Sca$ering from bulk material with topologically insula8ng surface states

Transcription

1 Forum for Electromagnetic Research Methods and Application Technologies (FERMAT) Sca$ering from bulk material with topologically insula8ng surface states Akhlesh Lakhtakia 1 and Tom G. Mackay 1,2 1 Pennsylvania State University Department of Engineering Science and Mechanics 2 University of Edinburgh School of Mathema8cs

2 Copyright The use of this work is restricted solely for academic purposes. The author of this work owns the copyright and no reproduction in any form is permitted without written permission by the author.

3 Abstract A homogeneous, linear, bianisotropic material that occupies a bounded region V-in, and whose surface S is charge-neutral and current-neutral, was considered. Analysis of the frequencydomain Maxwell postulates revealed that the axionic piece vanishes from both the parfal differenfal equafons valid throughout V-in and the boundary condifons on S. Thus, the Post constraint is reaffirmed. Also, scajering studies revealed that whatever scajering effect may be ajributed to the axionic piece can instead be ajributed to a surface admijance parameter quanftafng topologically insulafng surface states. Keywords: anionic piece, depolarization, surface admittance, surface state, topological insulator

4 Biography Akhlesh Lakhtakia received degrees from the Banaras Hindu University and the University of Utah. He is the Charles Godfrey Binder Professor of Engineering Science and Mechanics at the Pennsylvania State University. His research interests include surface multiplasmonics, bioreplication, forensic science, solar energy, sculptured thin films, and mimumes. He is a Fellow of Optical Society of America, SPIE, Institute of Physics (UK), American Association for the Advancement of Science, American Physical Society, Institute of Electrical & Electronic Engineers, and Royal Society of Chemistry. He received the 2010 SPIE Technical Achievement Award and the 2016 Walston Chubb Award for Innovation. Tom G. Mackay is a reader in the School of Mathematics at the University of Edinburgh and an adjunct professor in the Department of Engineering Science and Mechanics at the Pennsylvania State University. He is a graduate of the Universities of Edinburgh, Glasgow, and Strathclyde. He is a Fellow of the Institute of Physics (UK) and SPIE. His research interests include the electromagnetic theory of novel and complex materials, including homogenized composite materials.

5 Sca$ering from bulk material with topologically insula8ng surface states

6 Sca$ering from bulk material with topologically insula8ng surface states 1. Axionic piece of linear consftufve relafons 2. Post constraint 3. ScaJering contribufons of topologically insulafng surface states

7 PENN TATE E5M ENGi HRING CIE CE ANO MLCHANI S n 0 1

8 PENN STATE D _ W) = C 0 E(_ W H _ w) - v 0 Il._(_ w EV n exp(-iwt) J2 :r. w) ==f. w) Er. w +a(w) B(r w)+w(w)b(r,w) Ji r. w == J!..(w) Ji r. w)+f-3(w) E(r w)-w(w)e(r,w) r EV - n Trac [a(w) - f3(w)] = 0

9 PENN TATE ESM ENGi HRING CIE CE ANO MLCHANI S D(r w) == E 0 E(r w) H(r w) == v 0 B(r w) } 'I. E Vout f2(r. w) == (w) E '[ w)+a(w) B(r w)+w(w)b(r,w) Ji(r. w) == (w) fl_(r. w)+fj(w) E(r w)-w(w)e(r,w) Trace [a.(w) - /3(w)] = 0

10 PENN STATE D(r w) == E 0 E(r w) } H(r w) == v 0 B(r w) r E Vout J2 r w == w) Er w +a(w) B(r w)+w(w)b(r,w) Ji r. w == Jf..(w) fl. r. w)+/3(w) E(r w)-w(w)e(r,w) Trac [o: w)-/3(w)] =0 c:

11 Macroscopic Maxwell postulates PrimiFve fields: E, B InducFon fields: D, H

12 PENN STATE v7 B(r,w) == 0 v7 x E(r,w) - iwb(r,w) == 0 c 0 v7 E(r,w) == p(r,w) v 0 v7 x B(r,w) +iwc: 0 E(r,w) == J(r,w) ' r E Vout

13 PENN STATE V B(r,w)=O V x E(r,w) - iwb(r,w) = 0 c 0 V E(r,w) = p(r,w) v 0 V x B(r,w) + iws 0 E(r,w) = J(r,w), r E Vout [-... lve,1 J>,,.,.>, 0 :i::,<-. 0 ('D/N\l> n v' B(r,w)==O v' x E ( r, w) - iw B ( r, w) == 0 y v' (w) E(r w)+a(w) B(r, w)] +w(w) fi(r_, w) == p(r w) v' x [,s(w) E(r w) + v(w) [v' B(r w)] -W(w) x E_(r._,w) - iw_b_(r._,w)j + iw (w) E(r w)+a(w) B(r w)] == J(r w) c:

14 Vanishes from the PDEs

15 Vanishes from the PDEs Argument for Ψ: Ψ does NOT vanish from the boundary condifons Obukhov and Hehl, Phys. Le$. A 314, 357 (2005) Sihvola and Tretyakov, Op8k 119, 247 (2008) Obukhov and Hehl, Op8k 120, 418 (2009)

16 Vanishes from the PDEs

17 Vanishes from the PDEs

18 Vanishes from the PDEs

19 vanishes from the PDEs, but not from the BCs Anomaly BCs are derived from the PDEs (in electromagnefcs)

20 No Ψ

21 S: charge-neutral and current-neutral

22 S: charge-neutral and current-neutral No Ψ

23 Vanishes from the PDEs and the BCs Anomaly removed!

24 Post constraint Ψ = 0 Post, Fundamental Structure of Electromagne8cs (1962)

25 Surface States 1. Abrupt cessafon of microscopic morphology at the surface 2. Chemical modificafon of surface 3. Other reasons, e.g., topological insulafon

26 Surface States No effect on consftufve relafons (volumetric) Surface may not be charge/current-neutral

27 Surface States No Ψ

28 Surface States No Ψ

29 T. I. Surface States No Ψ S is not charge/current-neutral

30 T. I. Surface States: Example

31 T. I. Surface States: Example

32 T. I. Surface States: Example DepolarizaFon due to γ

33 T. I. Surface States: Example DepolarizaFon due to γ persists

34 Conclusions 1. Axionic piece Ψ is filtered out by the Maxwell postulates 2. Post constraint Ψ = 0 holds 3. Whatever is ajributed to Ψ 0 can be explained by the surface-state parameter γ

35 Further reading 1. A. Lakhtakia & T.G. Mackay, Proc. SPIE 9558, 95580C (2015). 2. A. Lakhtakia & T.G. Mackay, J. Nanophoton. 10, (2016). 3. A. Lakhtakia & T.G. Mackay, J. Opt. Soc. Am. B 33, (2016). 4. T.G. Mackay & A. Lakhtakia, J. Opt. Soc. Am. B 33, (2016). 5. A. Lakhtakia & T.G. Mackay, J. Nanophoton. 10, (2016).