The quadruplon in a monolayer semiconductor

Jiacheng Tang; Cun-Zheng Ning; Hao Sun; Qiyao Zhang; Xingcan Dai; Zhen Wang

doi:10.1186/s43593-025-00081-1

Your Location：

Home >

Browse articles >

The quadruplon in a monolayer semiconductor

eLight Vol. 5, (2025)

Research Article | Updated：2025-12-01

- The quadruplon in a monolayer semiconductor
- Affiliations：
- Author bio：
  
  b ningcunzheng@sztu.edu.cn
- Funds：
- DOI：10.1186/s43593-025-00081-1
  CLC：
- Received：29 June 2024，
  
  Revised：2025-02-07，
  
  Accepted：09 February 2025，
  
  Published Online：26 March 2025，
  
  Published：2025-12
- Accepted：
Scan QR Code
Jiacheng Tang, Cun-Zheng Ning, Hao Sun, et al. The quadruplon in a monolayer semiconductor[J]. eLight, 2025, 5.
DOI：

Jiacheng Tang, Cun-Zheng Ning, Hao Sun, et al. The quadruplon in a monolayer semiconductor[J]. eLight, 2025, 5. DOI： 10.1186/s43593-025-00081-1.

摘要

Abstract

The ultimate goal of understanding the structure of matter has spurred a constant search for composite particles

especially high-order correlated entities for nearly all forms of matter

from elementary particles

nuclei

and cold atoms

to condensed matter. So far

composite particles involving two or three constituent particles and their weak-coupling combinations have been experimentally studied

such as the Cooper pairs

excitons

trions

and bi-excitons in condensed matter physics

or diquarks

mesons

and di-mesons in quantum chromodynamics. Although genuine four-particle correlated entities have long been theorized in various materials

alternatively known as quadruplons (Rausch and Potthoff in New J. Phys. 18

2016)

quadrons (Quang et al. in Physica B 602

2021)

or quartets (Jiang et al. in Phys. Rev. B 95

2017)

the only closely related experimental evidence is the tetraquark observation at CERN (LHCb in Nat. Phys. 18

751–754

2022). In this article

we present for the first time the experimental evidence for the existence of a four-body entity in condensed matter

the quadruplon

involving two electrons and two holes in a monolayer of Molybdenum Ditelluride. Using the optical pump–probe technique

we discovered a series of new spectral features in addition to those of excitons and trions. Furthermore

we found that all these spectral features could be reproduced theoretically using transitions between the two-body and four-body complexes based on the Bethe–Salpeter equation. Interestingly

we found that the fourth-order irreducible cluster is necessary and sufficient for the new spectral features by using the corresponding cluster expansion technique. Thus

our experimental results combined with theoretical explanation provide strong evidence for the existence of a genuine four-particle entity

the quadruplon. In contrast to a bi-exciton which consists of two weakly interacting excitons

a quadruplon involves tightly bound four-particle entity without the presence of well-defined excitons. Our results could impact the understanding of the structure of materials in a wide range of physical systems and potentially lead to new photonic applications based on quadruplons.

关键词

Keywords

references

R. Rausch , M. Potthoff , Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model . New J. Phys. 18 ,( 2016 ). http://doi.org/10.1088/1367-2630/18/2/023033 http://doi.org/10.1088/1367-2630/18/2/023033

N.H. Quang , N.Q. Huong , T.A. Dung , H.A. Tuan , N.T. Thang , Strongly confined 2D parabolic quantum dot: Biexciton or quadron? . Physica B 602 ,( 2021 ). http://doi.org/10.1016/j.physb.2020.412591 http://doi.org/10.1016/j.physb.2020.412591

Y.-F. Jiang , Z.-X. Li , S.A. Kivelson , H. Yao , Charge-4 e superconductors: a Majorana quantum Monte Carlo study . Phys. Rev. B 95 ,( 2017 ). http://doi.org/10.1103/PhysRevB.95.241103 http://doi.org/10.1103/PhysRevB.95.241103

LHCb , Observation of an exotic narrow doubly charmed tetraquark . Nat. Phys. 18 , 751 - 754 ( 2022 ). http://doi.org/10.1038/s41567-022-01614-y http://doi.org/10.1038/s41567-022-01614-y

S.A. Moskalenko , D.W. Snoke , Bose-Einstein condensation of excitons and biexcitons: and coherent nonlinear optics with excitons ( Cambridge University Press , Cambridge , 2000 ). http://doi.org/10.1017/CBO9780511721687 http://doi.org/10.1017/CBO9780511721687

M. Kira , S.W. Koch , Many-body correlations and excitonic effects in semiconductor spectroscopy . Prog. Quantum Electron. 30 , 155 - 296 ( 2006 ). http://doi.org/10.1016/j.pquantelec.2006.12.002 http://doi.org/10.1016/j.pquantelec.2006.12.002

A. Almand-Hunter et al. , Quantum droplets of electrons and holes . Nature 506 , 471 - 475 ( 2014 ). http://doi.org/10.1038/nature12994 http://doi.org/10.1038/nature12994

T.B. Arp , D. Pleskot , V. Aji , N.M. Gabor , Electron–hole liquid in a van der Waals heterostructure photocell at room temperature . Nat. Photonics 13 , 245 - 250 ( 2019 ). http://doi.org/10.1038/s41566-019-0349-y http://doi.org/10.1038/s41566-019-0349-y

E. Berg , E. Fradkin , S.A. Kivelson , Charge-4 e superconductivity from pair-density-wave order in certain high-temperature superconductors . Nat. Phys. 5 , 830 - 833 ( 2009 ). http://doi.org/10.1038/nphys1389 http://doi.org/10.1038/nphys1389

J. Londergan , A. Mitra , Masses of q2 \bar q2 states in a Bethe-Salpeter model . Few-Body Syst. 2 , 55 - 70 ( 1987 ). http://doi.org/10.1007/BF01078974 http://doi.org/10.1007/BF01078974

Z. Liu , A tetraquark trophy . Nat. Phys. 18 , 732 - 733 ( 2022 ). http://doi.org/10.1038/s41567-022-01620-0 http://doi.org/10.1038/s41567-022-01620-0

M. Ablikim et al. , Observation of a charged charmoniumlike structure in e+e−→π+π−J/ψ at s= 4.26GeV . Phys. Rev. Lett. 110 , 252001 ( 2013 ). http://doi.org/10.1103/PhysRevLett.110.252001 http://doi.org/10.1103/PhysRevLett.110.252001

Z. Liu et al. , Study of e + e − →π + π − J/ψ and observation of a charged charmoniumlike state at belle . Phys. Rev. Lett. 110 ,( 2013 ). http://doi.org/10.1103/PhysRevLett.110.252002 http://doi.org/10.1103/PhysRevLett.110.252002

K.F. Mak , C. Lee , J. Hone , J. Shan , T.F. Heinz , Atomically thin MoS 2 : a new direct-gap semiconductor . Phys. Rev. Lett. 105 ,( 2010 ). http://doi.org/10.1103/PhysRevLett.105.136805 http://doi.org/10.1103/PhysRevLett.105.136805

A. Splendiani et al. , Emerging photoluminescence in monolayer MoS 2 . Nano Lett. 10 , 1271 - 1275 ( 2010 ). http://doi.org/10.1021/nl903868w http://doi.org/10.1021/nl903868w

K.F. Mak et al. , Tightly bound trions in monolayer MoS 2 . Nat. Mater. 12 , 207 - 211 ( 2013 ). http://doi.org/10.1038/nmat3505 http://doi.org/10.1038/nmat3505

J.S. Ross et al. , Electrical control of neutral and charged excitons in a monolayer semiconductor . Nat. Commun. 4 , 1 - 6 ( 2013 ). http://doi.org/10.1038/ncomms2498 http://doi.org/10.1038/ncomms2498

Y. You et al. , Observation of biexcitons in monolayer WSe 2 . Nat. Phys. 11 , 477 - 481 ( 2015 ). http://doi.org/10.1038/nphys3324 http://doi.org/10.1038/nphys3324

J. Shang et al. , Observation of excitonic fine structure in a 2D transition-metal dichalcogenide semiconductor . ACS Nano 9 , 647 - 655 ( 2015 ). http://doi.org/10.1021/nn5059908 http://doi.org/10.1021/nn5059908

G. Plechinger et al. , Identification of excitons, trions and biexcitons in single-layer WS2 . Physica. Status. Solidi. Rapid. Res. Lett. 9 , 457 - 461 ( 2015 ). http://doi.org/10.1002/pssr.201510224 http://doi.org/10.1002/pssr.201510224

E.J. Sie , A.J. Frenzel , Y.-H. Lee , J. Kong , N. Gedik , Intervalley biexcitons and many-body effects in monolayer MoS 2 . Phys. Rev. B 92 ,( 2015 ). http://doi.org/10.1103/PhysRevB.92.125417 http://doi.org/10.1103/PhysRevB.92.125417

A. Steinhoff et al. , Biexciton fine structure in monolayer transition metal dichalcogenides . Nat. Phys. 14 , 1199 - 1204 ( 2018 ). http://doi.org/10.1038/s41567-018-0282-x http://doi.org/10.1038/s41567-018-0282-x

M. Barbone et al. , Charge-tuneable biexciton complexes in monolayer WSe 2 . Nat. Commun. 9 , 1 - 6 ( 2018 ). http://doi.org/10.1038/s41467-018-05632-4 http://doi.org/10.1038/s41467-018-05632-4

S.-Y. Chen , T. Goldstein , T. Taniguchi , K. Watanabe , J. Yan , Coulomb-bound four-and five-particle intervalley states in an atomically-thin semiconductor . Nat. Commun. 9 , 1 - 8 ( 2018 ).

Z. Li et al. , Revealing the biexciton and trion-exciton complexes in BN encapsulated WSe 2 . Nat. Commun. 9 , 1 - 7 ( 2018 ).

Z. Ye et al. , Efficient generation of neutral and charged biexcitons in encapsulated WSe 2 monolayers . Nat. Commun. 9 , 1 - 6 ( 2018 ). http://doi.org/10.1038/s41467-018-05917-8 http://doi.org/10.1038/s41467-018-05917-8

K. Hao et al. , Neutral and charged inter-valley biexcitons in monolayer MoSe 2 . Nat. Commun. 8 , 1 - 7 ( 2017 ). http://doi.org/10.1038/ncomms15552 http://doi.org/10.1038/ncomms15552

D. Xiao , G.-B. Liu , W. Feng , X. Xu , W. Yao , Coupled spin and valley physics in monolayers of MoS 2 and other group-VI dichalcogenides . Phys. Rev. Lett. 108 ,( 2012 ). http://doi.org/10.1103/PhysRevLett.108.196802 http://doi.org/10.1103/PhysRevLett.108.196802

K.F. Mak , K. He , J. Shan , T.F. Heinz , Control of valley polarization in monolayer MoS 2 by optical helicity . Nat. Nanotechnol. 7 , 494 - 498 ( 2012 ). http://doi.org/10.1038/nnano.2012.96 http://doi.org/10.1038/nnano.2012.96

Tang, J. & Ning, C.-Z. Spectral Features of the Fourth Order Irreducible Correlations in a Monolayer Semiconductor. arXiv preprint arXiv:2405.01853 http://arxiv.org/abs/2405.01853 (2024).

Z. Wang et al. , Excitonic complexes and optical gain in two-dimensional molybdenum ditelluride well below the Mott transition . Light. Sci. Appl. 9 , 1 - 10 ( 2020 ). http://doi.org/10.1038/s41377-020-0278-z http://doi.org/10.1038/s41377-020-0278-z

J. Yang et al. , Robust excitons and trions in monolayer MoTe 2 . ACS Nano 9 , 6603 - 6609 ( 2015 ). http://doi.org/10.1021/acsnano.5b02665 http://doi.org/10.1021/acsnano.5b02665

A. Arora et al. , Valley Zeeman splitting and valley polarization of neutral and charged excitons in monolayer MoTe 2 at high magnetic fields . Nano Lett. 16 , 3624 - 3629 ( 2016 ). http://doi.org/10.1021/acs.nanolett.6b00748 http://doi.org/10.1021/acs.nanolett.6b00748

Q. Zhang et al. , Prolonging valley polarization lifetime through gate-controlled exciton-to-trion conversion in monolayer molybdenum ditelluride . Nat. Commun. 13 , 1 - 9 ( 2022 ).

S. Biswas et al. , Rydberg excitons and Trions in Monolayer MoTe 2 . ACS Nano ( 2023 ). http://doi.org/10.1021/acsnano.3c00145 http://doi.org/10.1021/acsnano.3c00145

A. Kormányos et al. , Monolayer MoS 2 : trigonal warping, the Γ valley, and spin-orbit coupling effects . Phys. Rev. B 88 ,( 2013 ). http://doi.org/10.1103/PhysRevB.88.045416 http://doi.org/10.1103/PhysRevB.88.045416

M. Drüppel , T. Deilmann , P. Krüger , M. Rohlfing , Diversity of trion states and substrate effects in the optical properties of an MoS 2 monolayer . Nat. Commun. 8 , 1 - 7 ( 2017 ). http://doi.org/10.1038/s41467-017-02286-6 http://doi.org/10.1038/s41467-017-02286-6

I. Kylänpää , H.-P. Komsa , Binding energies of exciton complexes in transition metal dichalcogenide monolayers and effect of dielectric environment . Phys. Rev. B 92 ,( 2015 ). http://doi.org/10.1103/PhysRevB.92.205418 http://doi.org/10.1103/PhysRevB.92.205418

F. Katsch , M. Selig , A. Knorr , Exciton-scattering-induced dephasing in two-dimensional semiconductors . Phys. Rev. Lett. 124 ,( 2020 ). http://doi.org/10.1103/PhysRevLett.124.257402 http://doi.org/10.1103/PhysRevLett.124.257402

F. Katsch et al. , Theory of the coherent response of magneto-excitons and magneto-biexcitons in monolayer transition metal dichalcogenides . Phys. Rev. B 102 ,( 2020 ). http://doi.org/10.1103/PhysRevB.102.115420 http://doi.org/10.1103/PhysRevB.102.115420

A. Torche , G. Bester , Biexcitons fine structure and non-equilibrium effects in transition metal dichalcogenides monolayers from first principles . Commun. Phys. 4 , 1 - 8 ( 2021 ). http://doi.org/10.1038/s42005-021-00563-x http://doi.org/10.1038/s42005-021-00563-x

R. Schmidt et al. , Ultrafast coulomb-induced intervalley coupling in atomically thin WS 2 . Nano Lett. 16 , 2945 - 2950 ( 2016 ). http://doi.org/10.1021/acs.nanolett.5b04733 http://doi.org/10.1021/acs.nanolett.5b04733

Z. Li et al. , Emerging photoluminescence from the dark-exciton phonon replica in monolayer WSe 2 . Nat. Commun. 10 , 1 - 7 ( 2019 ).

E. Liu et al. , Valley-selective chiral phonon replicas of dark excitons and trions in monolayer WSe 2 . Phys. Rev. Res. 1 ,( 2019 ). http://doi.org/10.1103/PhysRevResearch.1.032007 http://doi.org/10.1103/PhysRevResearch.1.032007

Z. Li et al. , Momentum-dark intervalley exciton in monolayer tungsten diselenide brightened via chiral phonon . ACS Nano 13 , 14107 - 14113 ( 2019 ). http://doi.org/10.1021/acsnano.9b06682 http://doi.org/10.1021/acsnano.9b06682

M. He et al. , Valley phonons and exciton complexes in a monolayer semiconductor . Nat. Commun. 11 , 1 - 7 ( 2020 ).

F. Coester , Bound states of a many-particle system . Nucl. Phys. 7 , 421 - 424 ( 1958 ). http://doi.org/10.1016/0029-5582(58)90280-3 http://doi.org/10.1016/0029-5582(58)90280-3

Tang, J. & Ning, C. Z. Many-Body Configurational Spectral Splitting between Trion and Charged Exciton in a Monolayer Semiconductor. arXiv preprint arXiv:2405.01862 http://arxiv.org/abs/2405.01862 (2024).

Tang, J. et al. in 2021 Conference on Lasers and Electro-Optics (CLEO). 1–2 (IEEE). https://doi.org/10.1364/CLEO_QELS.2021.FTu4I.1 10.1364/CLEO_QELS.2021.FTu4I.1 (Being a conference paper, this CLEO paper reported our preliminary results of the on-going investigation at the time and incorrectly identified the new spectral features as BXFS.)

R.A. Suris , Optical properties of 2D systems with interacting electrons ( Springer , Cham , 2003 ).

A. Koudinov et al. , Suris tetrons: possible spectroscopic evidence for four-particle optical excitations of a two-dimensional electron gas . Phys. Rev. Lett. 112 ,( 2014 ). http://doi.org/10.1103/PhysRevLett.112.147402 http://doi.org/10.1103/PhysRevLett.112.147402

E. Liu et al. , Exciton-polaron Rydberg states in monolayer MoSe 2 and WSe 2 . Nat. Commun. 12 , 1 - 8 ( 2021 ).

Y.-C. Chang , S.-Y. Shiau , M. Combescot , Crossover from trion-hole complex to exciton-polaron in n-doped two-dimensional semiconductor quantum wells . Phys. Rev. B 98 ,( 2018 ). http://doi.org/10.1103/PhysRevB.98.235203 http://doi.org/10.1103/PhysRevB.98.235203

Z. Sun et al. , Charged bosons made of fermions in bilayer structures with strong metallic screening . Nano Lett. ( 2021 ). http://doi.org/10.1021/acs.nanolett.1c02422 http://doi.org/10.1021/acs.nanolett.1c02422

D. Van Tuan , S.-F. Shi , X. Xu , S.A. Crooker , H. Dery , Six-body and eight-body exciton states in monolayer WSe 2 . Phys. Rev. Lett. 129 ,( 2022 ). http://doi.org/10.1103/PhysRevLett.129.076801 http://doi.org/10.1103/PhysRevLett.129.076801

D.B. Turner , K.A. Nelson , Coherent measurements of high-order electronic correlations in quantum wells . Nature 466 , 1089 - 1092 ( 2010 ). http://doi.org/10.1038/nature09286 http://doi.org/10.1038/nature09286

J. von Stecher , J.P. D’Incao , C.H. Greene , Signatures of universal four-body phenomena and their relation to the Efimov effect . Nat. Phys. 5 , 417 - 421 ( 2009 ). http://doi.org/10.1038/nphys1253 http://doi.org/10.1038/nphys1253

T. Kraemer et al. , Evidence for Efimov quantum states in an ultracold gas of caesium atoms . Nature 440 , 315 - 318 ( 2006 ). http://doi.org/10.1038/nature04626 http://doi.org/10.1038/nature04626

J. Ge et al. , Charge-4 e and Charge-6 e flux quantization and higher charge superconductivity in Kagome superconductor ring devices . Phys. Rev. X 14 ,( 2024 ).

Y. Hayamizu et al. , Biexciton gain and the Mott transition in GaAs quantum wires . Phys. Rev. Lett. 99 ,( 2007 ). http://doi.org/10.1103/PhysRevLett.99.167403 http://doi.org/10.1103/PhysRevLett.99.167403

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰