Dmitry Smirnov National High Magnetic Field Laboratory, Tallahassee, - PowerPoint PPT Presentation

Magneto-spectroscopy of excitons in monolayer transition metal dichalcogenides Valley splitting and polarization by magnetic field in monolayer MoSe 2 10 5 2.33 eV Field (T) σ + ! σ - ! 0 -5 -10 1.60 1.62 1.64 1.66 1.68 Energy (eV) Dmitry Smirnov National High Magnetic Field Laboratory, Tallahassee, FL

Magneto-spectroscopy of excitons in monolayer transition metal dichalcogenides Valley splitting and polarization by magnetic field in monolayer MoSe 2 Li, Y., Ludwig, J. et al. Phys. Rev. Lett. 113 , 266804 (2014). Columbia University, New York NY (USA) NHMFL Yilei Li Jonathan Ludwig Arend van der Zande Albert Rigosi Tony Low Zhengguang Lu Heather Hill Alexey Chernikov Zhiqiang Li Suk Hyun Kim Xu Cui Dmitry Smirnov James Hone Ghidewon Arefe Tony Heinz Young Duck Kim DMR-1122594 DE-SC0001085 DMR-1124894 DE-FG02-07ER46451 DMR-1106225 NHMFL UCGP No. 5087

Semiconducting monolayer TMDs MX 2 From ¡indirect ¡gap ¡(bulk) ¡to ¡direct ¡bandgap ¡in ¡monolayer ¡ Se (S, Te) Mo (W) Se (S, Te) Z Z X Bulk ¡MoS 2 ¡: ¡indirect-­‑gap

Semiconducting monolayer TMDs MX 2 From ¡indirect ¡gap ¡(bulk) ¡to ¡direct ¡bandgap ¡in ¡monolayer ¡ Se (S, Te) Mo (W) Ross et al. Nature Comm., 4:1474 (2013) Se (S, Te) Z Z X Bulk ¡MoS 2 ¡: ¡1.3 ¡eV ¡indirect-­‑gap

Semiconducting monolayer TMDs MX 2 Se (S, Te) Mo (W) Se (S, Te) m=0 Z m=2 Z X

Semiconducting monolayer TMDs MX 2 Se (S, Te) Mo (W) Spin-­‑valley ¡coupling ¡ Se (S, Te) Z Z X

Valley-spin coupling Circular Polarized PL at Resonance Excitation Strong polarization selectivity, preservation of circular state Creation of transient valley population imbalance Mak, K. F., He, K., Shan, J., & Heinz, T. F. Nature Nanotechn, 7, 494 (2012) Also experiments by X. Cui, J. Feng, B. Urbaszek groups

Valley-spin coupling Circular Polarized PL at Resonance Excitation Strong polarization selectivity, preservation of circular state Creation of transient valley population imbalance Open questions (motivation): • How to break the valley degeneracy and control the valley splitting? • How to create and control the steady-state valley polarization Answer (method): • Apply magnetic field and break the time reversal symmetry

Experimental details CCD Spectrometer 532 nm laser Excitation fiber Collection fiber 2.33 eV σ + ! σ - ! Sample plate Piezo -stages V G B ~ 2-3 mm travel SiO 2 /Si substrate

Gate control of neutral and charged excitons in a monolayer MoSe 2 Temperature dependence Gate voltage dependence x - T=10K 240K x - T= 10 K Sample 1114 200K +30 140K 80K 60K x 0 0 40K 3K x 0 1K x 0 x - -30 380mK 1.60 1.62 1.64 1.66 1.68 1.56 1.60 1.64 1.68 Energy (eV) Energy (eV) First shown by T.Heinz’ (MoSe 2 ) and Mak et al. Nature Mat., 12 , 207 (2013) X.Xu’s (MoSe 2 ) groups Ross et al. Nature Comm., 4:1474 (2013)

Zero-field PL vs gate voltage x - ~ 30 meV x 0 T= 10 K - 0 X X +15 10 5 Gate voltage (V) 0 0 -5 -15 -10 1.62 1.63 1.64 1.65 1.66 Energy (eV) 1.62 1.63 1.64 1.65 1.66 Energy (eV) Low-doping regime : X - and X 0 have similar intensity Sample 415 High-doping regime : X - dominates

Excitons in a monolayer MoSe 2 X0 exciton : neutral exciton “Dark” “Bright”

Excitons in monolayer MoSe 2 X- exciton : negatively charged trion “Bright” inter-valley exciton “Bright” intra-valley exciton

Valley Zeeman effect c / v + Δ E l c / v + Δ E k c / v Δ E Z = E s K valley K’ valley CB VB CB VB -µ B -µ B +µ B +µ B Spin Atomic d-orbitals 0 -2µ B 0 +2µ B (intracellular) ) Phase winding of Bloch function - α µ B - α µ B + α µ B + α µ B (intercellular) , α =m 0 /m C,V W. Yao, et al. PR B, 2008; X. Xu, et al. Nature Phys., 2014, T. C. Berkelbach et al. PRB, 2013

Valley Zeeman effect c / v + Δ E l c / v + Δ E k c / v ≈ 4 µ B B Δ E Z = E s σ + ! σ - ! K K’ B>0 B=0 B>0

Valley Zeeman effect in a monolayer MoSe 2 : low carrier density 22 +14 T 19 16 13 10 7 0 T 4 0 -4 -7 -14 T -10 1.60 1.62 1.64 1.66 1.68 1.60 1.62 1.64 1.66 1.68 Energy (eV) Energy (eV) Valley degeneracy is lifted σ + ! σ - !

Zeeman shift of exciton peaks Experimental,slope, X 0# +#0.12#meV/T# −# X −# +#0.12#meV/T# −# • Valley degeneracy is lifted due to the contribution from the valence band atomic orbitals, resulting in total Lande factor of 4.1 • Binding energies are not influenced by the magnetic field at low densities Li, Y., Ludwig, J. et al. Phys. Rev. Lett. 113 , 266804 (2014)

Variation of relative intensity • The relative intensities of X − and X0 +10T varies monotonically with magnetic field -10T • The trend is reversed for the opposite valleys 1.60 1.62 1.64 1.66 1.68 Energy (eV) 10 5 Field (T) 0 -5 -10 1.60 1.62 1.64 1.66 1.68 Energy (eV) Li, Y., Ludwig, J. et al. Phys. Rev. Lett. 113 , 266804 (2014)

Trion configuration • The relative intensities of X − and X0 +10T varies monotonically with magnetic field -10T • The trend is reversed for the opposite valleys 1.60 1.62 1.64 1.66 1.68 Energy (eV) 10 Inter-valley trion 5 Field (T) 0 B>0 B=0 -5 B>0 -10 1.60 1.62 1.64 1.66 1.68 B=0 Energy (eV) Li, Y., Ludwig, J. et al. Phys. Rev. Lett. 113 , 266804 (2014) Theory: H. Yu, et al. Nat. Commun. 5 , 3876 (2014).

Trion emission at high carrier density 30 20 10 Gate (V) 0 -10 300 • The slope is 0.18 meV/T , i.e. 50% increase compared with 0.12 meV/T in the regime of 200 -20 low carrier density 100 -30 • Estimated carrier density of 3x10 12 would 0 cause the Fermi level to be ~10meV above 1.60 1.62 1.64 1.66 1.68 Energy (eV) the CB edge Li, Y., Ludwig, J. et al. Phys. Rev. Lett. 113 , 266804 (2014)

Trion emission at high carrier density B>0 B=0 B>0 B=0 • The slope is 0.18 meV/T , i.e. 50% increase compared with 0.12 meV/T in the regime of • At E F >E C , the trion Zeeman shift low carrier density is expected to follow total VB • Estimated carrier density of 3x10 12 would contribution only (5 μ B ), which cause the Fermi level to be ~10meV above would result in 0.29 meV/T. the CB edge ??? Li, Y., Ludwig, J. et al. Phys. Rev. Lett. 113 , 266804 (2014)

Related works on valley Zeeman effect in monolayer TMDs Srivastava, A.,et al. (ETH, EPFL) Aivazian, G., et al. (Univ. of Wash.) Valley Zeeman effect in elementary optical Magnetic control of valley pseudospin in monolayer WSe 2 . excitations of monolayer WSe2. Nature Physics, 11 (2), 148 (2015) Nature Physics, 11 (2), 141 (2015) MacNeill, D., et al. (Cornell) Wang, G., et al. (Toulouse, Ioffe) Breaking of Valley Degeneracy by Magnetic Field in Magneto-optics in transition metal diselenide monolayers. Monolayer MoSe2. arXiv:1503.04105v1 (2015) Physical Review Letters, 114, 037401 (2015)

Valley splitting and polarization in monolayer MoSe 2 • Splitting of K/K’ valleys by application of perpendicular magnetic field (tuning valley DoF) • Charge imbalance in different valleys for doped samples – creation of steady-state valley polarization • Intervalley configuration is the lower energy state for the trion • Variation in the trion emission energy X-(B) with at high doping (call for more experimental and theoretical studies)