Calculation of Band Structure Using Local Sampling and Green's Functions

Complex band structure and plasmon lattice Green's function of a periodic metal-nanoparticle chain

When the surface plasmon resonance in a metal-nanoparticle chain is excited at one point, the response signal will generally decay down the chain due to absorption and radiation losses. The decay length is a key parameter in such plasmonic systems. By studying the plasmon lattice Green's function, we found that the decay length is generally governed by two exponential decay constants with phase factors corresponding to guided Bloch modes and one power-law decay with a phase factor corresponding to that of free space photons. The results show a high level of similarity between the absorptive an…

Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times

We extend the recently developed Quantum Quasi-Monte Carlo (QQMC) approach to obtain the full frequency dependence of Green functions in a single calculation. QQMC is a general approach for calculating high-order perturbative expansions in power of the electron-electron interaction strength. In contrast to conventional Markov chain Monte Carlo sampling, QQMC uses low-discrepancy sequences for a more uniform sampling of the multi-dimensional integrals involved and can potentially outperform Monte Carlo by several orders of magnitudes. A core concept of QQMC is the a priori construction of a "mo…

Interseries dipole transitions from yellow to green excitons in cuprous oxide

We study dipole interseries transitions between the yellow and green exciton series in cuprous oxide including the complex valence band structure. To this end, we extend previous studies of the spectrum of complex green exciton resonances [Phys. Rev. B 101, 075208 (2020)] to optical transitions between different exciton states in addition to transitions from the crystal ground state. This allows us to augment the calculations on interseries transitions using a hydrogen-like model [Phys. Rev. B 100, 085201 (2019)] by a more comprehensive treatment of the valence band structure.

The two-bands model of the magnetic tunnel junctions in the Fe/Cr/MgO/Fe structure

In this paper we present theoretical studies of spin dependent transport in Fe/Cr/MgO/Fe tunnel junctions with non-collinear alignment of magnetizations of metallic layers comprising these MTJs. Calculations are performed with use of non-equilibrium Green function technique in the framework of Keldysh formalism. WKB approximation is used for wave and Green functions in the trapezoidal barrier region under applied voltage. Electronic structure of ferromagnetic electrodes is modeled with two bands model, i.e. with majority s-electrons and minority d-holes. Furthermore, we introduce s-d hybridiza…

Simple electron-electron scattering in non-equilibrium Green's function simulations

In this work we include electron-electron interaction beyond Hartree-Fock level in our non-equilibrium Green's function approach by a crude form of GW through the Single Plasmon Pole Approximation. This is achieved by treating all conduction band electrons as a single effective band screening the Coulomb potential. We describe the corresponding self-energies in this scheme for a multi-subband system. In order to apply the formalism to heterostructures we discuss the screening and plasmon dispersion in both 2D and 3D systems. Results are shown for a four well quantum cascade laser with differen…

Green$'$s function approach to edge states in transition metal dichalcogenides

The semiconducting two-dimensional transition metal dichalcogenides MX$_{2}$ show an abundance of one-dimensional metallic edges and grain boundaries. Standard techniques for calculating edge states typically model nanoribbons, and require the use of supercells. In this paper we formulate a Green$'$s function technique for calculating edge states of (semi-)infinite two-dimensional systems with a single well-defined edge or grain boundary. We express Green$'$s functions in terms of Bloch matrices, constructed from the solutions of a quadratic eigenvalue equation. The technique can be applied to…

Impurity states on the honeycomb lattice using the Green's function method

Using the Green's function method, we study the effect of an impurity potential on the electronic structure of the honeycomb lattice in the one-band tight-binding model that contains both the nearest neighbor ($t$) and the second neighbor ($t'$) interactions. The model is relevant to the case of the substitutional vacancy in graphene. If the second neighbor interaction is large enough ($t' > t /3$), then the linear Dirac bands no longer occur at the Fermi energy and the electronic structure is therefore fundamentally changed. With only the nearest neighbor interactions present, there is partic…

RKKY Interaction in Graphene from Lattice Green's Function

We study the exchange interaction $J$ between two magnetic impurities in graphene (the RKKY interaction) by directly computing the lattice Green's function for the tight-binding band structure for the honeycomb lattice. The method allows us to compute $J$ numerically for much larger distances than can be handled by finite-lattice calculations as well as for small distances. % avoids the use of a cutoff function often invoked in the literature to curtail the diverging contributions from the linear bands and yields results that are valid for all distances. In addition, we rederive the analytical…

Simple formulas of directional amplification from non-Bloch band theory

Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to …

多能带非厄米系统的格林函数

Green's functions of multiband non-Hermitian systems

本文通过在黎曼面上考察多能带广义布里渊区，推导出多能带非厄米系统的开边界格林函数公式，可用于描述多能带系统中的定向放大现象。

Localization properties of Chern insulators

We study the localization properties of the equal-time electron Green's function in a Chern insulator in an arbitrary dimension and with an arbitrary number of bands. We prove that the Green's function cannot decay super-exponentially if the Hamiltonian is finite-range and the quantum Hall response is nonzero. For a general band Hamiltonian (possibly infinite-range), we prove that the Green's function cannot be finite-range if the quantum Hall response is nonzero. The proofs use methods of algebraic geometry.

Quantum confinement and edge effects on electronic properties of zigzag green phosphorene nanoribbons

First principles density-functional theory calculations were performed to investigate quantum confinement and edge effects on the electronic properties of zigzag green phosphorene nanoribbons (ZGPNRs) with edge chemical species including H, OH, F, Cl, O, and S for the ribbons width in the range of 0.5 \~{} 3.7 nm. The ZGPNRs were obtained from the relaxed two-dimensional (2D) green phosphorene monolayer with different cutting strategies and the most energetically favorable ribbon configuration was selected for further exploration of the size and edge effects. It was found that the electronic p…