- TBA

*Binding energies and structures of two-dimensional excitonic complexes in transition metal dichalcogenides*

Daniel W. Kidd, David K. Zhang. and Kálmán Varga

, volume 93, issue 12, page 125423 (1-10)*Physical Review B*

**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

, volume 15, issue 10, pages 7002-7005*Nano Letters*

**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 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 terms is reducible to the numerical solution of a
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.