Lysogorskiy Yury Vyacheslavovich

Mamin Rinat Fajzrahmanovich

Piyanzina Irina Ivanovna

Tayurskii Dmitrii Albertovich

Kazan Federal University Digital Repository

ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2018, Vol. 82, No. 3, pp. 234–237. © Allerton Press, Inc., 2018.Original Russian Text © I.I. Piyanzina, Yu.V. Lysogorskiy, D.A. Tayurskii, R.F. Mamin, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Seriya Fizicheskaya, 2018, Vol. 82,No. 3, pp. 275–278.Electronic Properties of a Two-Dimensional Electron Gasat the Interface between Transition Metal Complex OxidesI. I. Piyanzinaa, b, *, Yu. V. Lysogorskiyb, D. A. Tayurskiib, and R. F. Mamina, baKazan Federal University, Kazan, 420008 RussiabZavoisky Physicotechnical Institute, Kazan Scientific Center, Russian Academy of Sciences, Kazan, 420029 Russia*e-mail: i.piyanzina@gmail.comAbstract—The structural and electronic properties of heterostructures based on transition metal oxides con-taining strongly correlated electrons are compared. The investigated structures are LaAlO3/SrTiO3(LAO/STO), LaAlO3/BaTiO3 (LAO/BTO), and BaTiO3/SrTiO3 (BTO/STO). The role of structural relax-ation in the formation of a two-dimensional electron gas at the interface of two dielectrics is revealed. Thecontribution from different orbitals and atoms to conductivity is analyzed, along with the correlation betweenstructural distortions induced by the dipole moment in an LAO layer and conductivity.DOI: 10.3103/S1062873818030188In 2004, Ohtomo and Hwang [1] reported anobservation of a high-mobility electron gas at an inter-face between LaAlO3 (LAO) and SrTiO3 (STO). Sincethen, heterointerfaces of these two nonconductingand nonmagnetic oxides have been observed innumerous studies. It was found that a metallic phase ofnanometer thickness (a two-dimensional electron gas,2DEG) forms in STO layers in structures with morethan three LAO layers and interface LaO and TiO2layers. This phase becomes superconducting at tem-peratures below 300 mK [3]. The electron density insuch heterostructures can be as high as 3 × 1013 cm−2.In addition, ferromagnetism was observed in aLAO/STO heterostructure in [4].Since STO is often used as a substrate, combina-tions of it and other compounds were examined insearching for emerging conductivity. A 2DEG was alsoobserved at interfaces between other nonmagneticdielectrics (e.g., KTaO3/SrTiO3 [5]). In addition, a2DEG was found at the interface with antiferromagneticLaTiO3 [6] having a maximum density of 3 × 1014 cm−2.Several authors have assumed that the emergenceof conductivity is related to structural (and thus elec-tronic reconstructions), but a clear explanation andmodel of this phenomenon have yet to be presented.The aim of this work was therefore to examine therelationship between electronic correlations, struc-tural distortions, and electronic reconstructions inLAO/STO and LaAlO3/BaTiO3 (LAO/BTO) hetero-structures, which contain polar LaO and AlO2 layers,and the BTO/STO heterostructure, in which the lay-ers are electrically neutral but the emergence of ferro-electric polarization in BTO, which can switched as aresult of external influences, may be expected.The density functional theory approach [7]employed in VASP [8] was used as a research tool.Since strong correlations between the electrons ofd-orbitals must be considered in modeling the elec-tronic properties of transition metal oxides, we chosethe GGA + U approximation for this, with correctionsintroduced as proposed by Dudarev [9]. ParameterU‒J was added to the La 4f and Ti 3d orbitals (U = 8and 2 eV, respectively). The magnetic nature of thematerial was ignored. Exchange and correlation effectswere accounted for by using the GGA-PBE general-ized gradient approximation [10]. Kohn–Sham equa-tions were solved using the basis of plane waves (PAW)implemented in VASP, which was integrated intoMedeA [11]. The cut-off energy was set at 400 eV, theresidual forces were 0.05 eV Å−1, and the energy con-vergence was 10−5 eV. The Brillouin zone was sampledusing a 5 × 5 × 1 grid.The unit cell of heterostructures contained a cen-tral region of SrTiO3 or BaTiO3 (4.5 unit cells withboundary TiO2 layers) surrounded from both sides byfour LaAlO3 layers with boundary LaO at the interfaceand AlO2 at the surface (halves of unit cells are shownin Fig. 1). This structure ensured lack of polarity and adipole moment induced by asymmetry. To avoid inter-action between surfaces and their periodic copies, a20 Å vacuum region was introduced into the calcula-tions. Lattice constant a = b = 3.905 Å was taken fromthe experimental data for cubic bulk SrTiO3. Theexperimental conditions of heterostructure growthwere thus reproduced [1]. These lattice parameters234ELECTRONIC PROPERTIES OF A TWO-DIMENSIONAL ELECTRON GAS 235Fig. 1. Density of states spectra for the nLAO/4.5STO/nLAO n-type heterostructure (n = 2, 3, 4, 5) and the corresponding halvesof unit cells.0204060800–2–4 2 4020406080020406080020406080 2 LAO3 LAO4 LAO5 LAOSTOSTOSTOSTOSr O LaTi AlOTiLa2p3d4fEnergy, eVDensity of states, 1/eVwere fixed in heterostructure optimization in order toimitate the rigidity of the STO substrate.Let us discuss the obtained results. It was demon-strated in [12] that introducing the parameter of Cou-lomb repulsion in a heterostructure into calculations isessential not only for simulating electronic properties,but also for optimization. In order to examine the elec-tronic properties of the heterostructure and determinethe point of transition into a conducting state, thedensities of states of heterointerfaces with differentnumbers of LAO layers were calculated for an idealcell and after structural optimization. In the case ofideal atomic positions (a = b = ∆c = 3.905 Å, where∆c is the distance between atomic layers), all hetero-structures with an arbitrary number of LAO layers areconductors. Their conductivity is induced by the over-lap of surface O 2p states and interface Ti 3d states.The optimization procedure has a critical effect on theelectronic properties: a gap between surface O 2p levelsand interface Ti 3d levels forms (see Fig. 1 forLAO/STO and Fig. 2 for LAO/ВTO). This gapshrinks as more LAO layers are added. The depen-dence of the bandgap width on the number of LAOlayers is then linear, which agrees with the polarizationcatastrophe theory. It is important that structural dis-tortions arise during optimization. These wave-likedistortions are seen clearly in Figs. 1 and 2: Aluminumatoms emerge out of oxygen planes (with the displace-BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCESment of atoms near the interface (Fig. 3) being thelargest). This strong lattice polarization balances outthe dipole electrical field in LAO, which is induced bythe alternate arrangement of oppositely charged lay-ers, and keeps the system dielectric as long as it con-tains less than five LAO layers. Electronic rearrange-ment then occurs, electronic states overlap, and thespectrum of the density of states starts to resemble thatof an ideal heterostructure.The properties of LAO/STO and LAO/BTO aresimilar in three ways: (1) the transition to a conductingstate occurs when the number of layers goes from fourto five (Figs. 1 and 2), and conductivity is establishedby the overlap of surface oxygen states and levels ofinterface titanium; (2) the displacement of aluminum(and titanium) from oxygen planes becomes moreprominent near the interface; (3) an increase in thenumber of layers results in the suppression of thedipole electrical field in LAO, which is reflected in theoff-plane displacement of Al atoms (minimum dis-placement for a conducting heterostructure) and Tiatoms (maximum displacement for a conducting het-erostructure).The primary difference between the properties ofLAO/STO and LAO/BTO heterostructures is thenature of displacements in the STO (or BTO) layer.This may be attributed to the ferroelectric properties: PHYSICS  Vol. 82  No. 3  2018236 PIYANZINA et al.Fig. 2. Density of states spectra for the nLAO/4.5ВTO/nLAO n-type heterostructure (n = 2, 3, 4) and the corresponding halvesof unit cells.010203040–4 –2 0 2 4010203040010203040010203040502LAO3LAO4LAO5LAO BTOBTOBTOBTOO2p3d4fTiLaBaTiLaAlOEnergy, eVDensity of states, 1/eVof the BTO layer, where the displacement of Ti atomsis considerably larger (Fig. 3).Let us consider the case of STO/BTO. Both com-ponents of the heterostructure are composed of elec-BULLETIN OF THE RUSSIAN ACADEFig. 3. Displacement of Al and Ti atoms from oxygen planesin nLAO/4.5STO/nLAO and nLAO/4.5BTO/nLAO, wheren is the number of layers.00.050.100.15AlO2AlO2 AlO2TiO2 TiO2AlO2 AlO2 AlO2TiO200.050.100.150.20LAO/STOLAO/BTO23452345LAO layersLAO layersDisplacement from the oxygen plane, ÅIF IFIFIFtrically neutral (in the ion approximation) layers:Sr2+O2– and Ti4+ . This is why no atomic displace-ment is observed (Fig. 4). Although the bandgap widthshrinks slightly (from 0.8 eV with two BTO layers to0.65 eV with five layers), two-dimensional conductiv-ity does not emerge in these structures. However, thebandgap closes in a model heterostructure with Tiatoms in the BTO layers being displaced in a similarmanner to Al atoms in the LAO layer of LAO/STO.−22OMY OF SCIENCES: PHYSICS  Vol. 82  No. 3  2018Fig. 4. Displacement of Ti atoms from oxygen planes in thenBTO/4.5STO/nBTO heterostructure, where n is thenumber of layers.00.020.040.060.080.100.120.14TiO2 TiO2 TiO2 TiO2 TiO2 TiO2 TiO2 TiO22345BTO layersDisplacement from the oxygen plane, ÅELECTRONIC PROPERTIES OF A TWO-DIMENSIONAL ELECTRON GAS 237Magnetic order with a magnetic moment of 0.3782 μBthen arises.It is worth noting that additional effects possiblyassociated with the spatial rearrangement of chargecarriers at the interface were ignored in the abovemodeling. However, we have revealed the formation ofa 2DEG at the interface of two dielectrics and deter-mined the contribution from structural relaxation tothis phenomenon.ACKNOWLEDGMENTSThe work of I.I. Piyanzina was supported by theMinistry of Education and Science of the RussianFederation (project no. 3.9779.2017/8.9, subsidy allo-cated to Kazan Federal University). Computationalresources were provided by the Supercomputing Cen-ter of Moscow State University.REFERENCES1. Ohtomo, A. and Hwang, H.Y., Nature, 2004, vol. 427,p. 6973.2. Thiel, S., et al., Science, 2006, vol. 313, p. 5795.3. Reyren, N., et al., Science, 2007, vol. 317, p. 5842.4. Brinkman, A., et al., Nat. Mater., 2007, vol. 6, no. 7,p. 493.5. Kalabukhov, A., et al., Phys. Rev. B, 2007, vol. 75,no. 12, p. 121404.6. Biscaras, J., et al., Nat. Commun., 2010, vol. 1, p. 89.7. Hohenberg, P. and Kohn, W., Phys. Rev., 1964,vol. 136, no. 3B, p. B864.8. Kresse, G. and Furthmuller, J., Comput. Mater. Sci.,1996, vol. 6, no. 1, p. 15.9. Dudarev, S.L., et al., Phys. Rev. B, 1998, vol. 57, no. 3,p. 1505.10. Perdew, J.P., Burke, K., and Ernzerhof, M., Phys. Rev.Lett., 1996, vol. 77, no. 18, p. 3865.11. MedeA 2.20. http://www.materialsdesign.com/medea.12. Piyanzina, I.I., et al., J. Phys.: Condens. Matter, 2017,vol. 29, no. 9, p. 095501.Translated by D. SafinBULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS  Vol. 82  No. 3  2018

Electronic properties of a two-dimensional electron gas at the
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Electronic properties of a two-dimensional electron gas at the interface between transition metal complex oxides

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