Optical Conductivity of MoS2

Habib Rostami

IPM

10 Mehr 92

• Motivation

• Inversion Symmetry

• Gapped Graphene & Valley contrasting effect

• Monolayer MoS2&optical measurement

• Optical Conductivity of Monolayer MoS2

• Summery

Outline

3

Motivation

Kin Fai Mak, et al Phys.Rev.Lett. 105, 136805 (2010)

4

Optical phenomena

Photoluminescence:

Excitonic , Free electron,…

Absorbance:

Inter-band , intra-band

5

Circular dichroism

6

Inversion symmetry(real space)

7

Inversion symmetry(k space)

8

Symmetry of band structure

9

Inversion symmetry breaking& valley Hall effect

Di Xiao, et al Phys.Rev.Lett. 99, 236809 (2007).

10

Gapped Graphene & Valley physics Inversion symmetry breaking& valley pumping

W.Yao, D.Xiao, Q.Niu, Phys. Rev. B 77, 235406 (2008).

11

Light Emitting Diode(LED)

Electrically controlled emission polarization

W.Yao, D.Xiao, Q.Niu, Phys. Rev. B 77, 235406 (2008).

12

Monolayer Transition metal dichalcogenides semiconductor

• Direct Band Gap in visible range

• Broken inversion symmetry

13

Layered Compounds: Transition metal dichalcogenides ( 𝐌𝐗𝟐)

Chhowalla et al, Nature Chemistry 5, 263–275 (2013)

𝐻𝑓𝑆2: Insulator

𝑀𝑜𝑆2, W𝑆2: Semiconductor

𝑇𝑖𝑆𝑒2, 𝑊𝑇𝑒2: Semimetal

𝑁𝑏𝑆2, V𝑆𝑒2: Metal

Band Structure: DFT

14 Nature Chemistry 5, 263–275 (2013)

Symmetry & band structure

15 K. F. Mak et al., Nature Nanotech. 7, 494 (2012).

16

Optical Absorbance

17

Excitonic Absorbance

18

Optically Induced Valley Polarization K. F. M

ak e

t al., N

atu

re N

anote

ch. 7, 4

94 (2

012).

19

No Hanle effect

Zeng et al, Nature NanoTech. 7, 409 (2012).

Luminescence Polarization :

20

Lattice and Orbital symmetry& Circular Dichroism

T. Cao, et al., Nature Commun. 3, 887 (2012).

21

Spin-Valley coupling

K. F. Mak et al., Nature Nanotech. 7, 494 (2012).

22 Di Xiao, et al , Phys. Rev. Lett. 108,196802 (2012)

Spin-Valley coupling

23

H.R, and Reza Asgari (to be submitted)

24

Hamiltonian

Shun-Qing Shen, Topological Insulator, Springer(2012).

H.-Z. Lu,et al Phys.Rev.B 81, 115407(2010).

H. R, A. G. Moghaddam, R. Asgari, Phys. Rev. B 88, 085440 (2013).

25

Kubo’s Formula

Wang-Kong Tse and A.H.MacDonald,Phys.Rev.B 84,205327(2011).

T. Stauber, N. M. R. Peres, and A. K. Geim,Phys.Rev.B 78,085432 (2008).

Zhou Li and J. P. Carbotte,Phys. Rev. B 86, 205425(2012).

26

Optical spin/valley Conductivity

27

Optical Hall Conductivity

28

Optical Longitudinal Conductivity

29

Xiao’s Model

Di Xiao, et al , Phys. Rev. Lett. 108,196802 (2012)

30

Numerical Parameter

037.0 mme 044.0 mmh

05.0 mme 05.0 mmh

31

Static limit

32

Static limit: the effect of Beta

33

Dynamical Hall Conductivity

34

Dynamical Longitudinal Conductivity

35

Optical Conductivity(mass asymmetry)

36

Tuning the spin splitting by Fermi energy

37

Circular Polarization

38

Optical Transmission

A. C.-Gomez et al, Private communication

39

Summary

• Inversion symmetry breaking leads to valley contrasting physics

• Circular dichroism in monolayer MoS2 can be describe by intrinsic optical conductivity

• Charge, spin, and valley Hall effect

• Optical valley pumping

40

Thank You!