On the Origin of Two Dimensional Electron Gas States om TI

ISSN 0021�3640, JETP Letters, 2011, Vol. 94, No. 2, pp. 106–111. © Pleiades Publishing, Inc., 2011.Original Russian Text © T.V. Menshchikova, S.V. Eremeev, E.V. Chulkov, 2011, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2011, Vol. 94, No. 2,pp. 110–115.

106

The study of three�dimensional topological insula�tors is a rapidly developing field of physics. The surfaceof this type of materials has a metallic character,whereas the bulk is an insulator. The conducting prop�erties of the surface originate from the strong spin–orbit coupling, which leads to the formation of spin�split topological surface states that have Dirac�typedispersion. These states are protected from scatteringon defects by the time�reversal symmetry, which givesa potential possibility of using them in new spintronicdevices.

Recently, angle resolved photoemission measure�ment results have been published in [1] for the layeredtopological insulator Bi2Se3 [2]. After the formation ofthe surface, only the topological surface state wasobserved inside the bulk gap. After keeping the samplein a vacuum for 3 h, a shift in chemical potential wasdetected in Bi2Se3 in [1], which was accompanied bythe formation of new parabolic and M�shaped statesnear the conduction band bottom and inside thevalence band, respectively. The parabolic state wasinterpreted in [1] in terms of a two�dimensional elec�tron gas due to the band bending near the surface,which coexists with the surface topological state. TheM�shaped state was recognized in [1] as a surfacestate, but no analysis of its origin has been given. Bian�chi et al. [1] believe that the band bending at the sur�

face is caused by the emergence of different defects(impurities) at the surface. The presence of similarparabolic and M�shaped states was detected in [3, 4]after deposition of both para� and ferromagneticatoms at the Bi2Se3 surface, emerging regardless of thetype of deposited atoms. It has been shown in [5, 6]that impurities in layered compounds do not stay at thesurface, but diffuse into the van der Waals (vdW) gap,causing the gap expansion.

In this work, we show that the formation of bothparabolic and M�shaped states in Bi2Se3 is caused bythe effect of the broadening of the vdW gap rather thanby the chemical nature of the impurities. Using themodel of the broadening of the vdW gap nearest to thesurface, we show that the parabolic state form a two�dimensional electron gas, which is localized predomi�nantly in the outermost quintuple layer, whereas theM�shaped state inside the valence band is localizedpredominantly in the region of the expanded vdW gap.In order to confirm that this phenomenon is commonfor layered topological insulators, we also study theelectronic structures of binary Sb2Te3 topological insu�lator and ternary Sb2STe2 and Sb2SeTe2 compounds.We show that the ternary compounds are topologicalinsulators similar to Sb2Te3. In this work, we perform adetailed analysis of the effect of broadening for Sb2Te3,which reveals the formation of new surface states and

On the Origin of Two�Dimensional Electron Gas States at the Surface of Topological InsulatorsT. V. Menshchikovaa, S. V. Eremeeva, b, and E. V. Chulkovc

a Tomsk State University, pr. Lenina 36, Tomsk, 634050 Russiab Institute of Strength Physics and Materials Science, Russian Academy of Sciences, Siberian Branch,

Akademicheskii pr. 2/1, Tomsk, 634021 Russiae�mail: [email protected]

c Donostia International Physics Center (DIPC), and CFM, Centro Mixto CSIC�UPV/EHU, Departamento de Física de Materiales, UPV/EHU, Apdo. 1072, 20080 San Sebastián, Spain

Received May 18, 2011

The ab initio calculations of the electronic structure in the bulk and at the (0001) surface of narrow�bandBi2Se3, Sb2Te3, Sb2STe3, and Sb2SeTe2 semiconductors have been performed. It has been shown that ternarycompounds Sb2STe2 and Sb2SeTe2, as well as the previously known compounds Bi2Se3 and Sb2Te3, are three�dimensional topological insulators. The influence of the subsurface van der Waals gap expansion on the sur�face electronic structure of these compounds has been analyzed. It has been shown that this expansion leadsto the formation of new (trivial) surface states, namely a parabolic state in the conduction band and an M�shaped state in the valence band. These results explain the phenomena discovered recently in photoemissionexperiments and reveal the nature of new states that are caused by the adsorption of atoms on the surfaces ofthe layered topological insulators.

DOI: 10.1134/S0021364011140104

JETP LETTERS Vol. 94 No. 2 2011

ON THE ORIGIN OF TWO�DIMENSIONAL ELECTRON GAS STATES 107

their localization with various expansions of the vdWgap, which simulates the change in the concentrationof the impurity atoms and their atomic size. Similarly,the increase in the vdW gap causes the splitting of theparabolic state from the bottom of the conductionband in the ternary compounds, but it does not lead tothe formation of the M�shaped state because of smalllocal band gap in the valence band.

The electron band structure was calculated usingthe electron density functional formalism, imple�mented in the VASP code [7]. We employed the pro�jector augmented�wave method [8] in order to takeinto account the interaction between the ion cores andvalence electrons. In order to construct the exchange�correlation potential, the generalized gradient approx�imation (GGA) was used [9]. We included scalar rela�tivistic corrections into Hamiltonian. Spin–orbit cou�pling was taken into account by the second�variationmethod [10]. Experimental lattice parameters wereemployed for all of the studied systems.

Ternary compounds Sb2STe2 [11] and Sb2SeTe2

[12, 13] under study are characterized by a tetradym�ite�like structure as the well�known binary compoundsBi2Se3 and Sb2Te3. The unit cell of the hexagonal lat�tice of the ternary compounds can be represented asthree quintuple blocks that alternate in a series alongthe hexagonal c axis. The difference from Sb2Te3 is thatthe central layer in each quintuple block of the ternarycompounds is replaced by S or by Se (Fig. 1a). Thebonds inside these quintuple layers (Te–Sb–M(S,Se)–Sb–Te) have a predominantly ion�covalentcharacter, whereas weak van der Waals forces actbetween the blocks.

Since Bi2Se3 has been widely studied (see, e.g.,[14]), we show the calculated bulk band structuresonly for Sb2Te3, Sb2SeTe2, and Sb2STe2 in Figs. 1b–1d.One can see in Figs. 1b–1d that all these compoundsare narrow gap semiconductors with indirect bandgaps. The band gap in the case of Sb2Te3 is 125 meV.The substitution of Te by S or Se in the central layerdoes not change the character of the gap, but it causes

Fig. 1. (a) Hexagonal unit cell: M = S, Se (in the case of Sb2STe2 and Sb2SeTe2). Bulk spectra for (b) Sb2Te3, (c) Sb2STe2, and(d) Sb2SeTe2.

Sb2Te3

108


MENSHCHIKOVA et al.

its broadening up to 299 and 337 meV, respectively. Ananalysis of the orbital composition of the states at theedges of the band gap of Sb2SeTe2 and Sb2STe2 com�pounds has shown that, similar to binary Sb2Te3 chal�cogenide, there is an inversion of Sb and Te states near

that form the edges of the gap, which is induced bythe spin–orbit coupling. This gives evidence that ter�nary compounds Sb2SeTe2 and Sb2STe2 are also topo�logical insulators.

A considerably larger gap in these ternary com�pounds makes it possible to use their spin�polarizedtransport in a wider temperature region as comparedto binary Bi2Te3 and Sb2Te3 compounds. For this rea�son, these ternary compounds are as attractive forapplications as Bi2Se3. In order to interpret the newstates in Bi2Se3 found in [1, 3, 4], we consider a modelof a 40% expanded subsurface vdW gap. We show elec�tronic structures of the ideal Bi2Se3 (0001) surface andthe surface with the expanded vdW gap in Figs. 2a and2b, respectively. Since the electronic structure of theideal Bi2Se3 surface has been studied in numerousworks, we do not describe it in detail.

Γ

It can be seen in Fig. 2b that the Dirac state survivesafter the detachment of the outermost quintupleblock, but its charge density is redistributed from thisblock (in the case of an ideal surface [14]) to the sec�ond block from the surface (Fig. 2c). Both the para�bolic state inside the conduction band and the M�shaped state split from the valence band gap emergeduring this process. The charge density distribution ofthe parabolic state along the z axis is shown in Fig. 2c.It can be seen that broadening of the vdW gap leads tothe formation of the two�dimensional electron gasstate, which is well localized in the outermost quintu�ple block, formed predominantly by the pz�orbitals ofBi atoms. The M�shaped state is formed mainly by thepz�orbitals of Se atoms, situated on both sides of theexpanded vdW gap (Fig. 2c).

The formation of the new states as a result of theexpansion of the vdW gap should be a common phe�nomenon in layered systems. In order to analyze theprocess of the formation of new states, we study Sb2Te3

in detail during a successive expansion of the vdW gapfrom 10 to 40%.

Fig. 2. Band spectrum of Bi2Se3 for (a) ideal (0001) surface (gray color shows the projection of the bulk electron states and solidlines show the spectrum of a 30�layer film), (b) (0001) surface with 40% expansion of the vdW gap (the spectrum is shown in the

vicinity of the point). (c) Charge density of the (solid line) Dirac, (dashed line) parabolic, and (dash–dot line) M�shaped

states, which has been averaged over xy at the point.

Γ

Γ

1st



Fig. 3. (a) Band spectrum of the ideal (0001) surface of Sb2Te3. (b) Charge density of the Dirac state for the ideal surface. (c, e,g, i) Band spectrum for surfaces with the expansion of the vdW gap by 10, 20, 30, and 40%, respectively. (d, f, h, j) Charge densityfor the (dashed line) parabolic, (solid line) Dirac, (dash–dotted line) M�shaped states, which has been averaged over xy, for thesurface with the expansion of the vdW gap by 10, 20, 30, and 40%, respectively.

First, we consider the spectrum of an ideal Sb2Te3

surface and the constant energy cuts of the cone at var�ious energies (see inset in Fig. 3a). It can be seen in thisfigure that the shape of the cone is regular only nearthe Dirac point. Away from the Dirac point, the hex�agonal warping starts to emerge, and the constantenergy cut near the bottom of the conduction band hasthe shape of a snowflake similar to the case of Bi2Te3

[15]. A spin�split pxy surface state lies near the bottom

edge of the local gap in the valence band similar tothe case of Bi2Se3, and this state is mainly localizedwithin the outermost quintuple block at the central Teatom.

When the vdW gap is expanded by 10% (Fig. 3c), aweakly localized parabolic state appears at the bottomof the conduction band. One can see a large peak nearthe lower surface of the detached quintuple block inthe charge density distribution of this state (Fig. 3d).

Γ

The Dirac state starts to shift to the second quintupleblock: the weight of this state in the second blockincreases. A further 20–40% increase in the vdW gapcauses the detachment of the parabolic state from theconduction band. In the case of a 30–40% increase(Figs. 3h, 3j), this state becomes completely localizedinside the outer quintuple block, while the Dirac statelocalizes within the second quintuple layer. The M�shaped state also starts to detach from the bulk band,when expansion becomes as high as 20% (Fig. 3e).Further increasing of the vdW gap up to 30–40% leadsto the complete detachment of the M�shaped statefrom the valence band edge into the local energy gap(Figs. 3g, 3i) and to the redistribution of the chargedensity of this state into two upper quintuple blocks.

We now consider ternary layered compounds. Theband spectrum of the ideal Sb2SeTe2 surface is shownin Fig. 4a. The substitution of Te by Se in the centrallayer causes a shift of the Dirac point to the bulk gap as

110


MENSHCHIKOVA et al.

opposed to the case of Sb2Te3, where the Dirac pointwas below the top of the valence band. The local gapinside the valence region is considerably narrower thanthat in Sb2Te3. The surface pxy states shift to the upperedge of this gap. Similar features are also observed inthe valence band of Sb2STe2 (Fig. 4c). The Dirac pointin this compound is also inside the bulk gap, and thecone is more ideal than the cases described above (onecan see from the inset that hexagonal warping becomesvisible only near the bottom of the conduction band).

The charge density of the Dirac state in these sys�tems is localized within the outermost quintuple blockas in the case of the binary compounds. The expansionof the vdW gap in these compounds also leads to theformation of the parabolic band (Figs. 4b, 4d). Thecharge density distribution of both topological andparabolic states is similar to that of correspondingstates in binary compounds. However, as opposed tothe case of the binary compounds, there is no M�shaped state in ternary compounds. It can beexplained by the small value of the energy gap insidethe valence band, where the surface pxy states lie closeto the upper edge of this gap.

Finally, we have studied the electronic structure ofbinary compounds Sb2Te3 and Bi2Se3, as well as of ter�nary compounds Sb2STe2 and Sb2SeTe2. We haveshown that the ternary compounds based on Sb2Te3

are topological insulators. The substitution of Te by Sand Se in the central layer in Sb2Te3 leads to some pos�itive effects, i.e., a significant broadening of the bandgap, rise of the Dirac point to the Fermi level, and amore perfect shape of the Dirac cone. These proper�

ties make these compounds (in particular, Sb2STe2) asattractive for applications as Bi2Se3, which is widelystudied. We have shown that the expansion of the vdWgap, rather than the chemical nature of impurities,underlies the formation of the parabolic and M�shaped states, which were recently discovered inexperiments [1, 3, 4]. As a result of this expansion, thetopological state shifts to the second quintuple blockand becomes a deep surface state. The parabolic stateis localized inside the outermost quintuple layer andforms a well�localized two�dimensional electron gas.The M�shaped state is localized within the interfaceregion between the detached quintuple layer and thebulk crystal. This state does not form in the ternarycompounds due to their narrow valence band gap.

Numerical calculations were performed at theSKIF�Cyberia (Tomsk State University) and by Arina(Basque Country University) supercomputers.

REFERENCES

1. M. Bianchi, D. Guan, S. Bao, et al., Nature Commun.,No. 1:128 (2010). doi: 10.1038/ncomms1131.

2. K. Kuroda, M. Arita, K. Miyamoto, et al., Phys. Rev.Lett. 105, 076802 (2010).

3. L. A. Wray, S.�Y. Xu, and Y. Xia, Nature Phys. 7, 32(2011).

4. Z.�H. Pan, D. R. Gardner, and S. Chu, arXiv:1104.0966v1 (2011).

5. S. Sh. Kakhramanov, Inorg. Mater. 44, 13 (2008).

6. Y. S. Hor, A. J. Williams, J. G. Checkelsky, et al., Phys.Rev. Lett. 104, 057001 (2010).

Fig. 4. Band spectrum of (a, c) the ideal Sb2SeTe2 (0001) and Sb2STe2 surfaces, respectively, and (b, d) the respective surfaceswith 40% expansion of the vdW gap.



7. G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6,15 (1996).

8. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758(1998).

9. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. 77, 3865 (1996).

10. D. D. Koelling and B. N. Harmon, J. Phys. C 10, 3107(1977).

11. D. C. Grauer, Y. S. Hor, A. J. Williams, and R. J. Cava,Mater. Res. Bull. 44, 1926 (2009).

12. E. A. El�Sayad and G. B. Sakr, Cryst. Res. Technol. 40,1139 (2005).

13. R. L. Benbow, M. R. Thuler, and Z. Hurych, Phys. Rev.B 28, 4160 (1983).

14. S. V. Eremeev, Yu. M. Koroteev, and E. V. Chulkov,JETP Lett. 91, 387 (2010).

15. T. V. Menshchikova, S. V. Eremeev, Yu. M. Koroteev,et al., JETP Lett. 93, 15 (2011).

Translated by A. Kapustin

Documents

On the Origin of Two Dimensional Electron Gas States om TI