We theoretically study the contribution of quantum effects to the exciton diffusion coefficient in atomically thin crystals. It is related to the weak localization caused by the interference of excitonic wavefunctions on the trajectories with closed loops. Due to the weak inelasticity of the exciton–phonon interaction, the effect is present even if the excitons are scattered by long-wavelength acoustic phonons. We consider exciton interaction with longitudinal acoustic phonons with linear dispersion and flexural phonons with quadratic dispersion. We identify the regimes where the weak localization effect can be particularly pronounced. We also briefly address the role of free charge carriers in the exciton quantum transport and, within the self-consistent theory of localization, the weak localization effects beyond the lowest order.
References
1.
V. F.
Gantmakher
and Y. B.
Levinson
, Carrier Scattering in Metals and Semiconductors
(North-Holland Publishing Company
, Amsterdam
, 1987
).2.
Y.
Toyozawa
, Optical Processes in Solids
(Cambridge University Press
, Cambridge
, 2003
).3.
F.
Giustino
, “Electron-phonon interactions from first principles
,” Rev. Mod. Phys.
89
, 015003
(2017
).4.
A. S.
Alexandrov
and J. T.
Devreese
, Advances in Polaron Physics
(Springer
, Berlin Heidelberg
, 2010
).5.
6.
A. K.
Geim
and K. S.
Novoselov
, “The rise of graphene
,” Nat. Mater.
6
, 183
–191
(2007
).7.
K. F.
Mak
, C.
Lee
, J.
Hone
, J.
Shan
, and T. F.
Heinz
, “Atomically thin MoS2: A new direct-gap semiconductor
,” Phys. Rev. Lett.
105
, 136805
(2010
).8.
A.
Splendiani
, L.
Sun
, Y.
Zhang
, T.
Li
, J.
Kim
, C.-Y.
Chim
, G.
Galli
, and F.
Wang
, “Emerging photoluminescence in monolayer MoS2
,” Nano Lett.
10
, 1271
(2010
).9.
D.
Christiansen
, M.
Selig
, G.
Berghäuser
, R.
Schmidt
, I.
Niehues
, R.
Schneider
, A.
Arora
, S. M.
de Vasconcellos
, R.
Bratschitsch
, E.
Malic
, and A.
Knorr
, “Phonon sidebands in monolayer transition metal dichalcogenides
,” Phys. Rev. Lett.
119
, 187402
(2017
).10.
S.
Shree
, M.
Semina
, C.
Robert
, B.
Han
, T.
Amand
, A.
Balocchi
, M.
Manca
, E.
Courtade
, X.
Marie
, T.
Taniguchi
, K.
Watanabe
, M. M.
Glazov
, and B.
Urbaszek
, “Observation of exciton-phonon coupling in MoSe2 monolayers
,” Phys. Rev. B
98
, 035302
(2018
).11.
A. C.
Ferrari
, J. C.
Meyer
, V.
Scardaci
, C.
Casiraghi
, M.
Lazzeri
, F.
Mauri
, S.
Piscanec
, D.
Jiang
, K. S.
Novoselov
, S.
Roth
, and A. K.
Geim
, “Raman spectrum of graphene and graphene layers
,” Phys. Rev. Lett.
97
, 187401
(2006
).12.
S.
Pisana
, M.
Lazzeri
, C.
Casiraghi
, K.
Novoselov
, A.
Geim
, A.
Ferrari
, and F.
Mauri
, “Breakdown of the adiabatic Born–Oppenheimer approximation in graphene
,” Nat. Mater.
6
, 198
(2007
).13.
D. M.
Basko
, “Theory of resonant multiphonon Raman scattering in graphene
,” Phys. Rev. B
78
, 125418
(2008
).14.
I. A.
Eliseyev
, V. Y.
Davydov
, A. N.
Smirnov
, M. O.
Nestoklon
, P. A.
Dementev
, S. P.
Lebedev
, A. A.
Lebedev
, A. V.
Zubov
, S.
Mathew
, J.
Pezoldt
, K. A.
Bokai
, and D. Y.
Usachov
, “Optical estimation of the carrier concentration and the value of strain in monolayer graphene grown on 4H-SiC
,” Semiconductors
53
, 1904
–1909
(2019
).15.
I.
Paradisanos
, G.
Wang
, E. M.
Alexeev
, A. R.
Cadore
, X.
Marie
, A. C.
Ferrari
, M. M.
Glazov
, and B.
Urbaszek
, “Efficient phonon cascades in WSe2 monolayers
,” Nat. Commun.
12
, 538
(2021
).16.
G.
Kioseoglou
, A. T.
Hanbicki
, M.
Currie
, A. L.
Friedman
, D.
Gunlycke
, and B. T.
Jonker
, “Valley polarization and intervalley scattering in monolayer MoS2
,” Appl. Phys. Lett.
101
, 221907
(2012
).17.
Y.
Song
and H.
Dery
, “Transport theory of monolayer transition-metal dichalcogenides through symmetry
,” Phys. Rev. Lett.
111
, 026601
(2013
).18.
G.
Wang
, M. M.
Glazov
, C.
Robert
, T.
Amand
, X.
Marie
, and B.
Urbaszek
, “Double resonant Raman scattering and valley coherence generation in monolayer WSe2
,” Phys. Rev. Lett.
115
, 117401
(2015
).19.
B.
Miller
, J.
Lindlau
, M.
Bommert
, A.
Neumann
, H.
Yamaguchi
, A.
Holleitner
, A.
Högele
, and U.
Wurstbauer
, “Tuning the Fröhlich exciton-phonon scattering in monolayer MoS2
,” Nat. Commun.
10
, 807
(2019
).20.
I.
Lifshits
, “Low-temperature heat capacity of thin films and needles
,” Zh. Eksp. Teor. Fiz.
22
, 471
(1952
).21.
Statistical Mechanics of Membranes and Surfaces
, edited by D.
Nelson
, T.
Piran
, and S.
Weinberg
(World Scientific
, Singapore
, 2004
).22.
M. I.
Katsnelson
, The Physics of Graphene
(Cambridge University Press
, Cambridge
, 2020
).23.
M. I.
Katsnelson
, “Flexuron: A self-trapped state of electron in crystalline membranes
,” Phys. Rev. B
82
, 205433
(2010
).24.
M. A.
Semina
, M. M.
Glazov
, and E.
Sherman
, “Interlayer exciton–polaron in atomically thin semiconductors
,” Ann. Phys.
532
, 2000339
(2020
).25.
Z. A.
Iakovlev
, M. A.
Semina
, M. M.
Glazov
, and E. Y.
Sherman
, “Flexural deformations and collapse of bilayer two-dimensional crystals by interlayer excitons
,” Phys. Rev. B
105
, 205305
(2022
).26.
M.
Selig
, G.
Berghäuser
, A.
Raja
, P.
Nagler
, C.
Schüller
, T. F.
Heinz
, T.
Korn
, A.
Chernikov
, E.
Malic
, and A.
Knorr
, “Excitonic linewidth and coherence lifetime in monolayer transition metal dichalcogenides
,” Nat. Commun.
7
, 13279
(2016
).27.
D.
Unuchek
, A.
Ciarrocchi
, A.
Avsar
, K.
Watanabe
, T.
Taniguchi
, and A.
Kis
, “Room-temperature electrical control of exciton flux in a van der Waals heterostructure
,” Nature
560
, 340
–344
(2018
).28.
F.
Cadiz
, C.
Robert
, E.
Courtade
, M.
Manca
, L.
Martinelli
, T.
Taniguchi
, K.
Watanabe
, T.
Amand
, A. C. H.
Rowe
, D.
Paget
, B.
Urbaszek
, and X.
Marie
, “Exciton diffusion in WSe2 monolayers embedded in a van der Waals heterostructure
,” Appl. Phys. Lett.
112
, 152106
(2018
).29.
M.
Kulig
, J.
Zipfel
, P.
Nagler
, S.
Blanter
, C.
Schüller
, T.
Korn
, N.
Paradiso
, M. M.
Glazov
, and A.
Chernikov
, “Exciton diffusion and halo effects in monolayer semiconductors
,” Phys. Rev. Lett.
120
, 207401
(2018
).30.
J.
Zipfel
, M.
Kulig
, R.
Perea-Causín
, S.
Brem
, J. D.
Ziegler
, R.
Rosati
, T.
Taniguchi
, K.
Watanabe
, M. M.
Glazov
, E.
Malic
, and A.
Chernikov
, “Exciton diffusion in monolayer semiconductors with suppressed disorder
,” Phys. Rev. B
101
, 115430
(2020
).31.
J.
Wang
, Y.
Guo
, Y.
Huang
, H.
Luo
, X.
Zhou
, C.
Gu
, and B.
Liu
, “Diffusion dynamics of valley excitons by transient grating spectroscopy in monolayer WSe2
,” Appl. Phys. Lett.
115
, 131902
(2019
).32.
S. Z.
Uddin
, H.
Kim
, M.
Lorenzon
, M.
Yeh
, D.-H.
Lien
, E. S.
Barnard
, H.
Htoon
, A.
Weber-Bargioni
, and A.
Javey
, “Neutral exciton diffusion in monolayer MoS2
,” ACS Nano
14
, 13433
–13440
(2020
).33.
M. A.
Akmaev
, M. M.
Glazov
, M. V.
Kochiev
, P. V.
Vinokurov
, S. A.
Smagulova
, and V. V.
Belykh
, “Spatiotemporal dynamics of free and bound excitons in CVD-grown MoS2 monolayer
,” Appl. Phys. Lett.
119
, 113102
(2021
).34.
M. M.
Glazov
, “Quantum interference effect on exciton transport in monolayer semiconductors
,” Phys. Rev. Lett.
124
, 166802
(2020
).35.
L.
Gor'kov
, A.
Larkin
, and D.
Khmelnitskii
, “Particle conductivity in a two-dimensional random potential
,” JETP Lett.
30
, 228
(1979
); available at http://jetpletters.ru/ps/1364/article_20629.shtml.36.
E. L.
Ivchenko
, G. E.
Pikus
, B. S.
Razbirin
, and A. N.
Starukhin
, “Optical orientation and alignment of free excitons in under resonant excitation. Theory
,” JETP
45
, 1172
(1977
); available at http://jetp.ras.ru/cgi-bin/e/index/e/45/6/p1172?a=list.37.
A. A.
Golubentsev
, “Suppression of interference effects in multiple scattering of light
,” JETP
59
, 26
(1984
); available at http://www.jetp.ras.ru/cgi-bin/e/index/e/59/1/p26?a=list.38.
V. V.
Afonin
, Y. M.
Galperin
, V. L.
Gurevich
, and A.
Schmid
, “Weak localization of electrons in a classical gas
,” Phys. Rev. A
36
, 5729
–5741
(1987
).39.
M. J.
Stephen
, “Weak localization and the conductivity of nondegenerate electrons
,” Phys. Rev. B
36
, 5663
–5664
(1987
).40.
P. W.
Adams
and M. A.
Paalanen
, “Localization in a nondegenerate two-dimensional electron gas
,” Phys. Rev. Lett.
58
, 2106
–2109
(1987
).41.
A. M.
Dyakonov
and Y. V.
Kopelevich
, “Weak localization of electrons in CdS at 77 K observed by the acoustoelectronic amplification method
,” JETP Lett.
47
, 259
(1988
).42.
P.
Arseev
and A.
Dzyubenko
, “Exciton magnetotransport in two-dimensional systems: Weak-localization effects
,” JETP
87
, 200
(1998
).43.
K.
Wagner
, J.
Zipfel
, R.
Rosati
, E.
Wietek
, J. D.
Ziegler
, S.
Brem
, R.
Perea-Causín
, T.
Taniguchi
, K.
Watanabe
, M. M.
Glazov
, E.
Malic
, and A.
Chernikov
, “Nonclassical exciton diffusion in monolayer WSe2
,” Phys. Rev. Lett.
127
, 076801
(2021
).44.
F. P.
Laussy
, A. V.
Kavokin
, and I. A.
Shelykh
, “Exciton-polariton mediated superconductivity
,” Phys. Rev. Lett.
104
, 106402
(2010
).45.
O.
Cotleţ
, F.
Pientka
, R.
Schmidt
, G.
Zarand
, E.
Demler
, and A.
Imamoglu
, “Transport of neutral optical excitations using electric fields
,” Phys. Rev. X
9
, 041019
(2019
).46.
K. H. A.
Villegas
, M.
Sun
, V. M.
Kovalev
, and I. G.
Savenko
, “Unconventional Bloch-Grüneisen scattering in hybrid Bose–Fermi systems
,” Phys. Rev. Lett.
123
, 095301
(2019
).47.
K.
Wagner
, Z. A.
Iakovlev
, J. D.
Ziegler
, M.
Cuccu
, T.
Taniguchi
, K.
Watanabe
, M. M.
Glazov
, and A.
Chernikov
, “Diffusion of excitons immersed in a two-dimensional Fermi sea of free charges
,” (to be published).48.
M.
Rohlfing
and S. G.
Louie
, “Electron-hole excitations in semiconductors and insulators
,” Phys. Rev. Lett.
81
, 2312
–2315
(1998
).49.
D. Y.
Qiu
, T.
Cao
, and S. G.
Louie
, “Nonanalyticity, valley quantum phases, and lightlike exciton dispersion in monolayer transition metal dichalcogenides: Theory and first-principles calculations
,” Phys. Rev. Lett.
115
, 176801
(2015
).50.
P.
Cudazzo
, L.
Sponza
, C.
Giorgetti
, L.
Reining
, F.
Sottile
, and M.
Gatti
, “Exciton band structure in two-dimensional materials
,” Phys. Rev. Lett.
116
, 066803
(2016
).51.
G. L.
Bir
and G. E.
Pikus
, Symmetry and Strain-Induced Effects in Semiconductors
(Wiley/Halsted Press
, New York
, 1974
).52.
N. V.
Leppenen
, L. E.
Golub
, and E. L.
Ivchenko
, “Exciton oscillator strength in two-dimensional Dirac materials
,” Phys. Rev. B
102
, 155305
(2020
).53.
P.
Le Doussal
and L.
Radzihovsky
, “Anomalous elasticity, fluctuations and disorder in elastic membranes
,” Ann. Phys.
392
, 340
–410
(2018
).54.
I. V.
Gornyi
, V. Y.
Kachorovskii
, and A. D.
Mirlin
, “Anomalous Hooke's law in disordered graphene
,” 2D Mater.
4
, 011003
(2016
).55.
I. S.
Burmistrov
, I. V.
Gornyi
, V. Y.
Kachorovskii
, M. I.
Katsnelson
, and A. D.
Mirlin
, “Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
,” Phys. Rev. B
94
, 195430
(2016
).56.
M.
Katsnelson
and A.
Geim
, “Electron scattering on microscopic corrugations in graphene
,” Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci.
366
, 195
–204
(2008
).57.
A. N.
Rudenko
, A. V.
Lugovskoi
, A.
Mauri
, G.
Yu
, S.
Yuan
, and M. I.
Katsnelson
, “Interplay between in-plane and flexural phonons in electronic transport of two-dimensional semiconductors
,” Phys. Rev. B
100
, 075417
(2019
).58.
A.
Kormanyos
, G.
Burkard
, M.
Gmitra
, J.
Fabian
, V.
Zólyomi
, N. D.
Drummond
, and V.
Fal'ko
, “ theory for two-dimensional transition metal dichalcogenide semiconductors
,” 2D Mater.
2
, 022001
(2015
).59.
M. V.
Durnev
and M. M.
Glazov
, “Excitons and trions in two-dimensional semiconductors based on transition metal dichalcogenides
,” Phys. Usp.
61
, 825
–845
(2018
).60.
G.
Wang
, A.
Chernikov
, M. M.
Glazov
, T. F.
Heinz
, X.
Marie
, T.
Amand
, and B.
Urbaszek
, “Colloquium: Excitons in atomically thin transition metal dichalcogenides
,” Rev. Mod. Phys.
90
, 021001
(2018
).61.
D.
Vollhardt
and P.
Wölfle
, “Anderson localization in dimensions: A self-consistent diagrammatic theory
,” Phys. Rev. Lett.
45
, 842
–846
(1980
).62.
D.
Vollhardt
and P.
Wölfle
, “Diagrammatic, self-consistent treatment of the anderson localization problem in dimensions
,” Phys. Rev. B
22
, 4666
–4679
(1980
).63.
A. V.
Myasnikov
and M. V.
Sadovskii
, “Self-consistent theory of localization in dimension spaces
,” Sov. Phys. Solid State
24
, 2033
(1982
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.