1. State Kay Lab of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing , China

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1 Suppting Infmatin Indefinite by natue: fm ultavilet t teahetz Jingb Sun 1, 2, Natalia M Litchinitse 2, Ji Zhu 1, * 1. State Kay Lab f New Ceamics and Fine Pcessing, Depatment f Mateials Science and Engineeing, Tsinghua Univesity, Beijing , China 2. Electical Engineeing Depatment, Univesity at Buffal, The State Univesity f New Yk, Buffal, NY 14260, USA *T whm cespndence shuld be addessed. zhuji@mail.tsinghua.edu.cn Pages: 12 Figues: 9 Table: 1 Indefinite pemittivity f gaphite s1 Cnsideing that lage bulk cystalline gaphite is had t find in natue, highly iented pylytic gaphite (HOPG), a clsest mateial t single cystalline gaphite, is used f measuement. The HOPG sample in this expeiment was fabicated by the Institute f Metal Reseach, CAS. The msaic spead f the sample is esticted t f the c-axis (symmety axis, pependicula t the basal plane). The HOPG mateial was cut int a 1-mm-wide slab alng the c-axis. AFM (Seik, SPI4000&SPA300HV) was used t detemine the ughness f the ptical suface f the slab, and the t-mean-squae (RMS) ughness was 6.2 nm. Figue S1 J. A. Wllam spectscpic ellipsmete S1

2 F uniaxial cystals such as gaphite, the dielectic tens cntains tw independent dielectic functins, including the dinay dielectic functin (), which descibes light plaized alng the cabn-laye planes, and the extadinay dielectic functin e (), which descibes light plaized pependicula t the cabn-laye planes. Measuements wee pefmed using a spectscpic ellipsmete (J. A. Wllam, Figue S1, with attached sftwae WVASE 32) that pvides tw paametes and These paametes ae elated t the ati f eflectin cefficients f the light f p-plaizatin p and s-plaizatin s : i p tan( ) e. (S1) s Because f the anistpy f the mateial, p and s ae diffeent f thee ientatins: caa, aac and aca s2. Assuming 2 1/2 [ sin ( )], e, it can be shwn that these eflectin cefficients ae given by the fllwing expessins f the cases f caa: p ecs( ) e cs( ) e, s cs( 1) cs( ) 1, whee e { } 2 [ e sin( ) ] 1/2 (S2) e aac: p ave cs( 1), cs( ) ave 1 s cs( 1) cs( ) 1, (S3) whee 1/2 2 e[ sin( 1) ] ave 1/2 e, ave ( e) aca: p cs( 1) cs( ) 1, s cs( 1) e cs( ) 1 e, whee 2 1/2 e [ e sin( 1) ] (S4) Using the data in Figue S3(a-c) and Eq. S1-S4, we btain and e specta in the ange f 240~400nm as shwn in Figue S3(d). In the UV egin belw 282 nm, 1 is negative wheeas e1 is psitive, esulting in the indefinite pemittivity f gaphite. S2

3 Figue S2 Scheme f the ellipsmete measuements. (a) Measuements based n thee diffeent cystal ientatins; (b), (c) and (d) shw sample's displacement unde the thee ientatins. Figue S3 Pseuddielectic pemittivity in thee cystal ientatins (a, b, c) and the anistpic dielectic dispesin f the gaphite (d). Subscipt 1 dentes the eal pat and subscipt 2 dentes the imaginay pat 2. Indefinite pemittivity f MgB 2 Pevius studies s3 demnstated anistpic ptical cnductivity and pemittivity f MgB 2 between 24THz and 900THz at m tempeatue, btained n single cystals by spectscpic ellipsmety measuements, as shwn in Figue S4. Qualitatively, bth in-plane and c-axis specta exhibit a simila metallic behavi, chaacteized by Dude S3

4 mdel. Hweve, ne can ntice a stng anistpy. Thee is a bad plasma edge f the ed cuve at abut 482THz, whee the dielectic functin a1 almst eaches ze. Then, it vaies nnmntnically while emaining negative at least up t 900 THz. On the cntay, the c-axis plasma edge is significantly shape and is highe in fequency by abut 120THz. Cespndingly, c1 behaves mntnically and csses ze at p,c (628THz). F the fequency ange abve 628THz, the MgB 2 is indefinite mateial with c >0 and a <0, which may exhibit a negative efactin f blue puple light with cetain plaizatin. Figue S4 The eal pat f dielectic functin alng tw cystal diectins a and c: a1, c1. Optical anistpic specta at 300K is btained by the ellipsmety n a mncystalline MgB 2 sample with dimensins (a b c) f mm 3. The sample was kept in the flw f dy nitgen in de avid the deteiatin caused by the ai mistue. The chaacteizatin n the anistpic pemittivity f MgB 2 is simila t that f gaphite. Paamates and alng thee cystal ientatins wee measued using the ellipsmete and the pemittivities wee cmputed based n the Fesnel s equatins unde diffeent ientatins and diffeent incident angles s3. 3. Indefinite pemittivity f cupates Cupates, famus f the citical tempeatue abve the biling pint f liquid nitgen, cnstitute a new fcus amng the supecnducts, which stats the eseach n high tempeatue supecnduct. A majity f pevius studies f cupates fcused n the elatin between the high T c and thei anistpic ppeties, while nly a limited numbe f studies wee devted t the dielectic ppeties f these stngly anistpic mateials. Nevetheless, pevius studies pvide a lt f eflectance data f vaius cystalline cupates. Based n this available data, we investigated the indefinite ppeties f cupates. A fitting methd was used t btain the pemittivity. We use the Dude-Lentz mdel as fllws s4 : S4

5 ( ) 2 2 p An i n n in, (S5) whee is the elativity pemittivity cespnding t at infinity and the secnd tem n the ight-hand side is the usual Dude tem with plasma fequency p and damping fact. The tems in the summatin cespnd t ptical-phnn mdes, whee A n, n and n ae the stength, fequency and damping f the mde, espectively. Since all these mateials in m tempeatue ae nn magnetic mateials with pemeability equal t ne, accding t Fesnel eflectin cefficient: ( ) 1 ( ), ( ) 1 (S6) the eflectance can be cmputed fm Eq. (S5) and (S6): R * (S7) Theefe, dielectic dispesin is detemined by the eflectance specta fitting between the esults cmputed by equatin (S7) and measued in the expeiment. This methd is usually feasible t etieve mateial s dielectic dispesin specta based n well study n the mateial esnance mechanics s that the dielectic mdel Eq. S5 can be ppely built. Simila methd can als be fund in Ref. s5. The eflectance specta f GdBa 2 Cu 3 O 7-x alng tw diffeent cystal ientatins at the ange f 30~900THz, shwn in Figue S5(a, b), wee btained using a Pekin-Elme 16U spectmete at the m tempeatue by Zelezny et al. in Ref. s6. The ed dashed cuves shw fitting esults cmputed using Eq. (S7) that wee used t detemine the anistpic pemittivity shwn in Figue S5 (c, d). The indefinite dielectic dispesin is pltted in Figue S5(e). S5

6 Figue S5 Fitted eflectance specta and dielectic dispesin specta f GdBa 2 Cu 3 O 7-x (with the subscipt 1 dentes the eal pat f cmplex dielectic pemittivity; with the subscipt 2 dentes the imaginay pat). The eflectance specta f Bi 2 S 2 Ca n-1 Cu n O 2n+4+x alng thee diffeent cystal ientatins at the ange fm 20 t 120THz, shwn in Figue S6(a, b), wee btained using a Fuie tansfm infaed spectscpy (FTIR) at the tempeatue f 298K by Kim et al. in Ref. s7. The ed dashed cuves shw the fitting esults cmputed using Eq. (7) that wee used t detemine the anistpic pemittivity shwn in Figue S6(c, d). By cmpaing the eflectance specta with plaizatin alng ab-plane, we find that the esults in the tw cases in Figue S6 ae nt quite the same. The small diffeence esults fm the cystal stuctue, which als esults in a weak dielectic anistpy in ab-plane. Hweve, the Bi 2 S 2 Ca n-1 Cu n O 2n+4+x cystal is ften teated as a uniaxial cystal s8. F this easn we classify the Bi 2 S 2 Ca n-1 Cu n O 2n+4+x and GdBa 2 Cu 3 O 7-x int the same type. By the fitting esult, we can als pedict that the plasma fequency f Bi 2 S 2 Ca n-1 Cu n O 2n+4+x in the ab-plane shuld be 307THz, which is ut f the measuement ange. The indefinite dielectic dispesin is pltted in Figue S6(e). S6

7 Figue S6 Fitted eflectance specta and dielectic dispesin specta f Bi 2 S 2 Ca n-1 Cu n O 2n+4+x (hee with the subscipt 1 dentes the eal pat f cmplex dielectic pemittivity; with the subscipt 2 dentes the imaginay pat). The eflectance specta f La 1.92 S 0.08 CuO 4 in the ange f 1.2~120THz (Figue S7(a, b)) wee btained using a Fuie tansfm infaed spectscpy (FTIR) unde the tempeatue f 298K by Cllins et al. in Ref. s5. The fitting esults in the ange fm 1.2 t 30THz ae shwn in Figue S7. S7

8 Figue S7 Fitted eflectance specta and dielectic dispesin specta f La 1.92 S 0.08 CuO 4 (hee with the subscipt 1 dentes the eal pat f cmplex dielectic pemittivity; with the subscipt 2 dentes the imaginay pat). 4. Pevskite-like stuctues as indefinite mateials Ruthenate, S n+1 Ru n O 3n+1, is ne f the mst imptant Ruddlesden-Pppe phase mateials, exhibiting the abnmal electnic and magnetic ppeties due t its unusual cystal stuctue. The eflectance specta f S 2 RuO 4 in the ange f 2~1200THz, shwn in Figue S8(a, b), wee btained using a Fuie tansfm infaed spectscpy (FTIR) and a gating spectmete unde the tempeatue f 298K by Katsufuji et al. in Ref. s9. Fitted eflectance specta and dielectic dispesin specta ae shwn in Figue S8. S8

9 Figue S8 Fitted eflectance specta and dielectic dispesin specta f S 2 RuO 4 (hee with the subscipt 1 dentes the eal pat f cmplex dielectic pemittivity; with the subscipt 2 dentes the imaginay pat). The eflectance specta f S 3 Ru 3 O 7 in the ange f 1.8~900THz, shwn in Figue S9(a, b), wee btained using a apid scanning intefemete unde the tempeatue f 298K by Mii et al. in Ref. s10. Fitted eflectance specta and dielectic dispesin specta ae shwn in Figue S9. S9

10 Figue S9 Fitted eflectance specta and dielectic dispesin specta f S 3 Ru 3 O 7 (hee with the subscipt 1 dentes the eal pat f cmplex dielectic pemittivity; with the subscipt 2 dentes the imaginay pat). 5. The indefinite fequency ange wavelength ange f natual mateials Finally, we summaize the fequency wavelength anges f the indefinite ppeties and cespnding cystal ientatins, as shwn in Table S1. An example (nmal: b, ientatin: bc) f the ientatin is shwn in Figue S10. Fm Table S1, we find that the indefinite ppeties f these cystals cve the ange fm THz t UV fequencies, pening nealy unlimited pssibilities f device applicatins. Table S1 Mateials Nmal ientatin Fequency ange/wavelength ange Gaphite a ac 240~280(nm) b bc 240~280(nm) MgB 2 a ac 628~900(THz) b bc 628~900(THz) Bi 2 S 2 CaCu n O 8+x a ac 20~120(THz) b bc 20~120(THz) GdBa 2 Cu 3 O 7-x a ac 30~110(THz) S10

11 YBa 2 Cu 3 O 7-x La 2-x S x CuO 4 S 2 RuO 4 S 3 Ru 2 O 7 b bc 30~110(THz) a ac 0~207(THz) b ab 207~348(THz) b bc 0~348(THz) a/b ac 4.3~7.2, 14.1~14.9, 20.0~22.1(THz) c ac 7.6~10.8(THz) a ac 19.2~325.8(THz) b bc 19.2~325.8(THz) a ac 22.0~294.0(THz) b bc 22.0~294.0(THz) Figue S10 The schematic f the ientatin: nmal: b, ientatin: bc. k i and S i ae the incident wave vect and Pynting vect, espectively. k and S ae the efactive wave vect and Pynting vect, espectively. 6. Refeence (s1) Sun, J., Zhu, J., Li, B., Kang, F., Indefinite pemittivity and negative efactin in natual mateial: Gaphite. Appl. Phys. Lett. 2011, 98, (s2) Jellisn, G. E. J., Baba J. S., Pseuddielectic functins f uniaxial mateials in cetain symmety diectins. J. Opt. Sc. Am. A 2006, 23, (s3) Guitanu, V., Kuzmenk, A. B., Mael, D. V. D., Anistpic ptical cnductivity and tw cls f MgB 2. Phys. Rev. B 2006, 73, (s4) Ibach, H., and Lüth, H., Slid-State Physics. Spinge: Belin, 2003; pp (s5) Cllins, R. T., Schlesinge, Z., Chandashekha, G. V., Shafe, M. W., Infaed study f anistpy in single-cystal La 2-x S x CuO 4. Phys. Rev. B 1989, 39, (s6) Zelezny, V., Tanne, D. B., Kamaas, K., Kzeeva, L., P., Pavlyuk, A. A., Anistpic ptical ppeties f single-cystal GdBa 2 Cu 3 O 7-. Z. Phys. B 1995, 96, S11

12 (s7) Kim, J. H., Bzvic, I., Mitzi, D. B., Kapitulnik, A., Hais, J. S J., Optical anistpy f Bi 2 S 2 CaCu 2 O 8. Phys. Rev. B 1990, 41, (s8) Quijada, M. A., Tanne, D. B., Kelley, R. J., Onellin, M., a-b plane anistpy f single-dmain cystals f Bi 2 S 2 CaCu 2 O 8. Z. Phys. B 1994, 94, (s9) Katsufuji, T., Kasai, M., Tkua, Y., In-plane and ut-f-plane ptical specta f S 2 RuO 4. Phys. Rev. Lett. 1996, 76, (s10) Mii, C, Baldassae, L, Lupi, S, Otlani, M. Fittipaldi, R. Wecchine, A. Calvani, P., Anistpic ptical cnductivity f S 3 Ru 2 O 7. Phys. Rev. B 2008, 78, S12