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188  úËõ July 2011 Vol.24 No.4
(C) 2011 The Japanese Society for Synchrotron Radiation Researchðà ¡ úËõ ARPES ÅÆç¦ég|WJâÌÌ\Ê Dirac FermionüèiCCWjÌoHÅ

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i{pj¾¯Xsªñ]µC½vñèÌêÉÍ}C
Fig. 1(a) A spatially separated two counter current ows at theedges of sample when a quantum Hall (QH) eect occurs
under a strong magnetic eld applied perpendicular to thesurface plane. (b) Spin current ows along the sample edges
in the presence of a quantum spin Hall (QSH) eect without
an external magnetic eld.

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i|pjñ]·é±ÆÉÈéB±±ÅÊqÍw©
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Fig. 2Massless energy dispersions at the edges of topological insu­
lators for (a) larger and (b) smaller electron occupations.

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ÉLªé\ÊÉÎµCFig. 4(a)É¦·æ¤É\ÊÅXs¬ª¶¶éB2 ³ÌêÆ¯lÉ 3 ³g|WJâÌÌ\Êdqàü`ÌGlM[ªUÖWð¿ Fig.
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R[ÍOtFÆÍÈºÌ_Åêüðæ·Æ¾¦æ¤BOtFÌêÍCuA][Ì K _¨æÑ K_É»ê¼êXskÞµ½v 4 ÂÌ Dirac R[
ª¶Ý·éªC3 ³g|WJâÌÅÍCÅ¬ÅPêÆÈèCFig. 4(b)É¦·æ¤ÉdqXsÌûüªg
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Fig. 3

Two backscattering paths (clockwise and counter clockwise
directions) when an edge electron encounters an impurity.

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úËõ July 2011 Vol.24 No.4  189

Fig. 4(a) Schematic of the 3D topological insulator with spin cur­rent ows on the surfaces. (b) Dirac cone on the surface ofthe 3D topological insulator. Spin directions are denotedwith arrows. (c) Schematic of an elastic scattering on the 3D
topological insulator surface. The key property is that in thepresence of non­magnetic surface impurity the topologicalsurface state is protected from complete backscattering,
while it is not protected from scattering by arbitrary angles.

Fig. 5(a) Schematics of spin precession due to the Rashba eect.
(b) Energy dispersion curves of 2­dimensional electron gas
with a strong spin­orbit coupling as well as a broken space in­version symmetry (Rashba­type spin split bands). (c) Fermi
surface contour of the Rashba­type spin split bands with hel­
ical spin textures.

»Ìlqð Fig. 5(a)É¦µÄ¢éB

2.3\Ê Rashba øÊñ³©RdqKXÉÂ¢ÄÍ Rashba ÉæÁÄðª¦

3 ³g|WJâÌ\ÊãÌ Dirac dqÌXs³êÄ¨èCn~gjAªûüªgxNgÉÎµÄ¼ÉÅè³êé±ÆÉÂ¢Äð·é½ßÉC»\ÊÉ¨¯é Rashba øÊÉÂ¢ÄmÁÄ¨­ÆÖÅ

HSOaR(kxsy|kysxjC(3)

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5(b)É¦³êélÉCgûüÉXsªô·é±Æªí

VCp Í^®Êð\µÄ¢éB±±ÅCXsO¹©é18)B±ÌêCÔ½]ÎÌ«©ç ka0 ðîÆµÝìpÌn~gjAÍ E|;V ÌÖWðp¢Ä

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190  úËõ July 2011 Vol.24 No.4

ðà ¡ úËõ ARPES ÅÆç¦ég|WJâÌÌ\Ê Dirac Fermion

Fig. 6

Schematic band structures of semi­innite crystals of (a) the
conventional and (b) the topological insulators.

2.4

g|WJâÌÌ»è@ÆÊÌâÌÆÌæÊ

³ÄC±±ÅÍg|WJâÌÆÊÌâÌðÇÌæ¤ÉµÄæÊ·é©ÉÂ¢Äq×½¢BÜ¸ Fig. 6(a)É¦·lÉCÊíÌâÌÅÍGbWóÔª¶Ý·éêÅàCæqÌ Rashba ^ÌXsªôohÌ`ðÆéBêûCg|WJâÌÌêÍ Fig. 6(b)Ìæ¤ÉC`±ÑÆ¿dqÑðÂÈ®æ¤ÈGbWóÔÆÈéBÇ¿çÌêÅàÔ½]ÎÌ«ªFig. 7(a) Crystal structure of Bi1_xSbx with rhombohedral unit cell(solid line) as well as hexagonal unit cell (dashed line). Two
hexagonal layers indicate bi­layer (BL) of Bi1_xSbx. (b) Bulk
Brillouin zone of Bi1_xSbx. (c) Schematics of bandstructureof Bi1_xSbx.

é½ßÉCk0 ÉÎµÄXsª½ÎÌÉÈÁÄ¢éBêÊÉÍïÌIÈ¨¿ÉÂÊiqÉÍ 2 ÂÌ Bi(Sb) ´qªÜÜêéB±Ì»\¢¢ÄXsO¹Ýìpðæèüê½Î_IÈoh\ÉÍ_üÅ¦³êÄ¢éæ¤ÉCÊÉZû»ihexagonalj¢vZðp¢Äg|WJâÌª\ª³êéBg|ÆµÄÌPÊiqÌæèûª

WJâÌÅÅÍ HÊÌ» ÌPÊiq ðp¢Äbð ··ßÄ¢ ­Bé©Û©ÍC¨¿Ìg®ÖÌpe

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ÅÍgjÅÌg®ÖðA±IÉÏ»³¹ÄàÛ¶³ê

ibilayerBLjª¶ÝµÄ¢éÌªí©éBñíÉ»¡[é½ßC±êðg|WJsÏÊÆµÄè`·é±Æª¢_ÆµÄC±êç¼³fÌà Bi1_xSbx Í Sb ÌZxÌoéB±ÌpeB[Ìôï«Í®Q Z Ì¤QÆµÁÉ]ÁÄC»\¢»ÌàÌÍÏíçÈ¢ªC¼à®

Ä Z2 ªp¢çêé©çCZ2 g|WJsÏÊÆÄÎ¨âÌ¨¼à®ÖÆÏ»µC³çÉÍg|WJsÏêCÊÌâÌÍ Z2 g|WJsÏÊªuôié¢Í 1jvÆ

ÊàÏ»·éBFig. 7(b)ÉoNÆ(111)\ÊÌuA][ð¦·BoNÌuA][ÉÍ G, T ¨µÄªÞ³êéB·Èí¿ Fig. 6(a)Å¦·ÊíÌâÌÍ

æÑ 3 ÂÌ¿È L, X _Ìv 8 ÂÌ TRIM ªÜÜêéB

¢Í 0jvCg|WJâÌÍuïi

ég|WJsÏÊªuôvÅCFig. 6(b)ÌêÍuïv

Fig. 7 ( c )Ì ¶ ¤ É ¦ · l É C Bi P Ì Í L _ É Ä G l Éµ»ê¼êá¤NXÉ®·éB±êçÌÙÈéN

M[MbvðÂªCT _É¨¯é¿dqÑ¸ãª LXÌâÌÍÝ¢ÉA±IÉJÚ·é±ÆÍoÈ¢±_ÅÌ`±ÑêÌGlM[æèàãÉé½ß¼à®ÆÆ©çCÙÈéNXÌâÌÌEÊÅÍK¸GlM[ÈéBSb ZxðÁ³¹éÆCFig. 7(c)ÌÉ

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WJsÏÊªuôvÌÊÌâÌÅ

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ÅÍÊÌ_Å¿dqÑ¸ãÌGlM[ªÁ·é½ß¼³ÄïÌIÈâÌÉÂ¢Ä Z2 g|WJsÏÊðéæà®ÉßéiFig. 7(c)EjB±±ÅÚµ½¢ÌÍCL _vZ·é±ÆÉæèCg|WJâÌð\ªoéÉ¨¯é¿dqÑ¸ãyÑ`±ÑÌêÅÌg®ÖÌp

ªC±±©çÍ»Ìû@ðÈPÉÐîµæ¤B±±ÅÍeB[ÅBi1_xSbx Æ¢¤àðæèã°éBBiCSb ÆàÉ V °³fÅèC»Í Fig. 7(a)É¦·lÈHÊÌ»irhombo­

hedraljÉªÞ³êCåf^\¢éBBi PÌÌêCL _É¨¢Ä¿dqÑ¸ãÌpeB[ÍuïvC`±ÑÌêÅÍuôvÅ

é

iFig. 7(c)¶jBSb ZxªÁ·éÆ L _ÅÌGlM[é¢Í A7 ^\¢ÆÄMbvªêxÂ¶CÄxMbvªJ¢Äs­iFig. 7ÎêéBÀüÅ¦³êÄ¢éæ¤ÉCHÊÌ»ÆµÄÌP(c)ÌÆEjBMbvªÂ¶½ãÍ¿dqÑ¸ãÌpúËõ July 2011 Vol.24 No.4  191

Table 1
d(G)

d(L)

d(T)

d(X)

(n0; n1n2n3)

Bi

|1

|1

|1

|1

(0; 000)

Bi1_xSbx

|1

{1

|1

|1

(1; 111)

Sb

|1

{1

|1

|1

(1; 111)(|1)n  _ dn n n(6)0

nj0, 1

(|1)n



1 2 3

_

i1, 2, 3

njmi0, 1; ni1

( j1, 2, 3)

dn n n1 2 3(7)±êç 4 ÂÌg|WJio[in0; n1n2n3jÌÅàCn0 ªdvÈÓ¡ð¿Cn0 1 ÌÍ strong

topologicalinsulator, n00 ÌÍ weak topological insulator ÆÄÎ
eB[ªuôvC`±ÑÌêªuïvÆpeB[ÌtêªÞ³êéBTable 1 É¦·lÉCBi Í 4 ÂÌg|W]ªNéBÀÍ±ÌupeB[Ìt]v±»CÊÌâJsÏÊªSÄ[ÅÌ©çg|WJâÌÖÆÏ»·éKvðÈÌÅ

é½ßCÊíÌ¨¿ÉªÞ³ê

éªCBi1_xSbx Æ Sb Íin0; n1n2n3 )(1E111jÆÈÁÄ

éB¢é±Æ©ç strong topological insulator ÉªÞ³êéB

É Fu Æ Kane ÉæÁÄè®»³ê½g|WJâ½¾µCSb ÍÀÛÉÍ¼à®Å

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for angle­resolved photoemission spectroscopy (ARPES)
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Bi2Se3 Ì\Ê Dirac R[ÆGlM[Ê±Ì®ðp¢ÄC\ÊàÌñ³ÌGlM[ohªUBi1_xSbx ª 3 ³g|WJâÌÆÈé±Æª_ðèÅ«éBêûC\ÊÉ¼Èg¬ª k ÉÂ¢\ª³ê½ãCÜàÈ­ ARPES ðp¢Ä Bi1_xSbx (111)ÄÍà|eV V0 ðp¢ÄCÌæ¤É±©ê\ÊÉ¨¯éï{Ì\ÊohªÏª³êC3 ³g|

úËõ July 2011 Vol.24 No.4  193

WJâÌÅ

é±ÆªÀØ³ê½27_29) B´`±¨¿â­Ö¨¿ÈÇlXÈ¨¿ÉÂ¢ÄÌ@\­»@\ð²×é±ÆðÚIÆµÄCARPES ðp¢½¤Í±êÜ
Å·ñÉsíêÄ«½ªC±êçÍdCïRÌAªèªæÉsíêÄ¢éÌÉÎµÄC3 ³g|WJâÌÌêÍtÉ ARPES ªæsµÄ¢éÆ±ëª»¡[¢B»ÌãCÃ­©ç¢MdÏ·ø¦ðÂÞ¿ÆµÄmçêÄ¢½ Bi2Se3 â Bi2Te3 Ìwó 2 ³»¨ª 3 ³g|WJâÌÅ

é±Æª_\ª³ê30)CARPES

Fig. 9(a) Crystal structure of Bi2Se3. (b) (c) Experimental energy
dispersion curves of Bi2Se3 taken along G _M and G _K direc­
tions. (d) Intensity maxima of ARPES spectra along G _M
and G _K lines as denoted with boxes and circles, respec­tively. The solid and dashed lines are a t with the eective
Hamiltonian along the G _M and G _K directions, respec­tively.

Fig. 10(a) Energy dispersion curve along along G _M direction(left) and constant energy contours at several energies from
0 (Dirac point) to 350 meV (Fermi surface). Selected con­stant energy contours at (b) 350, (c) 200 and (d) 100 meV.

ðp¢ÄÀØ³ê½31_33)BBi2Se3 â Bi2Te3 Ìg|WJsÏÊÍin0En1n2n3)(1E000jÆ±o³êCPêÌ
tF~Êª G _ÌÝðÍÞ strong topological insulator
ÉªÞ³êéi2.4QÆjBÅà Bi2Se3 Í Bi1_xSbx Éä
×CÉ¦·lÈÁ·ðÂ±Æª¾ç©É³êCå«È Ú ð  Ñ é æ ¤ É È Á ½ B » ê Í Bi2Se3 ª 0.3 eV Æ
Bi1_xSbx Éä×10{Èãå«ÈGlM[Mbvð¿Cº·Åà\ªoNÌâ«ªÛ½êéÆ¢¤_ªÁ½©ç¾B³çÉ Bi1_xSbx ÍsK¥àÅ

éªC

Bi2Se3 ÍXgCLIgbNÈ»¨Æ¢¤_Å§äªs¢â·¢Æ¢¤Á·à éB½æèàÅåÌÁ·ÍCæqÌæ¤É G _É\Ê DiracR[ªêÂ¾¯¶Ý·éÆ¢¤ñíÉVvÈ_Åë¤B³Ä Bi2Se3 »ÍCFig. 9(a)É¦·lÉCSe_Bi_Se_Bi_Se Æ¢¤ 5 ´qwðêÂÌjbgÆµÄ»êçªärIã¢ÝìpÅÏwµÄ¢é\¢ðÆÁÄ¢éBµÎµÎ±Ì 5 ´qwjbgÍNCgDvC[iquintuple layerQLjÆÄÎêéBFig. 9(b)Æ(c)ÉÍC
ä X ª ú Ë õ ð p ¢ Ä ª è µ ½ Bi2Se3 ( 111 ) \ Ê Ì
ARPES XyNgð»ê¼ê\ÊuA][Ì G
_M yÑ G _K ûüÉÂ¢Ä¦·34) BÇ¿çÌûüÉÂ¢Äà¼üIÈGlM[ªUÖWª¾çêÄ¨èCfBbN_Í EB 450 meV ÌÆ±ëÉÊuµÄ¢éBBi2Se3
ÌêCtF~GlM[ÍoNohMbvÌfBbN_tßÉÊu·éªC_vZ©ç\z³êÄ¢éª30) CFig. 9(b)Æ(c)ð©éÆí©éæ¤ÉCÀ±ÅÍfBbN_æè200 meV ¾¯¢GlM[ÊuæèoN`±ÑªÏª³êCtF~GlM[ð¡Ø

Bi2Se3 ÉÂ¢ÄÍC±Ìæ¤ÈÚ×È`óÉÂ¢ÄÍ±ÁÄ¢éB±êÍÀÛÌ»ÉÍ Se ´qÌ¹ª­µ¶êÜÅÀ±IÉÍ¾ç©ÉÈÁÄ¢È©Á½B±Ìæ¤ÈÝµC©RÉdqh[v³ê½±ÆÉæètF~Gl

Zp`ÌGlM[ÊÌÏ`ÍÌlÈ k¥p Û®n~M[ªÁµÄ¢é±Æð¦µÄ¢éB»Ì½ßoNð

gjAÌÌøÊÆµÄð³êé35)Bâ»·é½ßÉÍC³Eðh[vµtF~GlM[
ðoNohMbvÉÁÄ±È¯êÎÈçÈ¢B

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ARPES Éæè¾çê½CDirac _©çtF~x

(1)

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ÜÅÌ¢­Â©ÌGlM[É¨¯éGlM[Ê}bvð Fig. 10(a)_(d)É¦·BDirac _tßÅÍGlM[
Êª~`ÉÈÁÄ¢éªCtF~xtßÅÍ G _M±±Å k}kx}ikyCn ÍtF~¬xCl ÍÏ`p[ûüÉ¸_ðÂæ¤ÈZp`ÉÏ`µÄ¢éÌªí©

¾çêéGlM[ªUÖWÍC

^Csz ÍpEsñxNgÌ z ¬ªÅéB(7)®©ç

éB±Ìæ¤ÈGlM[ÊÌÏ`ÍCBi2Te3 P»ÅÍ æè° É »êÄ é± Æª ñ³ êÄ ¢½ª31) C

194  úËõ July 2011 Vol.24 No.4

E}k2/2mÞ} n2k2{l2k6 cos2 (3u)(12)

ðà ¡ úËõ ARPES ÅÆç¦ég|WJâÌÌ\Ê Dirac Fermion

Fig. 11(a) Calculated constant energy contours at several energies
from the eective Hamiltonian. Selected constant energy
contours at (b) 350 and (c) 200 meV shown with calculated
constant energy contours with the eective Hamiltonian.
(d) Schematic of the warped Dirac cones on the surface ofthe 3D topological insulator. (e) Illustration of scatteringchannels for the ideal (bottom) and weakly warped (mid­dle) and heavily warped (top) constant energy contours.

ÆÈéB±±Å u Í G _K ûü©çvÁ½pxÅ

Fig. 12éB¢Ü EÞß n3/l Æè`µ 0EEÞÌÍÍÉ¨¢ÄCV½Ék
ßk n/l Ææè¼µ½gÉÂ¢ÄGlM[Êð0.2EÞ²ÆÉvbgµÄ¢éiFig. 11(a)jBÀ±Å¾ç(a) Theoretical surface state dispersion (solid lines) and k||
projected bulk band structure (shaded area). An arrowshows possible surface to bulk scattering channel. (b) Cal­
culated constant energy contours at 250, 300, 350 and 435
meV for a slab of 5 f.u. (c) Predicted surface perpendicular
projection of spin polarization for the constant energy con­tours at 350 and 435 meV.

ê½ÊÆär·éÆCx E0.6 EÞÌÉtF~Ê`óªÇ­êv·é±Æªª©Á½BÉCARPES ªèèL¤ÉÚ®·éÆÏ`ª³çÉ­­ÈèCXsÌÊ¼Å¾çê½tF~¬xª v3.55 eV¥Å Åé±Æ©ç¬ª à17÷Ææèå«­ Èé±Æª \z³êé34) BÀÏ`p[^Í l128 eV¥Å3 Æ©Ïàçêé34)B»Ì

ÍC±Ìæ¤ÈXsÊ¼¬ªÌo»ÉæèCdqU`Ê EÞ600 meV yÑ EF 360 meV ÆÈèCFig. 11(b)Ééæ¤ÉÀ±ÊðÇ­Ä»·éB³çÉ Fig. 11(c)lªV½ÉÁ·éBà¿ëñËRÆµÄC|k ©
ç{kié¢Í»ÌtßöjÌ®SãûUÍÖ~³êÅ¦·lÉ E0.33 EÞÉ¨¯évZÊÍ EB200 meVéªCÊ¼Xs¬ªª½sÉÈégÌÔÅÌU`

ÅÌÀ±ÌGlM[ÊðÇ­Ä»·éBÈã©çClÍeÉÈé±Æª Fig. 11(e)©çf¦éBÀÛÉC

ARPES À±Å¾çê½ Bi2Se3 ÌGlM[ÊÌ EB Ë

GlM[ÊÌÏ`p[^ªæèå«¢ Bi2Te3 \¶«â»ÌÏ`ÍCk¥p Û®n~gjAÅÇ­à¾³

Ê i l  250 eV ¥ Å3 j É ¨ ¢ Ä  ¸ ^ g  l  ° ÷ ¾

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iSTMjÉæèGlM[ÊÌÏ`ÉNö·és¨â

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Bi2Se3 ÉÂ¢ÄÌMÒçÌ ARPES ªèÉæÁÄCt

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¬ªª»êC»êª G _K ûüÅÅåÆÈéB±ÌXsµCBi2Te3 ÙÇ­¢Ï`ÅÍÈ¢½ßC\ÊdqÌsÊ¼¬ªÌo»ÍC(7)®Ì k¥p Û®n~gjAÌ¨UÍ»êÙÇå«­ÍÈ¢Í¸ÅÉ sz ª©©ÁÄ¢é±Æ©çð³êæ¤BÀÛ

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éB±êÜÅc_Fig. 12(b)É¦·lÉCvZÊÍÀ±ðÇ­Ä»µCFig.

ðÁÄ¨èCtF~GlM[ÌÊu³¦±ÌMb12(c)É¦·lÉCfBbN_©ç350 meV ãÌGl
M[ÊiÀ±ÅÍtF~ÊÉjÅÍC G _K ûüvÉÁÄ­êÎCs¨Uªå«­}§³ê½z
IÈg|WJâÌÆÈè¤éBêûCFig. 12(a)ÉÅ12÷ÌXsÊ¼¬ªª»êéª¦³êÄ¢éBñ¦·æ¤Èæê´vZÉæè¾çê½oh\¢ð©ÄúËõ July 2011 Vol.24 No.4  195¢½¾«½¢B±êð©éÆm©É G _ßTÅ\Ê Dirac
R[ÍoNohÌGlM[MbvàÉ¶ÝµÄ¢éBµ©µC¿dqÑÌ¸ãª G _©çÍOê½Æ±ëÉ èC`±ÑÌêª G _É¶Ý·éB»Ì½ß G _MûüÅ©éÆfBbN_æèºÌ\Ê Dirac R[ÍCoNÌ¿dqÑÆGlM[IÉÙÚdÈÁÄ¢éBoNóÔÍ·×ÄXskÞµÄ¢é½ßCFig. 12(a)É¦·æ¤É\Ê Dirac R[ÆoNóÔÆðÔdqU`lª¶Ý·é±ÆÉÈéBÁÉCtF~x
ª Dirac _â»êæèàºÌGlM[ÉÊu·éêFig. 13(a) Rhombohedral primitive cell of TlBiSe2. The equivalenthexagonal lattice of TlBiSe2 with atomic layers stacked in
the sequence _Tl_Se_Bi_Se_Tl_. (b) A schematic diagramof the bulk Brillouin zone (BZ) of TlBiSe2 and the two­
dimensional BZ of the (111) surface. (c) kz plot as a func­tion of k||. In going from hn70 to 98 eV, the whole Bril­louin zone is scanned along the c axis.

Fig. 14

Theoretical projected bulk band structure of TlBiSe2 ob­tained with ideal atomic positions (a) and with fully op­
timized geometry (b). Lines show constant kz contours.

ÉÍUª­·é±Æª\z³êéB±Ìæ¤È\Ê_oNdqUÉNö·édqg±Âp^[ªCMÒçÌ STM ªèÉæèÏª³ê½39)Bà¿ëñCtF~GlM[ª Dirac _æèàãÅ©Â`±ÑÌêÌGlM[æèàºÌÍÍÉÊuµÄ¢êÎC\ÊÉ¨¢Äg|WJÉÛì³ê½Xs¬ªúÒ³êéªCÀpãC
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Fig. 14(b)Íæê´vZãÅÅK»³ê½iqèðp\ÊÌuA][ð¦µÄ¢éB³ÄC±±ÅÍÜ¢½êÌoh\¢vZÊð¦·BÀ±Å¾çê½i¸CæÉq×½ Fu Æ Kane Ìè@ðp¢ÄC¢­Â©Ì _Å`±ÑÌêªtF~Gl
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é½ßCFig. 14(b)ÌÊªæèzIÅðà ¡ úËõ ARPES ÅÆç¦ég|WJâÌÌ\Ê Dirac FermionéÆ¢¦éB±Ìæ¤ÉC¯¶æê´vZÅàiqè

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Fig. 15 É hn58 eV ÌúËõðp¢Äªèµ½ TlBiSe2lM[âÎõð§ä·é±ÆÉæÁÄCARPES XyNÌ G _tßÌ ARPES ªèÌÊð¦·BFig. 15(a)Í p G _M yÑÎõzuÅªèµ½\ÊuA][ M_gÉ¨¯éoNóÔÌñ^ð¬³­·é±ÆªÅ«C\Ê Dirac R[ÌlqðÚ×É²×é±ÆªÂ\ÅK_ G _K ûüÉÂ¢ÄÌÊð»ê¼ê¶¤ÆE¤É¦é45)B·BÜ½Cã¤Í ARPES ÌC[W}bvCº¤ÍC^»±ÅCFig. 15(c)É¦·lÉCüËõGlM[ hn®ÊªzÈüiMDCjð¢­Â©ÌGlM[ÉÂ¢Ä58 eV Ì s ÎõÅªèµ½ TlBiSe2 Ì\Ê Dirac R[ðÀ×½àÌð¦µÄ¢éBFig. 15(a)ð©Ä¾ç©ÈlÉCBi2Se3 \ÊÌàÌÆärµÄ¢­±ÆÉ·éBFig. 15(c)X ^ÌGlM[ªUÖWª¾mÉÏª³êÄ¢éBü

ÅÍC¼ÒÉÂ¢Ä Dirac _ðîÆµÄvbgµÄ¢ËõÌGlM[ðÏ¦ÄàC±ÌGlM[ªUÖWÉéBÜ¸CÃ­±ÆÆµÄCBi2Se3 Ì\Ê Dirac R[ÍCÏ»ª©çêÈ©Á½±Æ©çCkz ûüÉGlM[ªDirac _æèàãÌGlM[ÅCoN`±ÑÉßÃ­UÌÈ¢ñ³IÈdqóÔC·Èí¿ 3 ³g|WÉÂ êÄå« ­È¦ð ÁÄ¢é±Æ ÅJâÌÁLÌ\Ê Dirac R[Å é±ÆªmM³ê
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tßÉoN¿dqÑª©©ÁÄ¢éªCK_hÌXÎªå«­ÈÁÄ¢éB±êÍÜ³ÉCTlBiSe2

Fig. 15éBê ûCARPES on TlBiSe2(111): k|| dispersion (upper) and momentum­space cuts (lower) measured with photon
energy of 58 eV with (a) p­ and (b) s­polarized light along G _M and G _K lines. (c) Intensity maxima of the sur­face state along G _K line together with the result for Bi2Se3 (ARPES energy dispersion for Bi2Se3 is in inset).

úËõ July 2011 Vol.24 No.4  197

Fig. 16(a) ARPES energy dispersions for hn84 eV in the wide k||range along M_
 G _M together with the momentum distribu­
tion curves at the binding energies of (b) 180, (c) 340, and(d) 620 meV (cut 1_cut 3). (e) The experimental energy
dispersion for hn98 eV.

Fig. 17

Schematic energy diagram of surface and bulk states of
TlBiSe2 derived from the experimental results.

ðÏª·é±ÆÉÈéªC±ÌêCFig. 16(e)É¦·l _tßÌoN`±ÑÌ­xª®SÉÁ¸µÄ¢
ÉC MÌ Dirac dqÌQ¬xªCBi2Se3 æèà¬¢±Æð\µÄéÌªí©éBÈãÌÊæèCoNdqóÔÆ\Ê¢éBÀÛÉ ARPES ªèÌÊ©çQ¬xð©ÏàéÆC

Dirac R[ÌÖWðÍ®IÉ¦µ½Ìª Fig. 17 Å

TlBiSe2 Ì Dirac d qÌQ ¬x Í3.9~ 105 m/s ÆÈ èC _Æ G _·Èí¿CTlBiSe2 ÌoN¿dqÑÌ¸ãÍ M

Bi2Se3 Ì2.9~105 m/s æèà30÷öxå«¢45)BM ÌÔÅ©Â EB540 meV ÌÆ±ëÉCoN`±ÑÌ±Ìæ¤É TlBiSe2 Ì\Ê Dirac R[ªCBi2Se3 ÉäéB _É¶Ý·éB³çÉdvÈ±êÍ EB 240 meV Å M

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hn84 eV ÅãNµ½ G _M ûüÌ ARPES ªèÌÊð^C vÌ¤ Æ¢¦éB {ðàÅq× ½lÈCú Ëõ¦·B±±ÅÍæêuA][Ì G1st _©çæ 2uA][Ì G2nd _ÜÅÌärIL¢gÌæÅ

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_Æ G2nd _ÅÍCÆàÉ¿È\Ê Dirac R[ªÏªÌÌ\Ê Dirac R[ÌwJXseNX`[ÜÅARPES ªo­_ÆÈÁÄÀ±ªiñÅ¢éÆ¢¤Vµ¢
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Bi1_xSbx â Bi2Se3 ÉÂ¢ÄÍÀÛÉXsªðªèªÈ³_tßÌdqóÔªÏª³êéB±±ÅÍ¦µÄ¢È¢ªêÄ¢é28,32)B½¾µêÊIÉÍC3 ³g|WJâhn74 eV ©çüËõGlM[ðÁ³¹Ä¢­Æ MÌÌ\Ê Dirac R[ÌtF~Êièé¢ÍGl_tßÉ»êé ARPES XyNgÌ©GlM[ªå

M[Êjª¬³­CQ¬xªå«¢½ßC¢gªð\«­ÈÁÄ¢«Cx hn84 eV ÅÜèÔ·lqªÏªªªèÉÍv³êéªC]^ÌXsoíðp¢½³ê½BFig. 16(b), (c), (d)Í»ê¼ê EB180, 340, 620ªèÅÍø¦ªá¢½ß¢¸xÅ\Ê Dirac R[ÌXmeV Å Ì MDC ð ¦ µ Ä ¢ é B » ê ð © é Æ EB  180sóÔð¨¦éÌª¢ïÅÁ½B»ÝC{¤O[meV É¨¢Ä M _Éã¢ÈªçàoN`±ÑÉÎ·vÅÍ]^æèà100{ø¦Ì¢Vµ¢^CvÌXs

éXyNg­xª»êCÜ½ EB620 meV É¨¢ÄÍoíðõ¦½Xsªð ARPES ªèuðúËõ

oN¿dqÑÉÎ·éóÔªÏª³êÄ¢éB±Ìær[CÉÄ§¿ã°Ä¢é46,47)B¡ãCVµ¢g|¤ÉúËõ ARPES ÉæÁÄCEB 240 meV ÉoN`WJâÌÌJ­ÆÆàÉC±¤¢Á½úËõXs±ÑÌêCEB 540 meV ÉoN¿dqÑÌ¸ãª­éªð ARPES ÌpªÜ·Ü·KvÆÈÁÄ­éÅ ë¤B±Æª¾ç©ÉÈÁ½BêûChn98 eV ÌGlM[ÅãNµ½êCFig. 13(c)ð©éÆ L _tßÌoNóÔ

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úËõ July 2011 Vol.24 No.4  199 ÒÐî Øººv

Låwåw@w¤È¨ÈwêUy³ö
E­mail: akiokhiroshima­u.ac.jp
êåF\Ê¨C¥«¨
mªðn
1995Nåãåwåw@îbHw¤ÈmãúÛö¨nêUC¹Cmiw)Båw¨«¤O¹úË¨«¤{Ý èCLåwåw@w¤ÈÉy³öBXspxªðõdqªõðp¢½¥«´âg|WJâÌÌXsdqóÔÌ¤É]B
1999N 4 æè»E

Surface Dirac Fermion captured by synchrotron
radiation ARPES
Akio KIMURA

Graduate School of Science, Hiroshima University
1_3_1 Kagamiyama, Higashi­Hiroshima 739_8526, Japan

Abstract Topological insulators, which are based on the totally new concept of solid state physics, possess
gapless states at edges and surfaces while they show insulating behavior without current ows inside. Be­
sides, massless and spin polarized Dirac Fermions exist at the edge and the surface of the topological insula­tor. These lead to a quite fascinating property such as a suppressed electron backscattering at defects and im­
purities, which opens a pathway to realize a dissipationless spin­based devices and a next­generation super­computer. Such surface Dirac Fermions can be well traced by the combination of synchrotron radiation andangle­resolved photoemission spectroscopy (ARPES). After an instruction of the topological insulator, our re­cent ARPES experiments on the surface Dirac cones of the 3D topological insulators will be shown. Finally, it
is emphasized here that the synchrotron radiation plays an important role in experimental realization of the
new family of 3D topological insulators using ARPES.

200  úËõ July 2011 Vol.24 No.4