An introduction to the optical spectroscopy of solids

Size: px

Start display at page:

Download "An introduction to the optical spectroscopy of solids"

Lucy Ward
5 years ago
Views:

1 An introduction to the optical spectroscopy of solids Nan Lin Wang Institute of Physics Chinese Academy of Sciences

2 Outline 1. Optical constants and their relations Optical constants, Kramers-Kronig transformation, intra- and interband transitions. Drude model of simple metal example of application 3. Spectroscopy of correlated electrons 4. THz time domain spectroscopy Particularly optical pump, THz probe

3 References C. Kittle, Solid State Physics F. Wooten, Optical properties of solids Academic Press, 197 M. Dressel and G. Grüner, Electrodynamics of solids Cambridge University Press, 00

and quasiparticle excitations in a material. D. Basov, et al.

4 I. Optical constants and their relations Optical spectroscopy is a primary tool to probe the charge dynamics and quasiparticle excitations in a material. D. Basov, et al. Rev. Mod. Phys. 011 Units:1 ev = 8065 cm -1 = K 1.4 ev=10000 cm -1

5 The electrodynamical properties of solids described by a number of so-called optical constants : complex refractive index, or complex dielectric constants, or complex conductivity. Those optical constants could be probed either directly ellipsometry, ultrfast laser-based time domain terahertz spectroscopy, or indirectly reflectance measurement over broad frequencies.

6 Optical constants Consider an electromagnetic wave in a medium index :refractive n, c/n /q v where 0 / 0 0 t c nx i t v x i t qx i y e E e E e E E If there exists absorption, K: attenuation factor 0 t c nx i c Kx y e e E E c Kx y e E E 0 I 0 t c x N i y e E E ik n N Introducing a complex refractive index: x y E Intensity

7 Reflectivity If n, K are known, we can get R, ; vice versa / K n K tg K n K n r E E R e K n K n ik n ik n e r r E E in ref i i in ref 1/ 1/ 1/ 1 1 cos sin 1 cos R n R R R k R R

8 Dielectric function 0, 0,,,,, 1 1 K n K n ik n i N q q photon q E q q D 0 /a~1å -1 Infrared q=/~10-4 Å n k or

9 conductivity In a solid, considering the contribution from ions or from high energy electronic excitations i 4 1 By electrodynamics, 1 i 4

10 Now, we have several pairs of optical constants: n, K R, 1, 1, Usually, only R can be measured experimentally.

11 Kramers-Kronig relation -- the relation between the real and imaginary parts of a response function. 1 ' 0 ' 'd ' P 1 ' 0 'd ' P For optical reflectance r R e i ln r 1/ ln R i P ln R ' d' 0 ' Low- extrapolations: Insulator: R~ constant Metal: Hagen-Rubens Superconductor: two-fluids model High- extrapolations: R~ -p p~0.5-1, for intermedate region R~ -n n=4, above interband transition

12 Reflectivity measurement

13 FTIR

14 In-situ overcoating technique FT-IR spectrometer In situ evaporation C. C. Homes et al. Applied Optics 3,

15 Interband transition Intraband transition E c k v, k, E k c, k, E k v c E g h Δk Δω E v k E k E k E k J E c v cv V ds 3 kecv k Kubo-Greenwood formula 8 e J pvc m Infrared light cannot be absorbed directly by electron-hole excitation. a Impurity-assisted absorption e - e - k,e k,e X b boson-assisted absorption k,e q,ω q k,e Holstein process, if phonons are involved.

16 简单金属 :Drude model 0 D 1 1i 4 1/ i 4i 1 R p 1 / p 1 1/ 4 1 p / Im{ } ' p ' p dc / Im-1/ / ' p p m * /mn eff 0 d 1 8 p energy

mcm 举例 :Parent compound 1T-TiSe 1T-TiSe was one of the first CDW-bearing materials Broken symmetry at 00 K with a xx superlattice Semiconductor or semimetal?

17 mcm 举例 :Parent compound 1T-TiSe 1T-TiSe was one of the first CDW-bearing materials Broken symmetry at 00 K with a xx superlattice Semiconductor or semimetal? Ti: 3d 4s Se: 4s 4p T K Ti : 3d band fully empty? Se: 4p band fully occupied? related to the CDW mechanism

18 Ti: 3d 4s Se: 4s 4p 4 Ti : 3d band Se: 4p band

19 Excitonic Phases W. Kohn, PRL 67 The electron-hole coupling acts to mix the electron band and hole band that are connected by a particular wave vector.

20 Reflectivity Reflectivity TiSe single crystal G. Li et al., PRL 07a K 5K 00K 150K 080K 050K 010K K 5K 00K 150K 080K 050K 010K TiSe Frequencycm Frequencycm -1

4000 1 S/cm 3000 000 1000 300 K 5 K 00 K 150 K 80 K 50 K 10 K 0.4 ev 0 0 000 4000 6000 cm -1 0.

21 S/cm K 5 K 00 K 150 K 80 K 50 K 10 K 0.4 ev cm ev Drude CDW gap Free carriers with very long relaxation time exist in the CDW gapped state FS is not fully gapped??

22 R 1/ cm K K dash curves: fit with Drude + two Lorentz p cm T K

23 mcm T K p n 4 h e m h n m e e Exciton-driven CDW G. Li et al., PRL 07a

24 R R Simple metal High-T c cuprates gold YBCO Bi cm cm -1

25 Electron correlations reflected in optical conductivity Simple metal Correlation effect:reducing the kinetic energy of electrons, or Drude spectral weight. Correlated metal

26 Q M Si, Nature Physics 009

27 Basov and Chubakov, Nature Physics 011

28 Hubbard U physics: VO3 DFMT

29 Sum rule f-sum rule: It has the explicit implication that at energies higher than the total bandwidth of a solid, electrons behave as free particles. Kubo partial sum-rule: kinetic energy in the tight binding model The upper limit of the integration is much larger than the bandwidth of a given band crossing the Fermi level but still smaller than the energy of interband transitions. For, the Kubo sum rule reduces to the f-sum rule. W K depends on T and on the state of the system because of n k --- "violation of the conductivity sum rule", first studied by Hirsch. In reality, there is no true violation: the change of the spectral weight of a given band would be compensated by an appropriate change in the spectral weight in other bands, and the total spectral weight over all bands is conserved.

30 Extended Drude Model Drude Model p i Let M, T 1/, T i, T 1/,T: Frequency dependent scattering rate p 1, T 4 M, T i p 1 4 1/, T i[1, T] * 1 p * 4 1/, T i : Mass enhancement m * =m1+ 1/, T p / 4 Re[1/, T] m m T */ 1 p / 4 Im[1/, ] e.g. Marginal Fermi Liquid model: M, T 1/, T i, T x g N 0 x i ln c Where x=max,t, or x= +T 1/

31 The extended Drude model in terms of optical self-energy, T p 1 4, T i i op According to Littlewood and Varma, i 1 i [ ] Optical self-energy Relation to the 1/ and m*/m 1/ 1 1 m / m * 1

32 Bi1 Hwang, Timusk, Gu, Nature 47,

33 1 cm 1 F The electron-boson phonon interaction 1/ 0 d tr F T=0 K P.B.Allen At 0K, based on Allen's formula F p F _0=500 cm-1 =100 cm-1 _p^=50000 cm Wave number cm -1

34 S. V. Dordevic, et al. PRB 71, Allen s formula for the scattering rate in the superconducting state 4 1/ d F E 1 0 P.B.Allen 1971 Ex is the second kind elliptic integral

35 Optical spectra of a superconductor T=0, London electrodynamics gives 1 8 ps i ps / 4 1 L 8 c 0 n 1 s d 1 or 1 L 4 c Ferrell-Glover-Tinkham sum-rule: missing area is equal to the superconducting condensate. Clean limit dirty limit dirty limit: >l Absorption starts at. clean limit: <l < > Absorption starts at +. pippard coherence length =v F /, =1/=v F /l

36 Coherent factors and characteristic spectral structures in density wave or superconductors

37 Gap feature in density waves 1-1 cm dc values 0 K 300 K 70 K K 15 K 8 K cm -1 URuSi 300 K 00 K 100 K 70 K 50 K

38 Gap structure in superconductors Ba 0.6 K 0.4 Fe As G. Li et al PRL 08 Cuprates, Homes data

39 Coherent peak below Tc T. Fischer et al PRB 010 R. V. Arguilar et al, arxiv: O.Klein et al PRB 94 铁基超导体的 THz 数据与 NMR 不同?S+- 配对?

41 Optical measurement under magnetic field Bruker 113v spectrometer 10 Tesla split coils from Cryomagnetic Inc. Liquid He

42 Josephson Plasma edge in K0.75Fe1.75Se from nanoscale phase separation R.H. Yuan et al, Scientific Reports 01 Josephson Plasma edge

43 Reflectivity % Effect of magnetic field: Magneto-Optical Reflectivity in EuB EuB 6 T=0 K 0 T 1 T T 3 T 4 T 5 T 6 T 7 T Frequency cm -1 Degiorgi et al., Phys. Rev. Lett. 79,

44 Pump-probe experiment based on femtosecond laser Quasiparticle relaxation after optical pump

46 飞秒激光光阑平移台计算机锁相放大器分光镜 ZnTe 平衡探测器太赫兹天线 /4 渥拉斯棱镜硅分光镜太赫兹时域光谱系统原理图样品恒温器或磁体系统

47 THz time domain spectroscopy

48 Optical e.g. midinfrared pump, THz probe! Manipulation and control Femtosecond laser can selectively excite certain modes of correlated electronic systems, and controllably push materials from one ordered phase to another.

49 Science 011

50 Thanks!

Superconductivity Induced Transparency

Superconductivity Induced Transparency Coskun Kocabas In this paper I will discuss the effect of the superconducting phase transition on the optical properties of the superconductors. Firstly I will give