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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
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