Symmetry-based calculation of single-particle states and intraband absorption in hexagonal GaN/AlN quantum dot superlattices
19
Citation
40
Reference
10
Related Paper
Citation Trend
Abstract:
We present a symmetry-based method for the efficient calculation of energy levels in hexagonal GaN/AlN quantum dots within the framework of a k·p model. The envelope functions are expanded into a plane wave basis on a hexagonal lattice and the group projector method is used to adapt the basis to exploit the symmetry, resulting in block diagonalization of the corresponding Hamiltonian matrix into six matrices and classification of the states by the quantum number of total quasi-angular momentum. The method is applied to the calculation of the electron and hole single-particle states in a quantum dot superlattice. The selection rules for absorption of electromagnetic waves in the dipole approximation are established and the intraband optical absorption matrix elements are found. Good agreement with the available experimental data on intraband optical absorption is found.Keywords:
Hamiltonian (control theory)
A quantum optics model of the asymmetric case of the interaction between two two-level atoms and quantum field, which obeys SU(1,1) Lie group, is proposed. The atom-atom interaction and the rotating wave approximation are suggested in the Hamiltonian operator. Our aim is to obtain the time-dependent wave function of asymmetric case analytically. The analytical method is based on the eigenvalues and corresponding eigenvectors of the coefficient matrix of the interaction Hamiltonian operator. The SU(1,1) quantum system is initially in the Perelomov coherent state. Therefore, the atomic inversion is obtained and discussed for different values of model parameters such as initial atomic angles, Perelomov coherent, the Bargmann index and the detuning parameters. Observe that the quantum optics model is sensitive to the variation in both the Perelomov coherent parameter and the Bargmann index. In addition, there are nonclassical properties of the proposed quantum model in the presence the detuning parameter changes.
Hamiltonian (control theory)
Operator (biology)
Cite
Citations (5)
Bohr model
Hamiltonian (control theory)
Operator (biology)
Cite
Citations (13)
Hamiltonian (control theory)
Wannier function
Cite
Citations (10)
The possibility of flat-band ferromagnetism in quantum dot arrays is theoretically discussed. By using a quantum dot as a building block, quantum dot superlattices are possible. We consider dot arrays on Lieb and kagom\'e lattices known to exhibit flat-band ferromagnetism. By performing an exact diagonalization of the Hubbard Hamiltonian, we calculate the energy difference between the ferromagnetic ground state and the paramagnetic excited state, and discuss the stability of the ferromagnetism against the second-nearest-neighbor transfer. We calculate the dot-size dependence of the energy difference in a dot model and estimate the transition temperature of the ferromagnetic--paramagnetic transition, which is found to be accessible within the present fabrication technology. We point out advantages of semiconductor ferromagnets and suggest other interesting possibilities of electronic properties in quantum dot superlattices.
Hamiltonian (control theory)
Cite
Citations (70)
Hamiltonian (control theory)
Eigenfunction
Bond dipole moment
Cite
Citations (57)
Hamiltonian (control theory)
Antisymmetric relation
Third order
Cite
Citations (2)
We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and the Zeeman lattice have incommensurate periods. Using the best rational approximations to such a quasiperiodic Hamiltonian, the problem is reduced to a description of spinor states in a superlattice. In the absence of constant Zeeman splitting, the system acquires an additional symmetry, which hinders the localization. However, if the lattices are deep enough, then localized states can appear even for Zeeman field with a zero or small mean value. Spatial distribution of localized modes is nearly uniform and is directly related to the topological properties of the effective superlattice: center-of-mass coordinates of modes are determined by Zak phases computed from the superlattice band structure. The best rational approximations feature the ``memory'' effect: Each rational approximation holds the information about the energies and spatial distribution of the modes obtained under preceding, less accurate approximations. Dispersion of low-energy initial wave packets is characterized by the law $\ensuremath{\propto}{t}^{\ensuremath{\beta}}$, with $\ensuremath{\beta}$ varying between $1/2$ at the initial stage and 1 at longer, but still finite-time, evolution. The dynamics of initial wave packets, exciting mainly localized modes, manifests quantum revivals.
Hamiltonian (control theory)
Dispersion relation
Cite
Citations (11)
Hamiltonian (control theory)
Nitrous oxide
Line (geometry)
Cite
Citations (9)
Current neural networks for predictions of molecular properties use quantum chemistry only as a source of training data. This paper explores models that use quantum chemistry as an integral part of the prediction process. This is done by implementing self-consistent-charge Density-Functional-Tight-Binding (DFTB) theory as a layer for use in deep learning models. The DFTB layer takes, as input, Hamiltonian matrix elements generated from earlier layers and produces, as output, electronic properties from self-consistent field solutions of the corresponding DFTB Hamiltonian. Backpropagation enables efficient training of the model to target electronic properties. Two types of input to the DFTB layer are explored, splines and feed-forward neural networks. Because overfitting can cause models trained on smaller molecules to perform poorly on larger molecules, regularizations are applied that penalize nonmonotonic behavior and deviation of the Hamiltonian matrix elements from those of the published DFTB model used to initialize the model. The approach is evaluated on 15 700 hydrocarbons by comparing the root-mean-square error in energy and dipole moment, on test molecules with eight heavy atoms, to the error from the initial DFTB model. When trained on molecules with up to seven heavy atoms, the spline model reduces the test error in energy by 60% and in dipole moments by 42%. The neural network model performs somewhat better, with error reductions of 67% and 59%, respectively. Training on molecules with up to four heavy atoms reduces performance, with both the spline and neural net models reducing the test error in energy by about 53% and in dipole by about 25%.
Overfitting
Hamiltonian (control theory)
Tight binding
Backpropagation
Cite
Citations (107)