Valleytronics in 2D materials

1. Valleytronics in 2D materials Yang shiqi 20180820

2. exploit valley polarizations • Degree of freedom(DOF) for electrons: Charge & Spin & Valley 2D materials: graphene semiconducting transition metal dichalcogenides (TMDCs) Host an easily accessible electronic valley degree of freedom, allowing for dynamic control. • Primary motivation: Valleytronicsystems whichcan offer information storage and possess advantages that complement or surpass modern charge- and spin-based semiconductor technologies.

3. (Mak, Xiao et al. 2018)

4. Valley contrasting physics • Photoluminescence measurements: coupling strength with optical fields (preferentially inject excitons) & degree of circular polarization (read out ) • Electrical measurements: Hall & FET • Valley • Valley magnetic moment • Berry curvatures • Inversion symmetry breaking (ISB) • Strong spin orbital coupling (SOC) • Hall effect: charge hall effect without magnetic field & spin hall effect & valley hall effect • Optical selection rule

5. 2007 Niu, Q. graphene with ISB can show various valley-dependent phenomena 2010 Mak, K. F. Monolayer MoS2 with direct bandgapand it’s A- and B-excitons 广播站播音员 •物理电子学院新传中心文字组负责人 2012 Xu, X. & Mak, K. F. & Cao, T. & Cui, X monolayer TMDs with ISB show various valley-dependent effects, including a valley-dependent optical selection rule. 2014 Mak, K. F. The first experimental report of valley Hall effect in monolayer TMDs by optical injection 2017.05 参加前往新加坡的短期游学项目 2016 Ye, Xiao first electrical valley polarization with spin injection from a ferromagnetic semiconductor Optical, magnetic, electric field … …

6. Contents • Valley contrasting physics (include optical selection rules & hall effect) • Various optical and electrical control of valley polarization • Challenges and outlook

7. Valley • These valleys can be represented by a binary pseudospinthat behaves like a spin 1/2 system. • Acarrier population distribution polarized in a +K or –K valley can store binary information. (Xiao, Yao, and Niu 2007)

8. Valley magnetic moment The Hamiltonian is given by: For q→0: Bohr magneton (electron spin) Intrinsic magnetic moment associated with the valley degree of freedom

9. Berry curvatures and ISB • Under time reversal symmetry : • Under spatial inversion symmetry: So ISB is needed for generating and detecting valleys, also for: (Mak, Xiao et al. 2018)

10. (Xiao, Liu et al. 2012) Monolayer MoS2 Energygap Spin-splitting (Mak, He et al. 2012)

11. Optical selection rule (no SOC) Couplingstrengthwith optical fields of circular polarization： (Xiao, Liu et al. 2012) Degree of optical polarization: (Cao, Wang et al. 2012)

12. Optical selection rule (no SOC) microscopic chiral selection rule: angular momentum selection rule m=-1 m=1 -ℏ +ℏ m=o (Cao, Wang et al. 2012)

13. Why circularly polarized photoluminescence (PL) measurements ? Photoluminescence measurements: preferentially inject excitons & read out We have degree of photoluminescence polarization by the helicityparameter: how good the chiral optical selectivity is (Mak, He et al. 2012) The polarization of PL how well the valley identity of charge carriers is preserved before recombination. (Cao, Wang et al. 2012)

14. Strong SOC in 2D TMDC • Opposite spin splitting at +K and –K valleys • Coupling between spin and valley pseudospin: manipulate spin by utilizing the valley properties spin and valley polarization lifetime couple to layer pseudospin (and electrical polarization) in multilayers (Xiao, Liu et al. 2012) (Xu, Yao et al. 2014) (Schaibley, Yu et al. 2016)

15. Optical selection rule (SOC) (Xiao, Liu et al. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides 2012)

16. (Mak, He et al. 2012) Optical control of valley polarization excitation Temperature: 14K bilayer

17. Optical control of valley polarization • Helicity for A exciton: bilayer Intravalleyrelaxation (for monolayer () and bilayer MoS2) Intervalleyrelaxation → large change of momentum involved & magnetic defects (Mak, He et al. 2012)

18. Optical control of valley polarization Polarization: flat feature Polarization inversely proportional Scattering rate proportional Population of these phonons (Zeng, Dai et al. 2012)

19. Bottom of conduction band Various Hall effect E → no Hall voltage Top of valance band E, () excitation → charge Hall effect E, linear excitation () → spin Hall effect E, excitation, excitation, valley Hall effect → (Mak, Xiao et al. 2018) (Mak, McGill et al. 2014) (Xiao, Liu et al. 2012)

20. Various Hall effect Anomalous Hall conductivity: Doping dependence of the anomalous Hall conductivity (Mak, McGill et al. 2014)

21. Control of the valley DOF • Optical control of the valley degree of freedom Excitonic valley coherence (WSe2) Form of a valley-selective optical Stark effect (WSe2, WS2) • Magnetic control (WSe2) • Electrical generation of valley magnetization or polarization Electrical injection (WS2) Magnetoelectricity (ME) effect based on the valley DOF (MoS2) (Jones, Yu et al. 2013) (Sie, McIver et al. 2014) (Aivazian, Gong et al. 2015) (Ye, Xiao et al. 2016) (Lee, Wang et al. 2017)

22. Excitons ( , ,) Monolayer MoSe2 Temperature: 20K 2.33 eV laser excitation PL n type (Ross, Wu et al. 2013)

23. Excitons ( , ,) Impurities after FET fabrication PL intensities (Ross, Wu et al. 2013)

24. Excitonic valley coherence excitation Monolayer WSe2 Temperature: 20K probably arises from the fine structure of (Jones, Yu et al. 2013)

25. Excitonic valley coherence A significant finding: (Jones, Yu et al. 2013)

26. Electrical injection (Ye, Xiao et al. 2016)

27. Valley magnetoelectricity (ME) effect Temperature: 30K ME susceptibility: (not carrier population → net M) (Lee, Wang et al. 2017)

28. Valley magnetoelectricity (ME) effect The valley ME effect persists at room temperature → gate & spatial image & bias dependence (Lee, Wang et al. 2017)

29. Challenges & Outlook • Long valley lifetime • Electrical methods to inject, control and read out valley polarization or magnetization for integration with the existing technologies. Electrical method • Broaden the materials • Heterostructures and bialayer or multilayers (Mak, Xiao et al. 2018) (Zhong, Seyler et al. 2017)

30. Thanks for listening !