2D materials; density-functional theory; electron-phonon; Kerr angle; mobility; transition metal dichalcogenides; 2d material; Density-functional-theory; Dichalcogenides; Electron phonon; Electron phonon scattering; Kerr rotation; Mobility; Semiconducting transition; Transition metal dichalcogenides; Chemistry (all); Materials Science (all); Condensed Matter Physics; Mechanics of Materials; Mechanical Engineering; General Materials Science; General Chemistry
Abstract :
[en] The transport and optical properties of semiconducting transition metal dichalcogenides around room temperature are dictated by electron-phonon scattering mechanisms within a complex, spin-textured and multi-valley electronic landscape. The relative positions of the valleys are critical, yet they are sensitive to external parameters and very difficult to determine directly. We propose a first-principles model as a function of valley positions to calculate carrier mobility and Kerr rotation angles, and apply it to MoS2, WS2, MoSe2, and WSe2. The model brings valuable insights, as well as quantitative predictions of macroscopic properties for a wide range of carrier density. The doping-dependent mobility displays a characteristic peak, the height depending on the position of the valleys. In parallel, the Kerr rotation signal is enhanced when same spin-valleys are aligned, and quenched when opposite spin-valleys are populated. We provide guidelines to optimize and correlate these quantities with respect to experimental parameters, as well as the theoretical support for in situ characterization of the valley positions.
Research Center/Unit :
CESAM - Complex and Entangled Systems from Atoms to Materials - ULiège
Disciplines :
Physics
Author, co-author :
Sohier, Thibault ; Université de Liège - ULiège > Département de physique > Physique des solides, interfaces et nanostructures ; Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, Montpellier, France
de Melo, Pedro M M C ; nanomat/Q-mat/CESAM, Department of Physics, European Theoretical Spectroscopy Facility, Université de Liège, Liège, Belgium ; Chemistry Department, Debye Institute for Nanomaterials Science, Condensed Matter and Interfaces, European Theoretical Spectroscopy Facility, Utrecht University, Utrecht, Netherlands
Zanolli, Zeila ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures ; Chemistry Department, Debye Institute for Nanomaterials Science, Condensed Matter and Interfaces, European Theoretical Spectroscopy Facility, Utrecht University, Utrecht, Netherlands
Verstraete, Matthieu ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures
Language :
English
Title :
The impact of valley profile on the mobility and Kerr rotation of transition metal dichalcogenides
Publication date :
April 2023
Journal title :
2D Materials
eISSN :
2053-1583
Publisher :
Institute of Physics
Volume :
10
Issue :
2
Pages :
025006
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif Tier-1 supercomputer
FWB - Fédération Wallonie-Bruxelles F.R.S.-FNRS - Fonds de la Recherche Scientifique
Funding text :
T S acknowledges support from the University of Liège under the Special Funds for Research, IPD-STEMA Programme. Z Z and P M M C M acknowledge financial support by the Netherlands Sector Plan program 2019–2023 and from the research program ‘Materials for the Quantum Age’ (QuMAT, Registration Number 024.005.006), part of the Gravitation program of the Dutch Ministry of Education, Culture and Science (OCW). P M M C M and M J V acknowledge the Fonds de la Recherche Scientifique (FRS-FNRS Belgium) for PdR Grant No. T.0103.19—ALPS, and ARC Project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege. Simulation time was awarded by PRACE (Optospin Project ID 2020225411) on MareNostrum at Barcelona Supercomputing Center, by the CECI (FRS-FNRS Belgium Grant No. 2.5020.11), as well as the Zenobe Tier-1 of the Fédération Wallonie-Bruxelles (Walloon Region Grant Agreement No. 1117545). The use of supercomputer facilities is also subsidized by NWO—Exact and Natural Sciences.T S acknowledges support from the University of Liège under the Special Funds for Research, IPD-STEMA Programme. Z Z and P M M C M acknowledge financial support by the Netherlands Sector Plan program 2019-2023 and from the research program ‘Materials for the Quantum Age’ (QuMAT, Registration Number 024.005.006), part of the Gravitation program of the Dutch Ministry of Education, Culture and Science (OCW). P M M C M and M J V acknowledge the Fonds de la Recherche Scientifique (FRS-FNRS Belgium) for PdR Grant No. T.0103.19—ALPS, and ARC Project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege. Simulation time was awarded by PRACE (Optospin Project ID 2020225411) on MareNostrum at Barcelona Supercomputing Center, by the CECI (FRS-FNRS Belgium Grant No. 2.5020.11), as well as the Zenobe Tier-1 of the Fédération Wallonie-Bruxelles (Walloon Region Grant Agreement No. 1117545). The use of supercomputer facilities is also subsidized by NWO—Exact and Natural Sciences.
Manzeli S Ovchinnikov D Pasquier D Yazyev O V Kis A 2017 2D transition metal dichalcogenides Nat. Rev. Mater. 2 17033 10.1038/natrevmats.2017.33
Xu X Yao W Xiao D Heinz T F 2014 Spin and pseudospins in layered transition metal dichalcogenides Nat. Phys. 10 343 50 343-50 10.1038/nphys2942
Xiao D Liu G-B Feng W Xu X Yao W 2012 Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides Phys. Rev. Lett. 108 196802 10.1103/PhysRevLett.108.196802
Gmitra M Fabian J 2015 Graphene on transition-metal dichalcogenides: a platform for proximity spin-orbit physics and optospintronics Phys. Rev. B 92 155403 10.1103/PhysRevB.92.155403
Dey P Yang L Robert C Wang G Urbaszek B Marie X Crooker S A 2017 Gate-controlled spin-valley locking of resident carriers in WSe2 monolayers Phys. Rev. Lett. 119 137401 10.1103/PhysRevLett.119.137401
Jin C et al 2018 Imaging of pure spin-valley diffusion current in WS2-WSe2 heterostructures Science 360 893 6 893-6 10.1126/science.aao3503
Kim J et al 2017 Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures Sci. Adv. 3 e1700518 10.1126/sciadv.1700518
Wang Q H Kalantar-Zadeh K Kis A Coleman J N Strano M S 2012 Electronics and optoelectronics of two-dimensional transition metal dichalcogenides Nat. Nanotechnol. 7 699 712 699-712 10.1038/nnano.2012.193
Chu L Schmidt H Pu J Wang S Özyilmaz B Takenobu T Eda G 2015 Charge transport in ion-gated mono-, bi- and trilayer MoS2 field effect transistors Sci. Rep. 4 7293 10.1038/srep07293
Yan J Shen Z X 2019 Two Dimensional Transition Metal Dichalcogenides Arul N S Nithya V D Singapore Springer pp 331 55 pp 331-55
Braga D Gutiérrez Lezama I Berger H Morpurgo A F 2012 Quantitative determination of the band gap of WS2 with ambipolar ionic liquid-gated transistors Nano Lett. 12 5218 23 5218-23 10.1021/nl302389d
Gutiérrez-Lezama I Ubrig N Ponomarev E Morpurgo A F 2021 Ionic gate spectroscopy of 2D semiconductors Nat. Rev. Phys. 3 508 19 508-19 10.1038/s42254-021-00317-2
Velický M 2021 Electrolyte versus dielectric gating of two-dimensional materials J. Phys. Chem. C 121 21803 9 21803-9 10.1021/acs.jpcc.1c04795
Radisavljevic B Radenovic A Brivio J Giacometti V Kis A 2011 Single-layer MoS2 transistors Nat. Nanotechnol. 6 147 50 147-50 10.1038/nnano.2010.279
Radisavljevic B Kis A 2013 Mobility engineering and a metal-insulator transition in monolayer MoS2 Nat. Mater. 12 815 20 815-20 10.1038/nmat3687
Kim S et al 2012 High-mobility and low-power thin-film transistors based on multilayer MoS2 crystals Nat. Commun. 3 1011 10.1038/ncomms2018
Lembke D Kis A 2012 Breakdown of high-performance monolayer MoS2 transistors ACS Nano 6 10070 5 10070-5 10.1021/nn303772b
Ovchinnikov D Allain A Huang Y-S Dumcenco D Kis A 2014 Electrical transport properties of single-layer WS2 ACS Nano 8 8174 81 8174-81 10.1021/nn502362b
Wang Y Sohier T Watanabe K Taniguchi T Verstraete M J Tutuc E 2021 Electron mobility in monolayer WS2 encapsulated in hexagonal boron-nitride Appl. Phys. Lett. 118 102105 10.1063/5.0039766
Zhang Y Ye J Matsuhashi Y Iwasa Y 2012 Ambipolar MoS2 thin flake transistors Nano Lett. 12 1136 40 1136-40 10.1021/nl2021575
Baugher B W H Churchill H O H Yang Y Jarillo-Herrero P 2013 Intrinsic electronic transport properties of high-quality monolayer and bilayer MoS2 Nano Lett. 13 4212 6 4212-6 10.1021/nl401916s
Jo S Costanzo D Berger H Morpurgo A F 2015 Electrostatically induced superconductivity at the surface of WS2 Nano Lett. 15 1197 202 1197-202 10.1021/nl504314c
Costanzo D Jo S Berger H Morpurgo A F 2016 Gate-induced superconductivity in atomically thin MoS2 crystals Nat. Nanotechnol. 11 339 44 339-44 10.1038/nnano.2015.314
Piatti E De Fazio D Daghero D Tamalampudi S R Yoon D Ferrari A C Gonnelli R S 2018 Multi-valley superconductivity in ion-gated MoS2 layers Nano Lett. 18 4821 30 4821-30 10.1021/acs.nanolett.8b01390
Li L J O’Farrell E C T Loh K P Eda G Özyilmaz B Castro A H 2016 Controlling many-body states by the electric-field effect in a two-dimensional material Nature 529 185 9 185-9 10.1038/nature16175
Mak K F McGill K L Park J McEuen P L 2014 The valley Hall effect in MoS2 transistors Science 344 1489 92 1489-92 10.1126/science.1250140
Echeverry J P Urbaszek B Amand T Marie X Gerber I C 2016 Splitting between bright and dark excitons in transition metal dichalcogenide monolayers Phys. Rev. B 93 121107 10.1103/PhysRevB.93.121107
Robert C Amand T Cadiz F Lagarde D Courtade E Manca M Taniguchi T Watanabe K Urbaszek B Marie X 2017 Fine structure and lifetime of dark excitons in transition metal dichalcogenide monolayers Phys. Rev. B 96 155423 10.1103/PhysRevB.96.155423
Xiao D Liu G-B Feng W Xu X Yao W 2012 Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides Phys. Rev. Lett. 108 196802 10.1103/PhysRevLett.108.196802
Kormányos A Burkard G Gmitra M Fabian J Zólyomi V Drummond N D Fal’ko V 2015 K·p theory for two-dimensional transition metal dichalcogenide semiconductors 2D Mater. 2 022001 10.1088/2053-1583/2/2/022001
Yuan H et al 2016 Evolution of the valley position in bulk transition-metal chalcogenides and their monolayer limit Nano Lett. 16 4738 45 4738-45 10.1021/acs.nanolett.5b05107
Sohier T Campi D Marzari N Gibertini M 2018 Mobility of 2D materials from first principles in an accurate and automated framework Phys. Rev. Mater. 2 114010 10.1103/PhysRevMaterials.2.114010
Sohier T Ponomarev E Gibertini M Berger H Marzari N Ubrig N Morpurgo A F 2019 Enhanced electron-phonon interaction in multivalley materials Phys. Rev. X 9 031019 10.1103/PhysRevX.9.031019
Kaasbjerg K Thygesen K S Jacobsen K W 2012 Phonon-limited mobility in n-type single-layer MoS2 from first principles Phys. Rev. B 85 115317 10.1103/PhysRevB.85.115317
Kaasbjerg K Thygesen K S Jauho A-P P 2013 Acoustic phonon limited mobility in two-dimensional semiconductors: deformation potential and piezoelectric scattering in monolayer MoS2 from first principles Phys. Rev. B 87 235312 10.1103/PhysRevB.87.235312
Li X Mullen J T Jin Z Borysenko K M Buongiorno Nardelli M Kim K W 2013 Intrinsic electrical transport properties of monolayer silicene and MoS2 from first principles Phys. Rev. B 87 115418 10.1103/PhysRevB.87.115418
Jin Z Li X Mullen J T Kim K W 2014 Intrinsic transport properties of electrons and holes in monolayer transition-metal dichalcogenides Phys. Rev. B 90 045422 10.1103/PhysRevB.90.045422
Li W 2015 Electrical transport limited by electron-phonon coupling from Boltzmann transport equation: an ab initio study of Si, Al and MoS2 Phys. Rev. B 92 075405 10.1103/PhysRevB.92.075405
Brumme T Calandra M Mauri F 2015 First-principles theory of field-effect doping in transition-metal dichalcogenides: structural properties, electronic structure, Hall coefficient and electrical conductivity Phys. Rev. B 91 155436 10.1103/PhysRevB.91.155436
Gunst T Markussen T Stokbro K Brandbyge M 2016 First-principles method for electron-phonon coupling and electron mobility: applications to two-dimensional materials Phys. Rev. B 93 035414 10.1103/PhysRevB.93.035414
Gaddemane G Gopalan S Van de Put M L Fischetti M V 2021 Limitations of ab initio methods to predict the electronic-transport properties of two-dimensional semiconductors: the computational example of 2H-phase transition metal dichalcogenides J. Comput. Electron. 20 49 59 49-59 10.1007/s10825-020-01526-1
Zhang C Chen Y Johnson A Li M Y Li L J Mende P C Feenstra R M Shih C K 2015 Probing critical point energies of transition metal dichalcogenides: surprising indirect gap of single layer WSe2 Nano Lett. 15 6494 500 6494-500 10.1021/acs.nanolett.5b01968
Dendzik M Michiardi M Sanders C Bianchi M Miwa J A Grønborg S S Lauritsen J V Bruix A Hammer B Hofmann P 2015 Growth and electronic structure of epitaxial single-layer WS2 on Au(111) Phys. Rev. B 92 245442 10.1103/PhysRevB.92.245442
Henck H et al 2018 Electronic band structure of two-dimensional WS2/graphene van der Waals heterostructures Phys. Rev. B 97 155421 10.1103/PhysRevB.97.155421
Jin W et al 2013 Direct measurement of the thickness-dependent electronic band structure of MoS2 using angle-resolved photoemission spectroscopy Phys. Rev. Lett. 111 106801 10.1103/PhysRevLett.111.106801
Kastl C et al 2018 Multimodal spectromicroscopy of monolayer WS2 enabled by ultra-clean van der Waals epitaxy 2D Mater. 5 045010 10.1088/2053-1583/aad21c
Le D Barinov A Preciado E Isarraraz M Tanabe I Komesu T Troha C Bartels L Rahman T S Dowben P A 2015 Spin-orbit coupling in the band structure of monolayer WSe2 J. Phys.: Condens. Matter 27 182201 10.1088/0953-8984/27/18/182201
Miwa J A Ulstrup S Sørensen S G Dendzik M Čabo A G Bianchi M Lauritsen J V Hofmann P 2015 Electronic structure of epitaxial single-layer MoS2 Phys. Rev. Lett. 114 046802 10.1103/PhysRevLett.114.046802
Nguyen P V et al 2019 Visualizing electrostatic gating effects in two-dimensional heterostructures Nature 572 220 3 220-3 10.1038/s41586-019-1402-1
Wilson N R et al 2017 Determination of band offsets, hybridization and exciton binding in 2D semiconductor heterostructures Sci. Adv. 3 e1601832 10.1126/sciadv.1601832
Zhang Y et al 2016 Electronic structure, surface doping and optical response in epitaxial WSe2 thin films Nano Lett. 16 2485 91 2485-91 10.1021/acs.nanolett.6b00059
Zhu Z Y Cheng Y C Schwingenschlögl U 2011 Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors Phys. Rev. B 84 153402 10.1103/PhysRevB.84.153402
Piatti E Romanin D Gonnelli R S 2019 Mapping multi-valley Lifshitz transitions induced by field-effect doping in strained MoS2 nanolayers J. Phys.: Condens. Matter 31 114002 10.1088/1361-648X/aaf981
Romanin D Brumme T Daghero D Gonnelli R S Piatti E 2020 Strong band-filling-dependence of the scattering lifetime in gated MoS2 nanolayers induced by the opening of intervalley scattering channels J. Appl. Phys. 128 063907 10.1063/5.0017921
Datye I M Daus A Grady R W Brenner K Vaziri S Pop E 2022 Strain-enhanced mobility of monolayer MoS2 Nano Lett. 22 8052 9 8052-9 10.1021/acs.nanolett.2c01707
Hosseini M Elahi M Pourfath M Esseni D 2015 Strain-induced modulation of electron mobility in single-layer transition metal dichalcogenides MX2 M = Mo, W; X = S, Se) IEEE Trans. Electron Devices 62 3192 8 3192-8 10.1109/TED.2015.2461617
Molina-Sánchez A Sangalli D Wirtz L Marini A 2017 Ab initio calculations of ultrashort carrier dynamics in two-dimensional materials: valley depolarization in single-layer WSe2 Nano Lett. 17 4549 55 4549-55 10.1021/acs.nanolett.7b00175
Ersfeld M Volmer F de Melo P M M C de Winter R Heithoff M Zanolli Z Stampfer C Verstraete M J Beschoten B 2019 Spin states protected from intrinsic electron-phonon coupling reaching 100 ns lifetime at room temperature in MoSe2 Nano Lett. 19 4083 90 4083-90 10.1021/acs.nanolett.9b01485
Nayak A P et al 2015 Pressure-dependent optical and vibrational properties of monolayer molybdenum disulfide Nano Lett. 15 346 53 346-53 10.1021/nl5036397
Chen Y et al 2017 Pressurizing field-effect transistors of few-layer MoS2 in a diamond anvil cell Nano Lett. 17 194 9 194-9 10.1021/acs.nanolett.6b03785
Wang Z et al 2018 Intravalley spin-flip relaxation dynamics in single-layer WS2 Nano Lett. 18 6882 91 6882-91 10.1021/acs.nanolett.8b02774
Frey G L Tenne R Matthews M J Dresselhaus M S Dresselhaus G 1999 Raman and resonance Raman investigation of MoS2 nanoparticles Phys. Rev. B 60 2883 92 2883-92 10.1103/PhysRevB.60.2883
Chakraborty B Bera A Muthu D V S Bhowmick S Waghmare U V Sood A K 2012 Symmetry-dependent phonon renormalization in monolayer MoS2 transistor Phys. Rev. B 85 161403 10.1103/PhysRevB.85.161403
Ma N Jena D 2014 Charge scattering and mobility in atomically thin semiconductors Phys. Rev. X 4 011043 10.1103/PhysRevX.4.011043
Sohier T Gibertini M Verstraete M J 2021 Remote free-carrier screening to boost the mobility of Fröhlich-limited two-dimensional semiconductors Phys. Rev. Mater. 5 024004 10.1103/PhysRevMaterials.5.024004
Zhang C Liu Y 2022 Phonon-limited transport of two-dimensional semiconductors: quadrupole scattering and free carrier screening Phys. Rev. B 106 115423 10.1103/PhysRevB.106.115423
Cheng L Zhang C Liu Y 2020 Why two-dimensional semiconductors generally have low electron mobility Phys. Rev. Lett. 125 177701 10.1103/PhysRevLett.125.177701
Mak K F Xiao D Shan J 2018 Light-valley interactions in 2D semiconductors Nat. Photon. 12 451 60 451-60 10.1038/s41566-018-0204-6
Mecklenburg M Regan B C 2011 Spin and the honeycomb lattice: lessons from graphene Phys. Rev. Lett. 106 116803 10.1103/PhysRevLett.106.116803
Sohier T Melo P M M C Zanolli Z Verstraete M J 2022 Materials Cloud Archive 2022.178 10.24435/materialscloud:er-mz
Giannozzi P et al 2009 QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials J. Phys.: Condens. Matter 21 395502 10.1088/0953-8984/21/39/395502
Giannozzi P et al 2017 Advanced capabilities for materials modelling with Quantum ESPRESSO J. Phys.: Condens. Matter. 29 465901 10.1088/1361-648X/aa8f79
Sohier T Calandra M Mauri F 2017 Density functional perturbation theory for gated two-dimensional heterostructures: theoretical developments and application to flexural phonons in graphene Phys. Rev. B 96 075448 10.1103/PhysRevB.96.075448
Sohier T Gibertini M Marzari N 2020 Profiling novel high-conductivity 2D semiconductors 2D Mater. 8 015025 10.1088/2053-1583/abc5d0
Sohier T (available at: https://gitlab.com/tsohier/transport-public)
Novko D 2020 Broken adiabaticity induced by Lifshitz transition in MoS2 and WS2 single layers Commun. Phys. 3 30 10.1038/s42005-020-0299-1
Garcia-Goiricelaya P Lafuente-Bartolome J Gurtubay I G Eiguren A 2020 Emergence of large nonadiabatic effects induced by the electron-phonon interaction on the complex vibrational quasiparticle spectrum of doped monolayer MoS2 Phys. Rev. B 101 054304 10.1103/PhysRevB.101.054304
Sangalli D et al 2019 Many-body perturbation theory calculations using the Yambo code J. Phys.: Condens. Matter 31 325902 10.1088/1361-648x/ab15d0