystals has been observed and its origin is currently under debate. It is not clear whether this phenomenon is energetic or depends on the growth kinetics. Using first-principles method, we show that the transition energies and defect formation energies of the donor and acceptor defects always increase as the quantum dot sizes decrease. However, for isovalent impurities, the changes of the defect formation energies are rather small. The origin of the calculated trends is explained using simple band-energy-level models.

Using first-principles methods, we have systematically calculated the defect formation energies and transition energy levels of group-III and group-V impurities doped in H passivated Si quantum dots (QDs) as functions of the QD size. The general chemical trends found in the QDs are similar to that found in bulk Si. We show that defect formation energy and transition energy level increase when the size of the QD decreases; thus, doping in small Si QDs becomes more difficult. ${\mathrm{B}}_{\mathrm{Si}}$ has the lowest acceptor transition energy level, and it is more stable near the surface than at the center of the H passivated Si QD. On the other hand, ${\mathrm{P}}_{\mathrm{Si}}$ has the smallest donor ionization energy, and it prefers to stay at the interior of the H passivated Si QD. We explained the general chemical trends and the dependence on the QD size in terms of the atomic chemical potentials and quantum confinement effects.

p-type doping is a great challenge for the full utilization of ZnO as short-wavelength optoelectronic material. Due to a large electronegative characteristic of oxygen, the ionization energy of acceptors in ZnO is usually too high. By analyzing the defect wave-function character, we propose several approaches to lower the acceptor ionization energy by codoping acceptors with donor or isovalent atoms. Using the first-principles band-structure method, we show that the acceptor transition energies of V-Zn-O-O can be reduced by introducing F-O next to V-Zn to reduce electronic potential, whereas the acceptor transition energy of N-O-nZn(Zn) (n=1-4) can be reduced if we replace Zn by isovalent Mg or Be to reduce the anion and cation kinetic p-d repulsion, as well as the electronic potential.

The isovalent oxygen impurity levels in the II-VI semiconductors ZnSe:O, ZnTe:O, and CdTe:O are studied using a method based on first-principles total energy and large scale charge patching band structure calculations. We find that, unlike the general expectation that these levels line up in an absolute energy scale, the positions of the isovalent ${a}_{1}(\mathrm{O})$ level depend sensitively on the local environment around the impurity, thus, the ${a}_{1}(\mathrm{O})$ levels align approximately only in the common-cation systems, whereas in the common-anion systems, the levels do not align. These general chemical trends also apply to other isovalent impurity systems.

This paper presents results of ab initio accuracy thousand atom calculations of colloidal quantum dots and wires using the charge patching method. We have used density functional theory under local density approximation (LDA), and we have corrected the LDA bulk band structures by modifying the nonlocal pseudopotentials, so that their effective masses agree with experimental values. We have systematically studied the electronic states of group III-V (GaAs, InAs, InP, GaN, AlN, and InN) and group II-VI (CdSe, CdS, CdTe, ZnSe, ZnS, ZnTe, and ZnO) systems. We have also calculated the electron-hole Coulomb interactions in these systems. We report the exciton energies as functions of the quantum dot sizes and quantum wire diameters for all the above materials. We found generally good agreements between our calculated results and experimental measurements. For CdSe and InP, the currently calculated results agree well with the previously calculated results using semiempirical pseudopotentials. The ratios of band-gap-increases between quantum wires and dots are material-dependent, but a majority of them are close to 0.586, as predicted by the simple effective-mass model. Finally, the size dependence of $1{S}_{e}\text{\ensuremath{-}}1{P}_{e}$ transition energies of CdSe quantum dots agrees well with the experiment. Our results can be used as benchmarks for future experiments and calculations.

A charge patching method and an idealized surface passivation are used to calculate the single electronic states of IV-IV, III-V, II-VI semiconductor quantum dots up to a thousand atoms. This approach scales linearly and has a 1000-fold speed-up compared to direct first-principles methods with a cost of eigenenergy error of about 20 meV. The calculated quantum dot band gaps are parametrized for future references.

A comprehensive density-functional calculation for the ZnS:Te isoelectronic impurity state is presented. We deploy a charge patching method that enables us to calculate systems containing thousands of atoms. We found that the impurity state is only weakly localized, and previous calculations using 64-atom cells were severely unconverged. Our calculated impurity binding energy agrees with experimental photoluminescence excitation spectrum. We have analyzed the impurity wave function in both real space and the reciprocal space, and in terms of the host bulk valence bands. We have also calculated the Stokes shifts and Jahn-Teller effects. We found small Stokes shift compared to the experimental results, which might indicate the limitations of the current method. We also calculated the ${\mathrm{Te}}_{n}$ clusters and their impurity states. We found six (counting spin) bound states inside the band gap of ZnS for all $1l~nl~4.$ We obtained pressure coefficients for ${\mathrm{Te}}_{n},$ all close to the value of bulk ZnS. This is consistent with the fact that the impurity states of ${\mathrm{Te}}_{n}$ consist almost entirely of the bulk valence bands of ZnS. Finally, we have calculated the effects of spin-orbit coupling for the impurity state eigenenergies.

Isoelectronic impurity states are localized states induced by stoichiometric single atom substitution in bulk semiconductor. Photoluminescence spectra indicate deep impurity levels of 0.5 to 0.9eV above the top of valence band for systems like: GaN:As, GaN:P, CdS:Te, ZnS:Te. Previous calculations based on small supercells seemingly confirmed these experimental results. However, the current ab initio calculations based on thousand atom supercells indicate that the impurity levels of the above systems are actually much shallower(0.04 to 0.23 eV), and these impurity levels should be compared with photoluminescence excitation spectra, not photoluminescence spectra.