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Jiajie Pei, Xue Liu, Andrés Granados del Águila, Di Bao, Sheng Liu, Mohamed-Raouf Amara, Weijie Zhao, Feng Zhang, Congya You, Yongzhe Zhang, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Han Zhang, Qihua Xiong

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[Switching of K-Q intervalley trions fine structure and their dynamics in n-doped monolayer WS<sub>2</sub>](https://mdr.nims.go.jp/datasets/13dd64d9-9513-4cad-aa65-1d53d834a1ec)

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Switching of K-Q intervalley trions fine structure and their dynamics in n-dopedmonolayer WS2Jiajie Pei, Xue Liu, Andrés Granados del Águila, Di Bao, Sheng Liu, Mohamed-Raouf Amara, Weijie Zhao,Feng Zhang, Congya You, Yongzhe Zhang, Kenji Watanabe, Takashi Taniguchi, Han Zhang and Qihua XiongCitation: Pei JJ, Liu X, del Águila AG, Bao D, Liu S et al. Switching of K-Q intervalley trions fine structure and theirdynamics in n-doped monolayer WS2. Opto-Electron Adv, 6, 220034(2023).https://doi.org/10.29026/oea.2023.220034Received: 12 February 2022; Accepted: 11 May 2022; Published online: 28 October 2022Related articlesLight-triggered interfacial charge transfer and enhanced photodetection in CdSe/ZnS quantum dots/MoS2mixed-dimensional phototransistorsZiwei Li, Wen Yang, Ming Huang, Xin Yang, Chenguang Zhu, Chenglin He, Lihui Li, Yajuan Wang, Yunfei Xie, Zhuoran Luo, Delang Liang,Jianhua Huang, Xiaoli Zhu, Xiujuan Zhuang, Dong Li, Anlian PanOpto-Electronic Advances    2021  4,  210017        doi: 10.29026/oea.2021.210017Optical properties and applications of SnS2 SAs with different thicknessMengli Liu, Hongbo Wu, Ximei Liu, Yaorong Wang, Ming Lei, Wenjun Liu, Wei Guo, Zhiyi WeiOpto-Electronic Advances    2021  4,  200029        doi: 10.29026/oea.2021.200029More related article in Opto-Electron Journals Group website  http://www.oejournal.org/oea  OE_Journal  @OptoElectronAdvhttps://www.oejournal.org/oea/https://doi.org/10.29026/oea.2023.220034https://www.oejournal.org/article/doi/10.29026/oea.2021.210017https://www.oejournal.org/article/doi/10.29026/oea.2021.210017https://doi.org/10.29026/oea.2021.210017https://www.oejournal.org/article/doi/10.29026/oea.2021.200029https://www.oejournal.org/article/doi/10.29026/oea.2021.200029https://www.oejournal.org/article/doi/10.29026/oea.2021.200029https://doi.org/10.29026/oea.2021.200029https://www.oejournal.org/article/doi/10.29026/oea.2023.220034#relative-articlehttps://www.oejournal.org/article/doi/10.29026/oea.2023.220034#relative-articlehttp://www.oejournal.org/oeaDOI: 10.29026/oea.2023.220034Switching of K-Q intervalley trions fine structureand their dynamics in n-doped monolayer WS2Jiajie Pei1,2, Xue Liu3, Andrés Granados del Águila3, Di Bao3, Sheng Liu3,Mohamed-Raouf Amara3, Weijie Zhao3, Feng Zhang1, Congya You4,Yongzhe Zhang4, Kenji Watanabe5, Takashi Taniguchi5, Han Zhang1*and Qihua Xiong6*Monolayer group VI transition metal dichalcogenides (TMDs) have recently emerged as promising candidates for photon-ic and opto-valleytronic applications. The optoelectronic properties of  these atomically-thin semiconducting crystals arestrongly governed by the tightly bound electron-hole pairs such as excitons and trions (charged excitons). The anomal-ous spin and valley configurations at the conduction band edges in monolayer WS2 give rise to even more fascinatingvalley many-body complexes. Here we find that the indirect Q valley in the first Brillouin zone of monolayer WS2 plays acritical role in the formation of a new excitonic state, which has not been well studied. By employing a high-quality h-BNencapsulated WS2 field-effect transistor, we are able to switch the electron concentration within K-Q valleys at conduc-tion band edges. Consequently, a distinct emission feature could be excited at the high electron doping region. Such fea-ture has a competing population with the K valley trion, and experiences nonlinear power-law response and lifetime dy-namics under doping. Our findings open up a new avenue for the study of valley many-body physics and quantum opticsin semiconducting 2D materials, as well as provide a promising way of valley manipulation for next-generation entangledphotonic devices.Keywords: 2D materials; WS2; charged excitons; trions; indirect Q-valley; valleytronicsPei  JJ,  Liu  X,  del  Águila  AG,  Bao  D,  Liu  S  et  al.  Switching  of  K-Q  intervalley  trions  fine  structure  and  their  dynamics  in  n-dopedmonolayer WS2. Opto-Electron Adv 6, 220034 (2023).  IntroductionTransition metal dichalcogenides (TMDs) have attractedgreat attention  as  potential  candidates  for  novel  opto-electronic  applications1,2 in  recent  years,  due  to  theirunique excitonic  properties  and  strong  many-body  ef-fects3. The tightly bound electron-hole quasiparticles (ex-citon, trion,  biexciton,  etc.)  that  originated from the ex-citonic effect are extremely crucial for the optoelectronicproperties of TMDs as well as their devices4−9. The coup-ling  of  valleys  to  excitonic  states  gives  rise  to  the 1Collaborative  Innovation  Center  for  Optoelectronic  Science  and  Technology,  International  Collaborative  Laboratory  of  2D  Materials  forOptoelectronic  Science  and  Technology  of  Ministry  of  Education  and  Guangdong  Province,  College  of  Optoelectronic  Engineering,  ShenzhenUniversity,  Shenzhen  518060,  China; 2College  of  Materials  Science  and  Engineering,  Fuzhou  University,  Fuzhou  350108,  China; 3Division  ofPhysics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore;4College  of  Materials  Science  and  Engineering,  Beijing  University  of  Technology,  Beijing  100124,  China; 5Research  Center  for  FunctionalMaterials,  International  Center  for  Materials  Nanoarchitectonics,  National  Institute  for  Materials  Science,  Tsukuba,  Ibaraki  305-0044,  Japan;6State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.*Correspondence: H Zhang, E-mail: hzhang@szu.edu.cn; QH Xiong, E-mail: qihua_xiong@tsinghua.edu.cnReceived: 12 February 2022; Accepted: 11 May 2022; Published online: 28 October 2022Opto-Electronic Advances ArticleApril 2023, Vol. 6, No. 4Open Access This article is licensed under a Creative Commons Attribution 4.0 International License.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023. Published by Institute of Optics and Electronics, Chinese Academy of Sciences.220034-1 https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034http://creativecommons.org/licenses/by/4.0/.so-called  valley  many-body  complexes10−13,  whichprovide  the  possibility  of  manipulating  the  valley  indexvia optical probes. Their unique properties provide an at-tractive  platform  for  research  in  fundamental  physics,quantum optics, valleytronics, etc14−24.For  molybdenum  compounds  (MoS2,  MoSe2), nor-mally  two  main  excitonic  species  are  observed  in  thephotoluminescence (PL) spectra, namely exciton and tri-on7,8,25,26,  owning to their aligned spin in the conductionband  minimum  (CB)  and  the  valance  band  maximum(VB).  In  contrast,  recent  studies  have  proved  that  thetungsten compounds (WS2, WSe2) have an opposite spinconfiguration in the conduction band minimum and thevalence  band  maximum27−29,  which  significantly  affectstheir excitonic  emissions,  underpinning  even  more  fas-cinating valley excitonic states in those compounds.  Forinstance,  the  brightening  of  spin-dark  exciton9,30,31,  theobservation of biexciton32−34, or even higher-order many-body complex6,35,36 have been reported. Normally the dir-ect  K  and  K’ valleys were  considered  during  the  inter-pretation  of  such  excitonic  states.  The  indirect  Q  valley(sometimes  also  referred  to  as  Λ or  Σ),  which  possessesthe same spin and very close energy level to the K valleyin the first Brillouin zone of monolayer WS237−39, has re-ceived  less  attention.  Such  valley  was  recently  found  tosignificantly influence  the  excited-state  distribution  un-der the above-gap excitation40−42.  Whereas the impact ofQ valley  on  the  formation  of  valley  many-body  com-plexes  has  not  been  well  studied  so  far.  To  unravel  theexact  nature  of  the  emissions,  it  is  crucial  to  probe  thetransition  processes  of  the  many-body  species  whilemodulating  the  carrier  densities  within  different  valleysat conduction band edges.Here we probed the indirect Q-valley charged states bytuning the Fermi energy with a high-quality h-BN encap-sulated  WS2 field-effect  transistor.  A  distinct  emissionfeature manifests  itself  as  ~20 meV lower in energy andcompeting  population  with  the  conventional  trion  ofmonolayer  WS2 was stimulated  when  the  sample  is  ex-posed  to  high  excitation  power  or  under  high  electrondoping.  We  found  that  the  actual  doping  level  of  thesample has  a  significant  impact  on  the  power-law  re-sponse of  this  emission feature.  And the carrier  lifetimeof  such  an  excitonic  state  probed  by  the  time-resolvedphotoluminescence  (TRPL)  measurement  also  shows  astrong  gate  dependence.  The  nonlinear  power  and  gateresponse  were  due  to  the  changing  Fermi  level-inducedvariation of  the  dark  exciton  population.  Our  study  re-veals the critical role of the indirect Q valley in the form-ation of valley many-body complexes, as well as providesan  efficient  way  of  manipulating  such  complexes  intransition  metal  dichalcogenides  for  future  opto-val-leytronic applications. ResultsUpon  photoexcitation  at  the  WS2 monolayer, the  elec-trons and holes are generated and then bound together atenergy degenerate valleys of the first Brillouin zone (Fig.1(a)),  giving  rise  to  various  types  of  valley  excitons  andtrions10−13.  Previous  studies  found  that  the  conductionband of monolayer WS2 has ~35 meV of spin splitting atthe K valley of the first Brillouin zone, while the spin ofconduction  band  minimum  is  opposite  to  the  valanceband  maximum27,29,37.  The  spin  configurations  of  theconduction band and valence band are illustrated in Fig.1(a) with  arrows  and  different  colors.  Such  spin-oppos-ite  valleys  at  K/K' points  of  the  conduction  band  havebeen  studied  extensively.  Recent  calculations  show  thatthe Coulomb interaction of electron-hole pairs in the in-termediate Q valley is rather strong (70~100 meV largerthan the K valley exciton) in WSe2/WS2, due to the muchlarger  effective  mass  of  the  Q  valley  compared  to  the  Kvalley27,29.  This  has  been proved recently  in  experimentswith time-resolved  XUV  micro-angle  resolved  photoe-mission  spectroscopy  for  WSe240 and  WS241,  where  themomentum-indirect  Q valley  excitons  were  found to  berather significant.XQTXQTThe  photoexcited  electrons  at  K  valley  could  bescattered  either  to  the  K' or  Q  valley  via  phonon  (Fig.1(a)) to form the so-called dark excitons27,41,42. Strong ex-citon binding energies of such excitons make them ener-getically more favorable than the K valley bright excitonin  WS2.  However,  they  are  normally  not  observable  inthe PL  spectra  due  to  the  nonzero  center-of-mass  mo-mentum.  When the  sample  is  electrically  n  doped,  boththe K' or Q valleys can be filled with electrons that inter-act  with  the  K  valley  exciton  directly  to  form  the  so-called intervalley trions,  as illustrated in Fig. 1(b).  Theseconfigurations give rise to two types of intervalley trionsXT and  in WS2. The former type has been classified asa  trion  fine  structure  previously11,13,  while  the  latter  one has not been reported before.We conducted optical spectroscopy measurement of amonolayer  WS2 sample,  configured as  a  typical  field-ef-fect  transistor,  to  unravel  the emission species  upon theback-gate  potential  modulation.  As  shown  in Fig. 1(c)Pei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-2 and 1(d),  the monolayer WS2 sample is encapsulated bytwo  pieces  of  few-layer  high-quality  h-BN  to  minimizethe influence of surface defect states on the PL spectra6,30.The WS2 sample is grounded and the back gate voltage isapplied to the degenerately doped n+ Si  substrate with a300 nm thickness SiO2 as the dielectric layer. The as-pre-pared FET displays an n-channel depletion mode behavi-or with a turn-on voltage of ~45 V (Fig. 1(e)).The PL spectrum of the sample measured at zero gatevoltage at 10 K is shown in Fig. 2(a). Six PL emission fea-tures are clearly observed:  the peak with the highest  en-ergy ~2.075 eV arising from the exciton (X0); the associ-ated  negatively  charged exciton (XT)  at  ~37  meV belowX0; three lower-energy peaks labeled as Ls which are nor-mally  attributed  to  localized  states30,34 or  related  to  thevalley  phonon  replicas  of  dark  trions43. The  fine  struc-ture  of  trion  XT could not  be  resolved  in  our  measure-XQTXQTXQTments, possibly because of peak broadening due to elec-tron  doping  or  insufficiently  low  sample  temperature.The  most  prominent  peak  ( )  located  at  ~2.025  eV  isthe focus of our current study. Fig. 2(b) shows the colorcontour plot of the PL spectra at different doping densit-ies  (corresponding  to  back-gate  voltages  from –60  V  to60 V). As the doping density of electrons is increased, theintensity of the X0 peak decreases gradually, while the in-tensity of XT peak and  peak increase slowly from –60V to 0 V. When the back gate voltage increases from 0 Vto  60  V,  the  X0 peak  disappears  and the  intensity  of  XTpeak drops rapidly.  On the contrary,  the intensity of peak  grows  dramatically  until  it  becomes  dominant  inthe spectrum at 60 V as a result of increased Fermi level.On the  other  hand,  the  increase  of  Fermi  level  will  en-large  the  magnitude  of  Stokes  shift8,  resulting  in  a  peakred-shift  of  the  trion  XT and  XTQ with  increasing Bottom BNTop BN1LWS2SiO2AuAu AuSiO2n+ SiD SVg−60 −40 −20 0 20 40 60−75−50−250255075I ds (nA)Vbg (V)1 V0.5 V0 V−0.5 V−1 VKK′K K′K′ KMΓQheσ+KChKeEFQC K′CQ K′MeKVeXTX QTX0ac d ebFig. 1 | Schematic diagram and device characterization. (a) Schematic drawing of the spin configurations for monolayer WS2 in the conduc-tion band and valence band at K and K’ point of the first Brillouin zone. The bands with two different spin configurations are schematically drawnusing two different colors (blue and red), annotated with arrows representing different spins. The symbols “e” and “h” represent electrons andholes, respectively. Scattering pathways of electrons are denoted by the orange arrows. The green wavy arrow represents the excitation photons.(b) The possible valley exciton and trions emissions from KV valley in the momentum space. Upon linear optical excitation, the landscape of ex-citons and trions with opposite spin configurations degenerates. Here, we display the valley excitons and trions for only one spin configuration.Fermi level changes are represented by orange and green dashed lines. The Coulomb interactions of exciton and trions are denoted by the filledareas  with  red,  orange,  and  green  colors.  (c)  Optical  micrograph  of  the  h-BN/1L-WS2/h-BN  sandwiched  sample.  The  scale  bar  is  5  μm.  (d)Schematic plot of the heterostructure device. (e) The drain-source current as a function of back-gate voltage for various source-drain biases. Withthis transition curve, it is found the WS2 monolayer is an n-type semiconductor. Note that the gate-dependent PL measurement in the main text ismeasured at zero source-drain bias.Pei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-3 XQTelectron  doping  (Fig. 2(b)). Figure 2(c) shows the  integ-rated  PL  intensities  of  such  emission  features,  extractedfrom detailed fitting results of all peaks as shown in Fig.S1. It is interesting to found the intensities of XT and appear  to  be  a  competitive  relationship  that  can  beswitched  by  the  gate  (Fig. 2(c)),  which  follows  theBoltzmann distribution  (will  be  calculated  later  in  Sup-plementary information Section 2).XQTXQTXQTXQTXQTThe  power-law analysis  was  normally  used  to  furthercharacterize  the  nature  of  excitonic  complexes3.However, we found that the power-law trend of  var-ies  with  the  actual  doping  of  the  sample  (Fig. 3(a, b),which could be due to the variation of exciton/trion pop-ulation induced  by  Fermi  level  changing.  The  corres-ponding  integrated  PL  intensity  for  peak as  a  func-tion of excitation power is shown in Fig. 3(c). When thesample is at –60 V back gate tuning, the power-law slopeof such a peak is α~1.42. Meanwhile, the increase of ex-citon X0 as a function of excitation power becomes sub-linear  with  a  power-law  slope  of α~0.84,  while  thepower-law  slope  for  the  trion  XT is α~1.16  (Fig.  S2).  Atransition from  excitons  to  trions  occurs  as  the  excita-tion  power  increases.  In  contrast,  when  the  sample  isheavily  n-doped  (at  60  V  back  gate  tuning),  the  power-law slope of  becomes α~0.95 (Fig. 3(c)), which meansthat  the  PL  intensity  of  such  feature  is  increasing  nearlinear with the excitation. The power-law slope of the could be tuned continuously from 1.42 to 0.95 by swap-ping the back gate voltage from –60 V to 60 V (Fig. 3(c)).Due to the variation of the power-law slope with sampledoping, it is important to note that the  feature is un-likely  to  be  a  biexciton  emission  as  previouslyreported32,44.  Actually,  it  has  been well  accepted recentlythat the binding energy of biexciton (~24 meV) is smal-ler than that of the trion36,45.The gate-dependent  power-law  responses  can  be  ex-plained  as  follows.  For  the –60  V  back  gate  tuning,  theFermi level is below the lower indirect valley. Upon low-power excitation, most of the electrons are scattered intothe lower-lying valley forming the dark excitons. Only asmall  amount  of  the  photoexcited  electrons  participatesin the photoluminescence process from the direct valley,as  illustrated  in  the  schematic  diagram  inserted  at  thebottom  of Fig. 3(c).  As  the  excitation  power  increases,the electron density in the indirect valley will continue toincrease  until  it  finally  reaches  saturation.  Most  of  theelectrons still remain in the direct valley, as illustrated inthe  right  upper  panel  of Fig. 3(c).  Thus,  the  total  PLemission  experienced  a  super-linear  increase  from  lowpower to high power. For the 60 V situation, the indirectvalley  has  already  been  filled  with  electrons  by  doping(left upper panel in Fig. 3(c)). At each power, the photo-excited electrons  will  recombine  through  the  direct  val-ley efficiently rather than scattering to other valleys. Thatexplains why the power-law slope of the PL emission wasclose to 1 under 60 V back gate voltage.XQTTime-resolved photoluminescence  (TRPL)  measure-ment  (Methods)  was  used  to  further  probe  the  carrierdynamics  of  such  excitonic  species. Figure 3(d) showsthe  normalized  TRPL  spectra  for  the  XT and  emis-sion  features.  Note  that  the  fast  X0 process is  not  dis-cussed  here  since  it  approaches  our  instrument  limit. 1.95 2.00 2.05 2.10Photon energy (eV)1L WS2PL intensity (a.u.)LsX QTX QTX QTXTXTXTX0X0X01.95 2.00 2.05 2.10−60−40−200204060Gate voltage (V)XX−25 μWPhoton energy (eV)20.0040.3581.40164.2331.3668.313482720−60 −40 −20 0 20 40 600102030405060Integrated PL intensity (a.u.)Gate voltage (V)a b cXQTXQTXQTFig. 2 | Electrical tuning of the PL spectra of excitonic species. (a) A typical PL spectrum of the monolayer WS2 at T=10 K excited by 2.33 eVlaser. The label X0 and XT represent bright exciton and trion, respectively. The labels  represents Q-valley charged state, and the rest threepeaks are labeled as Ls representing localized states. (b) Color plot of the measured PL spectra for monolayer WS2 as a function of back-gatevoltage at 25 μW excitation power. The black dashed lines are a guide to the eye showing the positions of the emission peaks. The red dashedarrow illustrates the transition trend for XX– peak intensity under doping, which should be opposite to the  feature. (c) Integrated PL intensitiesof the X0 (black circle), XT (blue circle), and  (red triangle) as a function of back-gate voltage. The solid lines are fitting results with the equa-tions in Supplementary information Section 2.Pei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-4 https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034XQTThe TRPL spectra experience a similar fast rise at the be-ginning, but the following decay processes differ signific-antly.  For  the  trion  XT,  the  decay  process  contains  twodistinct  time scales,  namely  a  fast  decay  (τ1)  with  ~85%of  the  weight  and  a  slow  decay  (τ2)  with  ~15%  of  theweight.  By  a  double  exponential  fitting,  the  values  of τ1and τ2 for  the  XT are  extracted  to  be  (20.9±2)  psand (249±8) ps, respectively. The fast decay τ1 of tens ofpicoseconds has  been  attributed  to  the  nonradiative  de-cay  lifetime  caused  by  the  carrier-carrier  scattering  orcarrier-phonon  scattering,  while  the  slow  decay τ2 ofhundreds  of  picoseconds  is  the  radiative  decay  lifetimethat is related to the interband electron-hole recombina-tion46,47. In contrast, the values of τ1 (~38.5±2 ps) and τ2(~316±5  ps)  for  the  emission  are  much  longer,  andXQTthe weight of radiative decay (~60%) is more prominent(Fig. 3(d)).  More  interestingly,  the  decay  process  of  the emission  shows  a  strong  gate  dependence  (Fig.3(e–f)), whereas the trion XT has negligible change as thegate changes (Fig. 3(f) and Fig. S3).XQTXQTOn  the  other  hand,  we  observed  similar  results  bychanging the excitation powers, as shown in Fig. S4. Theradiative  lifetime  (τ2)  of  XT does  not  show  a  noticeablechange as a function of laser power. However, the radiat-ive  lifetime  (τ2)  of  decreases  from  530  ps  to  328  ps,when we increase the laser power from 0.2 μW to 4 μW.These results indicate that the increase of laser power ex-periences  a  similar  process  of  carrier  dynamics  to  theelectron doping in monolayer WS2. The nonlinear carri-er  dynamics  of  the  feature  implies  the  transition 1.90 1.95 2.00 2.05 2.10 2.15Photon energy (eV)1.90 1.95 2.00 2.05 2.10 2.15Photon energy (eV)401 μW205 μW144 μW90 μW63 μW25 μW17 μW7.5 μW−60 V7.5 μW17 μW25 μW63 μW90 μW144 μW205 μW401 μW60 VIntegrated PL intensity (a.u.)1 10 100 10001101001000α=0.95−60 VLaser power (μW)peak60 Vα=1.420 0.2 0.4 0.6 0.8 1.00.010.11IRFTime (ns)0 Vτ1τ20 0.2 0.4 0.6 0.8 1.00.010.11Time (ns)−60 V60 V−60 −40 −20 0 20 40 600204060801002004006008001000Gate voltage (V)τ2τ1PL intensity (norm.)Normalized PL intensityNormalized PL intensityLifetime (ps)PL intensity (norm.)X QT X QTX QT X QTX QTXTXTX QTXTX0a b cd e fXQT XQTXQTXQTXQTXQTXQTFig. 3 | Influence of electrical doping on the carrier dynamics of excitonic species. (a, b) Normalized PL spectra at per μW excitation powerfor monolayer WS2 as a function of excitation power at –60 V and 60 V back gate voltages. The dashed lines are guided to the eye showing thepeak positions of X0 and . (c) Log-log plot of the integrated PL intensity for  as a function of excitation power and gate voltage from –60 V to60 V. The solid lines are power-law fittings with IPL=Pα.  The dashed line is guided to the eye showing the power-low slope of α=1. Insert illus-trates  the  electron  concentration  in  the  direct  and  indirect  valley  at  low and  high  doping  and  pumping.  (d)  Measured  time-resolved  PL  traces(dots) for the XT and  at a temperature of 10 K with pulsed laser excitation at a photon energy of 3.1 eV and power of 0.5 μW. The dashed lineIRF is the instrument response function. The solid lines are double exponential fitting using the equation I = Aexp(−t/τ1) + Bexp(−t/τ2) + C basedon the  convolution  with  respect  to  the  instrument  response.  The fast  decay lifetime τ1 for  the  XT and  were  extracted to  be 20.9±2 ps  and38.5±2 ps, respectively. The slow decay lifetime τ2 for the XT and  were extracted to be 249±8 ps and 316±5 ps, respectively. (e) Measuredtime-resolved PL traces (dots) for the  at different back-gate voltages (from –60 V to 60 V). The solid lines are corresponding double exponen-tial fitting curves. (f) The statistical values of the fast decay lifetime τ1 and slow decay lifetime τ2 for the fitting results of XT and  at differentback-gate voltages.Pei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-5 https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034XQTXQTrelationship  between  these  two  types  of  trions.  At  eachFermi level, the electrons scattering to the K'C valley arealways efficient due to their lower energy. Thus, the radi-ative lifetime (τ2) of XT trion is always short and has aninconspicuous  response  to  the  doping  (Fig. 3(f)).  Whilein terms of the  trion formation, it is suppressed at lowFermi levels but becomes more favorable when the Fermilevel  reaches  the  QC valley  as  a  result  of  the  strongerbinding strength of QC-KV electron-hole pairs27,29.  Thus,the  radiative  lifetime (τ2)  of  trion experiences  a  dra-matic  decrease  until  it  reaches  the  same  timescale  (250ps) as the XT (Fig. 3(f)) under doping.At last,  we show that the switching between such twotypes of intervalley trions could be observed as well  dueto the  thermalization  induced  K-Q  valley  energy  vari-ation (Fig. 4(a)).  As the temperature decreases from 295K, the intensity of X0 peak decreases gradually, while theintensity of XT peak increases first and then followed byXQTXQTa fast decay after 110 K. Meanwhile, the  peak starts toemerge  at  around  110  K.  For  quantitative  analysis,  thepeak energies and integrated PL intensities of such emis-sion features  are  collected  in Fig. 4(b, c),  extracted  fromdetailed fitting results  as  shown in Fig.  S5.  All  the  threepeaks experience  a  blue  shift  when  the  temperature  de-creases,  and  the  peak  energies  can  be  fit  well  (Fig. 4(b))using  a  standard  semiconductor  bandgap  dependenceequation7. The integrated PL intensities of such emissionfeatures  fit  with  the  model  provided  in  Supplementaryinformation Section 1. Noticed that the total emission ofXT and  follows  a  monotonic  increasing  trend  (Fig.4(c), violet curve) as a function of temperature. Thus, inthe calculation, we first estimated the populations of theneutral (X) and charged states (X–) using the mass actionmodel7.  Then,  the  populations  of  neutral  and  chargedstates were further split  into two substructures,  as a res-ult of the energy splitting of them. The concentration of 1.90 1.95 2.00 2.05 2.10 2.1520 K10 K30 KPhoton energy (eV)40 K60 K80 K110 K140 K295 K260 K230 K200 K170 K0 50 100 150 200 250 3001.961.982.002.022.042.062.08Peak energy (eV)Temperature (K)0 50 100 150 200 250 3000510152025Temperature (K)Intergrated PL energy (a.u.)0 50 100 150 200 250 300050100150200ΔEQK (meV)Temperature (K)ΔEQK=15+0.24 (kBT)2KQKQTΔEQKPL intensity (a.u.)X QTX QTXTXT+X QTX QTX TX0XTX0X0a bcdeXQTXQTℏ ℏXQTXQTFig. 4 | Temperature-dependent PL spectra of the monolayer WS2. (a) PL spectra at different temperatures from 295 K to 10 K. The spectraare vertically shifted for clarity. The dashed lines are a guide to the eye showing the peak positions of X0, XT and . (b) Peak energy of X0, XTand  emissions in dependence of temperature. The solid lines are fitting curves with a standard semiconductor bandgap dependence: Eg(T) =Eg(0)−S ω[coth( ω/2kBT)−1], where Eg(0) is the ground state transition energy at 0 K, S is a dimensionless coupling constant and ħω is an av-erage phonon energy. The fitting parameters for X0 are: Eg(0)=2.08 eV, S =1.807, ħω=11.91 meV; the fitting parameters for XT are: Eg(0)= 2.043eV, S = 2.038, ħω= 14.69 meV; the fitting parameters for  are: Eg(0)= 2.022 eV, S = 1.373, ħω= 13.6 meV. (c) Integrated PL intensity of X0,XT, and  emissions in dependence of temperature. The solid lines are fitting curves with the equations in Supplementary information Section 1.The violet dashed line is the sum of the red and blue solid curves. (d) Schematic drawing of the thermalization induced shrinking and expansionof lattice and related bandgap renormalization. (e) The Q-K valley energy difference at each temperature that extracted from the fit of the experi-mental results in c based on the equations in Supplementary information Section 1. The temperature-dependent ΔEQK is about twice the energyoffset value of the X0 peak, which implies that the offset between the K-Q valleys is in the opposite direction.Pei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-6 https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034energy-split  substructures  at  each  temperature  could  beestimated  with  the  Boltzmann  distribution28 (Supple-mentary  information  Section  1).  Here,  a  calibration  ofthe Q-K valley energy difference (ΔEQK) at each temper-ature  is  necessary.  According  to  the  density  functionaltheory  calculation39,  the  temperature  variation  inducedstrain can result in a band renormalization that changesthe value of ΔEQK, i.e., the bandgap expands at the K val-ley and contracts at the Q valley when the sample is sub-jected  to  compressive  strain,  as  illustrated  in Fig. 4(d).The calculated result matches well with the experimentaldata  (Fig. 4(c) & Fig.  S6)  by  adding  this  term  into  theBoltzmann distribution  equation  (Supplementary  in-formation  Section  1).  The  Q-K  valley  energy  differenceas  a  function  of  temperature  was  fit  to  be  as  ΔEQK =15+0.24(kBT)2,  and  the  temperature-dependent  curve  isshown in Fig. 4(e). Since the peak energy of exciton X0 isblue-shifted  (Fig. 4(b))  and  the  value  of  ΔEQK decreasesat  low  temperature  (Fig. 4(e)),  which  implies  that  thesample tends  to  experience  compressive  strain  as  tem-perature decreases.XQTXQTXQTThe population of XT and  as a function of the dop-ing level can be estimated by further taking into accountthe gate-dependent Fermi energy change (ΔEF) (Supple-mentary  information  Section  2).  The  Fermi  energy  as  afunction of back-gate voltage was extracted from the re-flectance  contrast  spectra48 (Fig.  S7).  In  the  calculation,the  range  of  Q-K valley  energy  difference  ΔEQK was  setas from –200 meV to 200 meV to involve the configura-tions of other TMDs materials. The calculated results areshown in Fig. S8, in which the Q-K valley energy differ-ences for the monolayer MoS2 (~60 meV), MoSe2 (~190meV),  WSe2 (~30  meV),  mono-  and  bilayer  WS2 (~20and ~–150 meV) marked with dashed lines were extrac-ted from the density functional theory calculation37. Thevariation  of  electronic  band  structure  with  electric  fieldcan be ignored here,  since the threshold for band struc-ture tuning is  about  2  V/Å (1 Å＝0.1 nm) according tothe calculation49, while the maximum value in our exper-iments  is  0.02 V/Å (60 V/300 nm).  The calculated gate-dependent  PL  transition  curves  between  XT and  areshown  in Fig.  S8, which  are  consistent  with  the  experi-mental observation (Fig. 2(c) and Fig. S9). The  emis-sion  peak  in  bilayer  WS2 dominates  the  spectra  even  at–60 V back gate voltage (Fig. S9) due to the much lowerQ valley energy level (~–150 meV). For monolayer MoS2and  MoSe2,  the  Q  valley  is  not  normally  accessible  bygate tuning because of the much higher energy level (~60and  ~190  meV).  Nevertheless,  it  is  still  possible  if  thesamples have high initial doping or compressive strain.XQTXQTFinally,  we  note  that  the  feature  differs  from  thepreviously  reported  trion-exciton  complex  (XX–)6,35,36,45.According to the previous observation, the XX– only ap-peared at the very low doping region of the sample, andthe  gate-dependent  intensity  experienced  an  oppositetrend  under  electron  doping  (as  illustrated  with  the  reddashed  arrow  in Fig. 2(b)).  In  some  literature,  a  similarfeature  has  been  observed  at  the  high  doping  region  ofmonolayer  WSe2 that  labeled  as  a  fine  structure  oftrion10,50, or its next charging state35,45, yet the interpreta-tion of its  exact nature was lacking. Recently,  it  also hasbeen suggested that  the trion feature originates  from anexciton interacting  with  short-range  intervalley  plas-mons  (for  W  compounds)51,  or  an  exciton  interactingwith a Fermi sea of excess carriers termed as exciton po-laron (for  Mo compounds)22,52. Actually,  our  interpreta-tion is compatible with both by considering the indirectQ valley. The trion /XT could be viewed as a K valleyexciton interacting  with  short-range  intervalley  plas-mons at the indirect Q/K' valley in the momentum space,or  be viewed as  an exciton polaron fine structure in thereal space. Anyhow, our observations suggest that the in-direct Q valley has a significant impact on the relaxationpathways  of  exciton  complexes  when  its  energy  level  islower  or  close  to  that  of  the  direct  K  valley,  whichprovides a new perspective for understanding the materi-al. Nevertheless, more experiments are needed in the fu-ture to fully  reveal  the role  of  Q valley.  We also remindthat  the  Q valley  at  the  first  Brillouin  zone  results  fromthe strong hybridization of p- and d-orbitals between thechalcogen  atom  X  and  the  transition  metal  atom  M37,which makes  these  valleys  highly  sensitive  to  the  envir-onmental  stimulus,  such as  the strain,  doping,  magneticfield, dielectric  field,  etc.  The strong Q-K valley interac-tion  suggests  that  such  states  are  good  candidates  fortuning  the  spin/valley  entanglement  in  these  materialsand their heterostructures. ConclusionWe  have  demonstrated  that  the  indirect  Q  valley  inmonolayer  WS2 significantly affects  the  transition  path-ways of exciton complexes at the band edges. By varyingthe back-gate, we are able to switch the electron concen-tration  within  the  K  and  Q  valleys  in  the  conductionband. As a result,  a remarkable PL emission feature loc-ated at the ~20 meV lower energy side of the conventionalPei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-7 https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034trion  could  be  excited  and  even  becomes  dominant  athigh  electron  doping.  With  increasing  Fermi  level,  thescattering of electrons to the Q valley becomes more effi-cient  facilitating  the  formation  of  such  a  charged  state.Consequently, we  are  able  to  tune  its  power-law  re-sponse from linear (α~0.95) to superlinear (α~1.42), andradiative lifetime τ2 from 880 ps to 250 ps efficiently  bygate modulation. These findings provide a new perspect-ive for  understanding  and  manipulating  the  valley  dy-namics  of  the monolayer  TMDs.  The Q-valley excitonicstates  in  two-dimensional  TMDs  are  expected  to  playcritical  roles  in  developing  next-generation  entangledphotonics and valleytronics applications. Materials and methodsSample  reparations. The  heterostructure  consisting  ofbottom h-BN, monolayer WS2, and top h-BN was fabric-ated  by  standard  PDMS  stamp  dry  transfer  technique53.Few  layer  h-BN  (10~20  nm)  and  monolayer  WS2 wereexfoliated  from the  bulk  crystals  using  scotch  tape  ontoPDMS  stamp  first.  Then  each  2D  layer  was  transferredonto 300 nm SiO2/Si substrate to form the hetero-stack-ing  region.  The  alignment  was  carefully  done  to  exposepart  of  the  WS2 for  the  contacts.  Followed  by  electronbeam  lithography  patterning,  Cr  (5  nm)/Au  (50  nm)contact  layer  was  deposited  by  thermal  evaporation.  Alift-off process in acetone was used to remove the sacrifi-cial PMMA  layer.  The  as-fabricated  sample  was  an-nealed at 120 °C for 2 hours under a high vacuum (< 10–5mTorr(1 Torr=133 Pa)).Optical  measurements. Steady-state photolumines-cence spectroscopy was conducted using a spectrometer(Horiba HR-Evolution)  equipped with a  liquid nitrogencooled  charge-coupled  device  (CCD).  A  532  nm  solidstate  laser  was  used  as  excitation  source,  whose  powerwas changed from a few micro-watts to above 400 μW bya continuous  neutral  density  filter.  The numerical  aper-ture  of  the  objective  used  in  our  experiment  is NA=0.5.For  time-resolved  photoluminescence  spectroscopymeasurements,  A  Ti:sapphire  femtosecond-pulsed  laser(400 nm, frequency-doubled) with 100 fs pulse durationand 80 MHz repetition rate was used for excitation. 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Pei acknowledgesthe  National  Natural  Science  Foundation  of  China  (Grant  No.  61905156),the China Postdoctoral Science Foundation (Grant No. 2017M622764), andthe Natural Science Foundation of Fujian Province (Grant No. 2022J01555).Y.  Z.  Zhang  acknowledges  the  National  Natural  Science  Foundation  ofPei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-9 https://doi.org/10.1038/natrevmats.2016.55https://doi.org/10.1038/nphys2942https://doi.org/10.1364/OE.22.007249https://doi.org/10.1038/nphys3949https://doi.org/10.1103/PhysRevLett.118.237404https://doi.org/10.29026/oea.2021.200029https://doi.org/10.29026/oea.2021.200029https://doi.org/10.1021/acsnano.7b03909https://doi.org/10.1002/smll.201501949https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1103/PhysRevLett.115.257403https://doi.org/10.1038/ncomms13279https://doi.org/10.1103/PhysRevLett.119.047401https://doi.org/10.1038/s41565-017-0003-0https://doi.org/10.1038/nphys3324https://doi.org/10.1038/nphys3324https://doi.org/10.1021/nn5059908https://doi.org/10.1103/PhysRevLett.121.057402https://doi.org/10.1038/s41467-018-05632-4https://doi.org/10.1038/s41467-018-05863-5https://doi.org/10.1002/andp.201400128https://doi.org/10.1103/PhysRevResearch.3.043198https://doi.org/10.1021/acs.nanolett.8b04786https://doi.org/10.1126/science.aba1029https://doi.org/10.1021/acs.nanolett.1c01839https://doi.org/10.1088/2053-1583/ab817ahttps://doi.org/10.1038/s41467-020-14472-0https://doi.org/10.1002/pssr.201510224https://doi.org/10.1038/s41467-019-09781-yhttps://doi.org/10.1021/nn303973rhttps://doi.org/10.1039/C8TC06343Ehttps://doi.org/10.1039/C8TC06343Ehttps://doi.org/10.1103/PhysRevLett.115.126802https://doi.org/10.1039/C4CP00966Ehttps://doi.org/10.1021/acs.nanolett.9b02132https://doi.org/10.1103/PhysRevB.99.085301https://doi.org/10.1103/PhysRevLett.124.187602https://doi.org/10.1088/2053-1583/1/1/011002https://doi.org/10.1038/natrevmats.2016.55https://doi.org/10.1038/nphys2942https://doi.org/10.1364/OE.22.007249https://doi.org/10.1038/nphys3949https://doi.org/10.1103/PhysRevLett.118.237404https://doi.org/10.29026/oea.2021.200029https://doi.org/10.29026/oea.2021.200029https://doi.org/10.1021/acsnano.7b03909https://doi.org/10.1002/smll.201501949https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1103/PhysRevLett.115.257403https://doi.org/10.1038/ncomms13279https://doi.org/10.1103/PhysRevLett.119.047401https://doi.org/10.1038/s41565-017-0003-0https://doi.org/10.1038/nphys3324https://doi.org/10.1038/nphys3324https://doi.org/10.1021/nn5059908https://doi.org/10.1103/PhysRevLett.121.057402https://doi.org/10.1038/s41467-018-05632-4https://doi.org/10.1038/s41467-018-05863-5https://doi.org/10.1002/andp.201400128https://doi.org/10.1103/PhysRevResearch.3.043198https://doi.org/10.1021/acs.nanolett.8b04786https://doi.org/10.1126/science.aba1029https://doi.org/10.1021/acs.nanolett.1c01839https://doi.org/10.1088/2053-1583/ab817ahttps://doi.org/10.1038/s41467-020-14472-0https://doi.org/10.1002/pssr.201510224https://doi.org/10.1038/s41467-019-09781-yhttps://doi.org/10.1021/nn303973rhttps://doi.org/10.1039/C8TC06343Ehttps://doi.org/10.1039/C8TC06343Ehttps://doi.org/10.1103/PhysRevLett.115.126802https://doi.org/10.1039/C4CP00966Ehttps://doi.org/10.1021/acs.nanolett.9b02132https://doi.org/10.1103/PhysRevB.99.085301https://doi.org/10.1103/PhysRevLett.124.187602https://doi.org/10.1088/2053-1583/1/1/011002China (Grant No. 61575010), the Beijing Municipal Natural Science Found-ation (Grant No. 4162016). A. G. del Águila gratefully acknowledges the fin-ancial  support  of  the  Presidential  Postdoctoral  Fellowship  program  of  theNanyang Technological University. K. Watanabe and T. Taniguchi acknow-ledge  support  from  the  Elemental  Strategy  Initiative  conducted  by  theMEXT, Japan and the CREST (JPMJCR15F3), JST.Author contributionsJ. J. Pei, H. Zhang and Q. H. Xiong conceived the idea. J. J. Pei, X. Liu and A.G.  del  Águila  designed the experiments.  J.  J.  Pei  prepared the samples  andperformed  the  experiments.  D.  Bao,  S.  Liu  helped  with  the  set  up  for  lowtemperature measurement.  M.  R.  AMARA  helped  with  the  set  up  for  life-time measurement. C. Y. You and X. Liu helped with the device fabrication.K. Watanabe and T. Taniguchi provided the h-BN crystals. J. J. Pei, X. Liu,D. Bao, A. G. del Águila and Q. H. Xiong analyzed the data. F. Zhang, W. J.Zhao, Y. Z. Zhang and H. Zhang helped with the theoretical analysis. J. J. Peiwrote  the  manuscript  with  input  from  all  authors.  H.  Zhang  and  Q.  H.Xiong supervised the whole project.Competing interestsThe authors declare no competing financial interests.Supplementary informationSupplementary information for this paper is available athttps://doi.org/10.29026/oea.2023.220034Pei JJ et al. Opto-Electron Adv  6, 220034 (2023) https://doi.org/10.29026/oea.2023.220034220034-10 https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034https://doi.org/10.29026/oea.2023.220034 Introduction Results Conclusion Materials and methods References