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Binding energies and structures of two-dimensional excitonic complexes in transition metal dichalcogenides
Daniel W. Kidd, David K. Zhang. and Kálmán Varga
Physical Review B, volume 93, issue 12, page 125423 (1–10)
DOI: 10.1103/PhysRevB.93.125423
Published online on March 18, 2016.

Abstract: The stochastic variational method is applied to excitonic formations within semiconducting transition metal dichalcogenides using a correlated Gaussian basis. The energy and structure of two- to six-particle systems are investigated along with their dependence on the effective screening length of the two-dimensional Keldysh potential and the electron-hole effective mass ratio. Excited state biexcitons are shown to be bound, with binding energies of the L=0 state showing good agreement with experimental measurements of biexciton binding energies. Ground and newly discussed excited state exciton-trions are predicted to be bound and their structures are investigated.

Excited Biexcitons in Transition Metal Dichalcogenides
David K. Zhang, Daniel W. Kidd, and Kálmán Varga
Nano Letters, volume 15, issue 10, pages 7002–7005
DOI: 10.1021/acs.nanolett.5b03009
Published online on September 30, 2015.

Abstract: The Stochastic Variational Method (SVM) is used to show that the effective mass model correctly estimates the binding energies of excitons and trions but fails to predict the experimental binding energy of the biexciton. Using high-accuracy variational calculations, it is demonstrated that the biexciton binding energy in transition metal dichalcogenides is smaller than the trion binding energy, contradicting experimental findings. It is also shown that the biexciton has bound excited states and that the binding energy of the $L=0$ excited state is in very good agreement with experimental data. This excited state corresponds to a hole attached to a negative trion and may be a possible resolution of the discrepancy between theory and experiment.

Excited Biexcitons in Transition Metal Dichalcogenides (contributed conference talk)
David K. Zhang
MAR16 Meeting of the American Physical Society
Talk delivered March 15, 2016, 4:30 PM–4:42 PM
See conference program listing and published abstract.

Abstract: Recently, experimental measurements and theoretical modeling have been in a disagreement concerning the binding energy of biexctions in transition metal dichalcogenides. While theory predicts a smaller binding energy (∼20 meV) that is, as logically expected, lower than that of the trion, experiment finds values much larger (∼60 meV), actually exceeding those for the trion. In this work, we show that there exists an excited state of the biexciton which yields binding energies that match well with experimental findings and thus gives a plausible explanation for the apparent discrepancy. Furthermore, it is shown that the electron-hole correlation functions of the ground state biexciton and trion are remarkably similar, possibly explaining why a distinct signature of ground state biexcitons would not have been noticed experimentally.

A General Algorithm for the Efficient Derivation of Linear Multistep Methods (contributed conference talk)
David K. Zhang and Samuel N. Jator
AMS Southeastern Spring Sectional Meeting #1097 (UT Knoxville)
Talk delivered March 22, 2014, 3:15 p.m.
See conference program listing and published abstract.

Abstract: Traditionally, linear multistep methods (LMMs) for the numerical solution of initial value problems, such as Adams methods and backward differentiation formulas, have been derived through the use of polynomial interpolation and collocation through continuous schemes. While these methods can be implemented in modern computer algebra systems, they require the use of highly expensive operations such as symbolic matrix inversion. This imposes a severe limit on the complexity of LMMs that can be derived. In this presentation, we present a generalized algorithm for deriving LMMs based upon Taylor series expansion. By our approach, we show that the derivation of a LMM containing $k + 1$ terms is reducible to the numerical solution of a $k \times k$ linear system, allowing for the efficient derivation of methods including hundreds or thousands of terms. Furthermore, we show that this algorithm is trivially generalizable to methods including arbitrarily many off-grid points, and that it can be generalized to create LMMs for directly solving initial value problems of arbitrarily high order, with the inclusion of all intermediate derivative terms. Specific methods are stated and tested numerically on well-known problems given in the literature.