First-Principles Ultrafast Exciton Dynamics and Time-Domain Spectroscopies Dark-Exciton Mediated Valley Depolarization in Monolayer WSe 2 Hsiao-Yi Chen1 2 3and Marco Bernardi1 2

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First-Principles Ultrafast Exciton Dynamics and Time-Domain Spectroscopies:

Dark-Exciton Mediated Valley Depolarization in Monolayer WSe2

Hsiao-Yi Chen1, 2, 3 and Marco Bernardi1, 2, ∗

1Department of Applied Physics and Materials Science,

California Institute of Technology, Pasadena, California 91125

2Department of Physics, California Institute of Technology, Pasadena, California 91125

3RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, 351-0198, Japan

Calculations combining ﬁrst-principles electron-phonon (e-ph) interactions with the Boltzmann

equation enable studies of ultrafast carrier and phonon dynamics. However, in materials with

weak Coulomb screening, electrons and holes form bound excitons and their scattering processes

become correlated, posing additional challenges for modeling nonequilibrium physics. Here we show

calculations of ultrafast exciton dynamics and related time-domain spectroscopies using ab initio

exciton-phonon (ex-ph) interactions together with an excitonic Boltzmann equation. Starting from

the nonequilibrium exciton populations, we develop simulations of time-domain absorption and

photoemission spectra that take into account electron-hole correlations. We use this method to study

monolayer WSe2, where our calculations predict sub-picosecond timescales for exciton relaxation

and valley depolarization and reveal the key role of intermediate dark excitons. The approach

introduced in this work enables a quantitative description of nonequilibrium dynamics and ultrafast

spectroscopies in materials with strongly bound excitons.

I. INTRODUCTION

First-principles methods based on density functional

theory (DFT) [1,2] can characterize electron-phonon

(e-ph) interactions, enabling quantitative studies of

nonequilibrium electron dynamics [3–5] and transport

properties in materials ranging from semiconductors to

organic crystals and correlated electron systems [6–10].

However, these methods focus on the independent dy-

namics of electron and hole carriers, whereas in many

semiconductors, wide-gap insulators, and nanostructured

materials, where the Coulomb interaction is weakly

screened, excited electrons and holes can form charge-

neutral bound states (excitons) which dominate optical

response and light emission [11–13].

Exciton are key to many scientiﬁc and technological

advances −exciton diﬀusive dynamics governs the eﬃ-

ciency of energy and light-emitting devices [14,15], and

excitons trapped in two-dimensional (2D) materials can

provide stable optical qubits [16]. Excitons can addition-

ally carry spin and valley quantum numbers, with poten-

tial applications to information storage and processing in

spintronic and valleytronic devices [17–19]. Atomically-

thin transition metal dichalcogenides (TMDs) have be-

come a widely used platform for experimental studies of

exciton physics due to their robust excitonic eﬀects per-

sisting up to room temperature [12,13].

Time-domain spectroscopies can probe the energy and

internal structure of excitons, and characterize their

interactions and dynamics down to the femtosecond

timescale [12,20–22]. Yet, microscopic interpretation of

these experiments is diﬃcult, especially in cases where

excitons are present. Therefore the development of theo-

retical methods to study exciton dynamics and its spec-

∗bmarco@caltech.edu

troscopic signatures remains a priority.

Although analytical and semiempirical models have

been proposed to study exciton dynamics [23–26], predic-

tive ﬁrst-principles calculations would be desirable to in-

terpret novel experiments in this rapidly evolving arena.

Much ﬁrst-principles work on excitons has focused on

improving the description of their binding energy, opti-

cal response, and radiative lifetime, typically using the

ab initio Bethe-Salpeter equation (BSE) approach [27–

32]. Combined with linear-response DFT, this frame-

work has recently enabled calculations of exciton-phonon

(ex-ph) interactions and the associated phonon-induced

exciton relaxation times and photoluminescence (PL)

linewidths [33,34]. These advances set the stage for real-

time simulations of exciton dynamics and time-domain

spectroscopies.

Here we show calculations of ultrafast exciton dynam-

ics based on exciton properties and ex-ph interactions

computed from ﬁrst principles with the BSE and vali-

dated via the PL linewidth. Our real-time simulations

employ a bosonic Boltzmann transport equation (BTE)

to evolve in time the exciton populations and character-

ize phonon-induced exciton relaxation. We apply this

method to monolayer WSe2, where we determine the ul-

trafast timescales for phonon-induced bright-to-dark ex-

citon relaxation (∼0.5 ps at 300 K) and exciton valley

depolarization (185 fs at 77 K and 65 fs at 300 K).

By comparing these results with hole carrier dynamics

in the single-particle picture, we show that dark exci-

tons can debottleneck intervalley exciton scattering and

speed it up by orders of magnitude. Using the exci-

ton populations as input, we also predict time-resolved

angle-resolved photoemission (tr-ARPES) and transient

absorption spectra including excitonic eﬀects. This work

demonstrates a quantitative framework for exciton dy-

namics and sheds light on ultrafast optical processes in

2D-TMDs.

arXiv:2210.05964v1 [cond-mat.mtrl-sci] 12 Oct 2022

II. METHODS

A. Exciton band structure

The eﬀective mass approach has been widely used to

model exciton dynamics [35,36], but now one can com-

pute the full exciton band structure from ﬁrst principles

using DFT plus the ﬁnite-momentum BSE [33,37–39].

With this approach, we compute the exciton energies

and wave functions in monolayer WSe2for exciton mo-

menta Qon a regular Brillouin zone (BZ) grid (see Ap-

pendix A). The resulting exciton band structure is shown

in Fig. 1(a), where we highlight the energy of the two de-

generate optically-active (or “bright”) excitons at Γ, also

known as A-excitons in 2D-TMDs, whose computed en-

ergy of E0=1.665 eV agrees with experiments [40]. These

two A-excitons consist, respectively, of an electron-hole

pair in the electronic K- or K0-valleys [12].

The exciton band structure has two nearly-degenerate

minima associated with a spin-singlet dark exciton at

Q and a spin-triplet dark exciton at M, with the latter

lower by 20 meV due to the lack of exchange repulsion.

In Fig. 1(b), we show the main electronic transitions that

make up the dark excitons with momenta Q= K, Q, and

M, together with the corresponding electron-hole pairs in

the electronic BZ. For these dark excitons, the hole oc-

cupies the valence band edge at the K or K0BZ corner,

and the electron occupies the conduction band minima

at K or Q.

Exciton energy (eV)

bright exciton!

(E=1.665 eV)

Μ Γ KΜQ

(a)

(b)

Μ+-

minimum !

(E=1.51 eV)

1.50

1.60

1.70

1.80

K’

Electron energy (eV)

Exciton energy (eV)

bright exciton!

(E=1.665 eV)

Μ Γ KΜQ

(a)

(b)

minimum !

(E=1.51 eV)

1.50

1.60

1.70

1.80

K’

Electron energy (eV)

exciton energy (eV)

phonon window

bright exciton!

(E=1.665 eV)

Μ Γ KΜQ

(a)

(b)

Minimum !

(E=1.510 eV)

1.50

1.60

1.70

1.80

exciton energy (eV)

phonon window

bright exciton!

(E=1.665 eV)

Μ Γ KΜQ

(a)

(b)

Minimum !

(E=1.510 eV)

1.50

1.60

1.70

1.80

exciton energy (eV)

phonon window

bright exciton!

(E=1.665 eV)

Μ Γ KΜQ

(a)

(b)

Minimum !

(E=1.510 eV)

1.50

1.60

1.70

1.80

(b)

FIG. 1. (a) Exciton energy vs. momentum dispersion in

monolayer WSe2, with minima at M and Q. The two lowest

bright excitons are the 3rd and 4th states at Γ, with energy

E0= 1.665 eV indicated with a blue dot. (b) Electronic band

structure showing the transitions that make up dark excitons

with Q= (K,Q,M) (left) and the corresponding electron-

hole pairs shown schematically in the electronic BZ (right).

B. Exciton-phonon interactions and PL linewidth

We compute the ex-ph interactions in monolayer WSe2

starting from the e-ph interactions and the BSE exci-

ton wave functions, using an approach we developed in

Ref. [33] (see Appendix B). The resulting ex-ph matrix

elements Gnmν (Q,q) describe the probability amplitude

for an exciton in state |Sn(Q)ito transition to state

|Sm(Q+q)iwhen scattered by a phonon with mode ν

and momentum q. Our e-ph, BSE, and ex-ph calcula-

tions include spin-orbit coupling by using fully relativis-

tic pseudopotentials.

We validate the accuracy of our ex-ph interactions

by computing the intrinsic PL linewidth due to ex-ph

processes and comparing it with experiments. We fo-

cus on the bright A-exciton, which can recombine ra-

diatively by emitting circularly polarized light [18], and

compute its ex-ph scattering rate to obtain the intrinsic

PL linewidth [33,42]:

ΓnQ(T) = 2π

NqX

mνq

|Gn,mν (Q,q)|2

×(Nνq+1+FmQ+q)×δ(EnQ−E0

mQ+q−~ωνq)

+(Nνq−FmQ+q)×δ(EnQ−E0

mQ+q+~ωνq),

(1)

where we set n= 3 and Q= 0 for the A-exciton, and

Nqis the number of q-points in the BZ, EmQare ex-

citon energies, and ωνqare phonon frequencies; Nνq(T)

is the thermal occupation for phonons and FmQ(T) for

excitons, both satisfying the Bose-Einstein distribution

at temperature T.

The temperature dependence of our computed PL

linewidth, shown in Fig. 2, agrees with experiments from

Ref. [41], although to match the experimental curve we

Linewidth (meV)

Temperature (K)

FIG. 2. Computed PL linewidth from ex-ph interactions in

monolayer WSe2, shown as a function of temperature and

compared with experiment [41]. The inset shows two main

ex-ph scattering processes for bright exciton relaxation, Γ to

M and Γ to K. The computed results are shifted upward by

7 meV to match experiment.

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First-PrinciplesUltrafastExcitonDynamicsandTime-DomainSpectroscopies:Dark-ExcitonMediatedValleyDepolarizationinMonolayerWSe2Hsiao-YiChen1,2,3andMarcoBernardi1,2,1DepartmentofAppliedPhysicsandMaterialsScience,CaliforniaInstituteofTechnology,Pasadena,California911252DepartmentofPhysics,CaliforniaInst...

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First-Principles Ultrafast Exciton Dynamics and Time-Domain Spectroscopies Dark-Exciton Mediated Valley Depolarization in Monolayer WSe 2 Hsiao-Yi Chen1 2 3and Marco Bernardi1 2

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