Pyridine intercalated Bi 2 Se 3 heterostructures: controlling the topologically protected states
PPyridine intercalated Bi Se heterostructures: controlling the topologically protected states I. S. S. de Oliveira a) and R. H. Miwa Departamento de F´ısica, Universidade Federal de Lavras, C.P. 3037, 37200-000, Lavras, MG,Brazil Instituto de F´ısica, Universidade Federal de Uberlˆandia, C.P. 593, 38400-902, Uberlˆandia, MG,Brazil (Dated: 26 October 2018)
We use ab initio simulations to investigate the incorporation of pyridine molecules (C H N) in the vander Waals gaps of Bi Se . The intercalated pyridine molecules increase the separation distance betweenthe Bi Se quintuple layers (QLs), suppressing the parity inversion of the electronic states at the Γ-point.We find that the intercalated region becomes a trivial insulator. By combining the pristine Bi Se regionwith the one intercalated by the molecules, we have a non-trivial/trivial heterojunction characterized by thepresence of (topologically protected) metallic states at the interfacial region. Next we apply an externalcompressive pressure to the system, and the results are (i) a decrease on the separation distance between theQLs intercalated by pyridine molecules, and (ii) the metallic states are shifted toward the bulk region, turningthe system back to insulator. That is, through a suitable tuning of the external pressure in Bi Se , intercalatedby pyridine molecules, we can control its topological properties; turning-on and -off the topologically protectedmetallic states lying at the non-trivial/trivial interface.Three dimensional topological insulators (TIs) are in-sulator materials in the bulk phase, but they presentmetallic topological surface states (TSSs), which are pro-tected by time-reversal symmetry; as a result backscat-tering processes by time-reversal invariant impurities ordefects are forbidden . These materials are of greatpromise for spintronics applications, due to the formationof nearly dissipationless spin-polarized surface current .Currently, Bi Se is one of the most investigated TI dueto its large band gap ( ∼ . Bi Se presents a rhombohedral structure composed by quintu-ple layers (QLs) of Se and Bi atoms, forming a sequenceof Se–Bi–Se–Bi–Se atoms covalently bonded; these QLsare stacked along the c –axis of a hexagonal structure byvan der Waals (vdW) interactions.Recent experiments have been exploring the possibil-ity of inserting guest species in the vdW gaps of Bi Se ,this process is known as intercalation. Koski et al. have added various zerovalent metals in the vdW gaps ofBi Se nanoribbons, it is expected that new propertiesand/or tuning of the Bi Se properties can be achievedby intercalation, e.g. superconductivity . Beside met-als, molecules have been intercalated in Bi Se , for in-stance, it has been shown that pyridine molecules inBi Se present interesting properties for optoelectronicapplications .In this work we aim to investigate the geometry andelectronic structure of Bi Se intercalated by pyridinemolecules (py-Bi Se ). Upon the presence of the pyri-dine molecules between the QLs, we find that the py-Bi Se system becomes a trivial insulator. By consider-ing a heterojunction composed by py-Bi Se and pristineBi Se (py-Bi Se /Bi Se ), we analyze (i) the occurrence a) Electronic mail: igor.oliveira@dfi.ufla.br of topologically protected metallic states embedded inpy-Bi Se /Bi Se , and (ii) the control of those metallicstates (turning-on and -off) upon the application of ex-ternal pressure.The calculations are performed based on the density-functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) . We use the gen-eralized gradient approximation (GGA), in the form pro-posed by Perdew, Burke and Ernzerhof , to describethe exchange-correlation functional. The Kohn-Sham or-bitals are expanded in a plane wave basis set with an en-ergy cutoff of 400 eV. The electron-ion interactions aretaken into account using the Projector Augmented Wave(PAW) method . All geometries have been relaxed un-til atomic forces were lower than 0.02 eV/˚A. The Bril-louin Zone is sampled according to the Monkhorst-Packmethod , using at least a 3 × × , whichis implemented on VASP . The inclusion of van derWaals forces in the simulations is necessary to obtain thecorrect vdW gap between two QLs , the interaction be-tween molecule and Bi Se is also better described withthe inclusion of vdW interactions.Initially we calculate the equilibrium distance ( z ) be-tween two consecutive QLs of Bi Se , vdW gap. Here wehave considered two isolated QLs and minimize the totalenergy as a function of the width of vdW gap (∆ z ) .As shown in Fig. 1 (squares), we find the energy mini-mum for z = 2.65 ˚A; this result is in agreement with ex-perimental measurements , and recent theoretical stud-ies . By using the same procedure, we determine z upon the presence of a pyridine molecule intercalated inbetween the QLs. The QLs present a 2 × × − mol./˚A . In this case, we find that (i) there1 a r X i v : . [ c ond - m a t . m t r l - s c i ] S e p ∆ z [Å] -1-0.500.5 ∆ E [ e V ] FIG. 1. Formation energy for two Bi Se QLs at variousseparation distances. Black line (circles) represents the pris-tine system and red line (squares) the system with a pyridinemolecule intercalated between the 2 QLs. is no chemical bonding between the molecule and theBi Se QLs, and (ii) the vdW gap increases by 3.85 ˚A, z = 2.65 → Se QLs is still an exothermic process.TIs present a parity inversion between valence andconduction bands due to spin–orbit coupling (SOC). ForBi Se the bulk phase presents a band parity inversionat the Γ-point, namely the SOC induces a band inver-sion between Se pz -orbitals in the valence band and Bi p z -orbitals in the conduction band . We use this charac-teristic to determine whether the material is behaving astrivial or topological insulator. Thus, by turning-off theSOC, we observe that higher energy levels of the valenceband have higher contribution from the Se pz -orbitals,while the lower energy levels of the conduction band aredominated by Bi pz -orbitals. Meanwhile, by turning-onthe SOC we observe an inversion between valence andconduction band orbitals around the Γ–point, promot-ing the (band) parity inversion. The same procedure wasapplied to examine if such a band inversion still occursin py-Bi Se . By considering the pyridine concentrationof 1.64 × − mol./˚A intercalated in Bi Se , we verifythat when the SOC is not included the py-Bi Se sys-tem is an insulator, where the valence band maximumis dominated by Se pz -orbitals and the conduction bandminimum by Bi pz -orbitals [Fig. 2(a)], as observed for thepristine Bi Se bulk. In contrast, by turning SOC on weobserve the lack of band inversion around the Γ–point[Fig. 2(b)], suggesting that pyridine molecules interca-lated in Bi Se bulk suppress its topological properties,namely, the py-Bi Se system is a trivial insulator.This topological–trivial transition in the Bi Se struc-ture is possibly caused by the increase in the vdW gapsdue to the pyridine intercalation. In order to verify suchan assumption, we calculate the electronic band struc-ture of Bi Se , but keeping the equilibrim geometry of FIG. 2. Band structures for (a) Bi Se bulk with intercalatedpyridine molecules excluding SOC, and in (b) including SOC.(c) Bi Se bulk with the vdW gap obtained in the system withintercalated molecules (Fig. 1), excluding SOC; and in (d)including SOC. The symbols are contributions of pz –orbitalsfor Se (red) and Bi (green) atoms. the pyridine intercalated Bi Se system. Our results arepresented in Figs. 2(c) and 2(d), by turning-off and -onthe SOC we observe that the band inversion at the Γ–point is still absent.In experiments we would most likely observe regionswith pyridine molecules intercalated between the vdWgaps and regions of pristine Bi Se , as a result wemay have a trivial/topological insulator heterojunctioncomposed by py-Bi Se and Bi Se (py-Bi Se /Bi Se ).To simulate such a heterojunction, we have consid-ered a supercell containing 9 QLs, where we have threeQLs intercalated by the molecules and six consecu-tive pristine QLs, (py-Bi Se ) /(Bi Se ) . As shown inFig. 3, the pyridine molecules are intercalated betweenQL(1) and QL(4), characterizing the (py-Bi Se ) re-gion, and QL(4)/QL(5)/.../QL(9)/QL(1) forms the pris-tine (Bi Se ) region. Given that geometry, the triv-ial/topological interface are characterized by QL(1) andQL(4). Band structure calculations reveal the presenceof metallic states forming a Dirac-like cone at the Γ-point, indicated by solid black lines in Fig. 3. To lo-calize these states we compute the pz -orbitals contribu-tion from various QLs around the Γ-point, and projectthese states in the energy levels shown in the band struc-ture . We find that the electronic states around theDirac point are mainly attributed to the Bi pz -orbitalslying at the py-Bi Se /Bi Se interface region, QL(1)and QL(4). In contrast, there are no electronic contri-bution to the metallic states from the py-Bi Se bulkregion, QL(2) and QL(3). Somewhat similarly, the elec-tronic contributions to the Dirac-like cone coming fromthe bulk region of Bi Se [QL(5)–QL(8)] are almost neg-ligible. Those findings allow us to conclude that (py-Bi Se ) m /(Bi Se ) n heterostructures (or superlattices)give rise to topologically protected metallic states, em-2 IG. 3. Each panel shows the band structure (full black lines)for the structure shown on the right side. The pz -orbitalstates is projected on the band structure for the first four QLs,where green circles represent Bi pz -orbitals and red circles Se pz -orbitals. bedded at the trivial/topological interface region. How-ever, it is worth noting that the appearence of those topo-logically protected sufaces states depends on the topo-logical film (Bi Se ) thickness (n). In Ref. the au-thors verified the presence of converged TSS for 3 QLsof Bi Se . On the other hand, in a recent study, we ver-ify the formation of TSSs for an interlayer spacing, i.e. vdW gap, larger than ∼ . Thus, we can inferthat it is possible to get topologically protected metallicchannels by considering just a single layer of py-Bi Se embedded in Bi Se .In order to verify the statement above, we construct asupercell containing one molecule separated by six Bi Se QLs, (py-Bi Se ) /(Bi Se ) , this structure is shown inFig. 4 (c). Indeed, we find the TSSs forming a Dirac-like cone at the Γ-point, as shown in Fig. 4 (a). Thosestates lie at the (py-Bi Se ) /(Bi Se ) interface region.The spin-texture of TSSs is constrained by the time re-versal symmetry. Here we calculate the expected valueof spin-polarization components ( (cid:104) S n ( k ) (cid:105) ) for the TSSs,of (py-Bi Se ) /(Bi Se ) , near the Dirac point. (cid:104) S n ( k ) (cid:105) can be written as (cid:104) S n,α ( k ) (cid:105) = ( (cid:126) / (cid:104) φ n ( k ) | σ α | φ n ( k ) (cid:105) , incartesian coordinates ( α = x, y, z ), where σ represents FIG. 4. (a) Band structure for the system depicted in (c),along the path shown in the projected surface 2D Brillouinzone represented in (b). The inset in (a) shows the spin-texture inside the blue square region around the Γ–point. the Pauli matrices, and φ n ( k ) the single particle Kohn-Sham eigenfunction, and n represents the band index.We have considered φ n ( k ) for wave vectors ( k ) alongthe Γ-M and Γ-K directions. As depicted in the inset ofFig. 4(a), for the electronic states parallel to the Γ-M di-rection, we find (i) positive (negative) values of (cid:104) S n,x ( k ) (cid:105) for the occupied (empty) states, while (ii) (cid:104) S n,y ( k ) (cid:105) = (cid:104) S n,z ( k ) (cid:105) = 0; whereas for k parallel to the Γ-K direc-tion, we find (iii) negative (positive) values of (cid:104) S n,y ( k ) (cid:105) for the occupied (empty) states, (iv) (cid:104) S n,x ( k ) (cid:105) = 0, and(v) (cid:104) S n,z ( k ) (cid:105) values are negligible around the Γ-point.Such a picture of (cid:104) S n,α ( k ) (cid:105) , for the TSSs lying at the(py-Bi Se ) /(Bi Se ) interface, is practically the sameas that obtained for the TSSs on the Bi Se (111) sur-face .We now propose a mechanism to gain control overthe topologically protected metallic states in (py-Bi Se ) m /(Bi Se ) n . In particular, we considered the(py-Bi Se ) /(Bi Se ) system. We apply a compres-sive pressure directed along the c –axis, namely normalto the QLs, decreasing the separation distance in thevdW gap (∆ z ) from 6.50 ˚A to 4.12 ˚A, upon an externalpressure of P ≈ . Se structures . The energy difference between the re-laxed and compressed (py-Bi Se ) /(Bi Se ) is shownin the upper part of Fig. 5. An energy of ∼
10 meV/˚A needs to be added to compress the system from ∆ z =6.50 to 4.12 ˚A. In the lower part of Fig. 5 we show theband structure for four values of ∆ z , starting from 6.50 ˚Awhich has already been shown to have metallic states.For ∆ z = 5 .
65 ˚A, the metallic states at the Γ-point arestill present. Upon further decrease of ∆ z , the metallicstates start to move in the bulk band direction. For ∆ z Γ M-0.300.30.6 E n e r gy [ e V ] ∆ z = 6.50 Å K Γ M ∆ z = 5.65 Å K Γ M ∆ z = 4.71 Å K Γ M ∆ z = 4.12 Å ∆ z [Å]0510 E [ m e V / Å ] FIG. 5.
Upper panel:
Energy per area to compress the re-laxed structure shown in Fig. 4 (c), reducing the vdW gapbetween the QLs separated by the molecule.
Lower panels:
Band structure for the various ∆ z values. = 4.71 ˚A, the Dirac point has been suppressed, as wefind an energy gap at the Γ-point. The energy gap at theΓ-point is even larger for ∆ z = 4 .
12 ˚A, washing out theTSSs at the (py-Bi Se ) /(Bi Se ) interface region. Byremoving the pressure the system can reversibly return toits original geometry, and again the metallic states will bepresent. Thus, we can combine pressure application andpyridine molecules intercalation to the Bi Se structureto turn the topologically protected metallic states on andoff, going from an insulator to a semi-metallic materialby taking advantage of the TI properties of Bi Se . Theresults presented above can be extended to any numberof QLs intercalated by molecules, assuring that we havea Bi Se /py-Bi Se junction.We have performed an ab initio study of pyridinemolecules intercalated in the vdW gaps of Bi Se (py-Bi Se ). In py-Bi Se the inter-QL distance increases,which turns the TI material into a trivial insulator. Byconsidering (py-Bi Se ) m /(Bi Se ) n heterojunctions, wefind a trivial/topological interface, characterized by thepresence of topologically protected metallic states (form-ing a Dirac-like cone) embedded at the interface region ofthe heterostructure. Such metallic states can be presenteven for a single QL incorporated by pyridine molecules,(py-Bi Se ) /(Bi Se ) n . Lastly, we have shown the pos-sibility to control the occurrence of such metallic statesin (py-Bi Se ) m /(Bi Se ) n , upon an external compres-sive strain; turning-on and -off those metallic states atthe heterojunction interface. Acknowledgments
This work was supported by the BrazilianNanocarbon Institute of Science and Technology(INCT/Nanocarbono), and the Brazilian agencies CNPqand FAPEMIG. The authors also acknowledge thecomputational support from CENAPAD/SP.
REFERENCES M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. , 3045(2010). D. Pesin and H. MacDonald, Nature Materials , 409(2012). H. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, andS. C. Zhang, Nature Phys. , 438 (2009). Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin,A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z.Hasan, Nature Phys. , 398 (2009). D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier,J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P.Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S.Hor, R. J. Cava, and M. Z. Hasan, Nature Lett. ,1101 (2009). K. J. Koski, C. D. Wessells, B. W. Reed, J. J. Cha,D. Kong, and Y. Cui, Journal of the American Chem-ical Society , 13773 (2012), pMID: 22830589. K. J. Koski, J. J. Cha, B. W. Reed, C. D. Wessells,D. Kong, and Y. Cui, Journal of the American Chem-ical Society , 7584 (2012), pMID: 22524598. Y. S. Hor, A. J. Williams, J. G. Checkelsky,P. Roushan, J. Seo, Q. Xu, H. W. Zandbergen, A. Yaz-dani, N. P. Ong, and R. J. Cava, Phys. Rev. Lett. ,057001 (2010). J. J. Cha, K. J. Koski, K. C. Y. Huang, K. X. Wang,W. Luo, D. Kong, Z. Yu, S. Fan, M. L. Brongersma,and Y. Cui, Nano Letters , 5913 (2013), pMID:24266743. G. Kresse and J. Furthm¨uller, Phys. Rev. B , 11169(1996). J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996). G. Kresse and D. Joubert, Phys. Rev. B , 1758(1999). H. J. Monkhorst and J. D. Pack, Phys. Rev. B , 5188(1976). A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. ,073005 (2009). T. Bucko, S. Leb`egue, J. Hafner, and ´Angy´an, Phys.Rev. B , 064110 (2013). H. Lind, S. Lidin, and U. H¨aussermann, Phys. Rev. B , 184101 (2005). The atomic positions of the Bi Se QLs and the inter-calated molecules were fully relaxed. H. Lind and S. Lidin, Solid State Sciences , 47 (2003),dedicated to Sten Andersson for his scientific contribu-tion to Solid State and Structural Chemistry. W. Zhang, R. Yu, H. J. Zhang, and Z. Fang, New J.Phys. , 065013 (2010). K. Park, J. J. Heremans, V. W. Scarola, and D. Minic,Phys. Rev. Lett. , 186801 (2010). O. V. Yazyev, J. E. Moore, and S. G. Louie, Phys.Rev. Lett. , 266806 (2010). L. Seixas, L. B. Abdalla, T. M. Schmidt, A. Fazzio,and R. H. Miwa, J. Appl. Phys. , 023705 (2013). L. B. Abdalla, L. Seixas, T. M. Schmidt, R. H. Miwa,4nd A. Fazzio, Phys. Rev. B , 045312 (2013). J. J. Hamlin, J. R. Jeffries, N. P. Butch, P. Syers, D. A.Zocco, S. T. Weir, Y. K. Vohra, J. Paglione, andM. B. Maple, Journal of Physics: Condensed Matter , 035602 (2012). K. Kirshenbaum, P. S. Syers, A. P. Hope, N. P. Butch,J. R. Jeffries, S. T. Weir, J. J. Hamlin, M. B. Maple,Y. K. Vohra, and J. Paglione, Phys. Rev. Lett.111