The electronic structure of the molecular superconductor β−(BEDT−TTF)2IBr2 has been studied by means of first-principles density functional calculations. The calculated transverse cross section of the Fermi surface is in excellent agreement with that reconstructed from magnetoresistance measurements. It is shown that the cylindrical Fermi surface exhibits warping (the dispersion along the interlayer direction is of the order of 0.8–1.7 % of the dispersion in the conducting plane) and that it does not contain any additional small pocket. These features provide support for a recent proposal concerning the much debated question of the origin of the slow magnetoresistance oscillations exhibited by this material.Peer reviewe

Canadell, E.

Lee, Y. J.

Nieminen, Risto M.

Ordejon, P.

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This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.Author(s): Lee, Y. J. & Nieminen, Risto M. & Ordejon, P. & Canadell, E.Title: First-principles characterization of the electronic structure of themolecular superconductor beta-(BEDT-TTF)2IBr2Year: 2003Version: Final published versionPlease cite the original version:Lee, Y. J. & Nieminen, Risto M. & Ordejon, P. & Canadell, E. 2003. First-principlescharacterization of the electronic structure of the molecular superconductorbeta-(BEDT-TTF)2IBr2. Physical Review B. Volume 67, Issue 18. 180505/1-4. ISSN1550-235X (electronic). DOI: 10.1103/physrevb.67.180505.Rights: © 2003 American Physical Society (APS). This is the accepted version of the following article: Lee, Y. J. &Nieminen, Risto M. & Ordejon, P. & Canadell, E. 2003. First-principles characterization of the electronicstructure of the molecular superconductor beta-(BEDT-TTF)2IBr2. Physical Review B. Volume 67, Issue 18.180505/1-4. ISSN 1550-235X (electronic). DOI: 10.1103/physrevb.67.180505, which has been published infinal form at http://journals.aps.org/prb/abstract/10.1103/PhysRevB.67.180505.All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, andduplication or sale of all or part of any of the repository collections is not permitted, except that material maybe duplicated by you for your research use or educational purposes in electronic or print form. You mustobtain permission for any other use. Electronic or print copies may not be offered, whether for sale orotherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org)First-principles characterization of the electronic structure of the molecular superconductorb-BEDT-TTF2IBr2Y. J. Lee,1 R. M. Nieminen,1 P. Ordejon,2 and E. Canadell21COMP/Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland2Institut de Cie`ncia de Materials de Barcelona (CSIC), Campus de la UAB, 08193 Bellaterra, Spain~Received 3 January 2003; published 29 May 2003!The electronic structure of the molecular superconductor b-(BEDT-TTF)2IBr2 has been studied by means offirst-principles density functional calculations. The calculated transverse cross section of the Fermi surface is inexcellent agreement with that reconstructed from magnetoresistance measurements. It is shown that the cylin-drical Fermi surface exhibits warping ~the dispersion along the interlayer direction is of the order of 0.8–1.7 %of the dispersion in the conducting plane! and that it does not contain any additional small pocket. Thesefeatures provide support for a recent proposal concerning the much debated question of the origin of the slowmagnetoresistance oscillations exhibited by this material.DOI: 10.1103/PhysRevB.67.180505 PACS number~s!: 74.70.Kn, 71.15.Mb, 71.18.1y, 71.20.2bThe organic donor molecule bis~ethylenedithio!- tetrathi-afulvalene ~BEDT-TTF! gives rise to a number of metallicand superconducting salts with inorganic anions, which havebeen the focus of continued attention and debate for almosttwo decades. A common structural pattern to practically allof these materials is that they have layers of donor BEDT-TTF molecules alternating with layers of the anions in onecrystallographic direction ~see, for instance, Fig. 1!.1 Sincethe BEDT-TTF layers are those responsible for the electricalconductivity, these materials are very anisotropic quasi-two-dimensional ~Q2D! metals. This fact and the possibility togrow high purity single crystals have led to an impressivenumber of physical studies of these salts.2 A key aspect inunderstanding the physics of their normal and superconduct-ing states is the nature of the band structure and the shape ofthe Fermi surface ~FS!. The Shubnikov–de Haas ~SdH! andde Haas–van Alphen ~dHvA! effects have been extensivelyused in order to provide experimental information about theFS.3–7 A wealth of interesting data concerning magneticquantum oscillations as well as a number of semiclassicalmagnetotransport phenomena has been obtained, stimulatingadvances in the theory of the Q2D SdH and dHvA effects.3–5In this context, the absence of detailed high-level first-principles studies of the electronic structure of these materi-als may be surprising. Certainly, the success of simple tight-binding treatments in providing an understanding of thegross features of the FS of many of these salts5 can be part ofthe reason. In addition, the large unit cells and the mixedtype of bonding associated with their molecular nature facethe computational physicists with a real challenge. However,accurate first-principles calculations are needed at this stageof the research in order to better exploit the experimentalinformation, to test existing theoretical models, and to sug-gest new experiments. With this in mind we have initiated ageneral study of the electronic structure of molecular con-ductors and carefully studied the conditions to be fulfilled bya computational approach in order to be both accurate andapplicable to solids with unit cells as large as those of TTF-TCNQ, the Bechgaard salts, the a , b , or k salts of BEDT-TTF, etc., in order to provide a solid computational frame-work. We recently have shown8 that this kind ofcomputations appropriately describe the change from metal-lic to weakly activated conductivity in single component mo-lecular conductors induced by a subtle chemical modifica-tion.Here we report our results concerning the molecular su-perconductor b-(BEDT-TTF)2IBr2,9 a material subject tointense interest because of the much debated question of theorigin of the slow magnetoresistance oscillations.3–5 It doesnot exhibit superstructure transitions or metal-to-insulatorinstabilities, being metallic down to >2K, at which temper-ature it exhibits a superconducting transition.9 This relativelysimple behavior has made it the target of many dHvAand SdH studies. The slow oscillations of magneto-resistance were initially discovered in this material,10and later they were also observed in b-(BEDT-TTF)2I3,11 k-(BEDT-TTF)2Cu2(CN)3,12 and k-(BEDT-TSF)2C(CN)3.13 These oscillations were supposed to origi-nate from small pockets of the FS because their behaviorstrongly resembles that of the SdH effect. However, the ori-gin of such slow oscillations has remained one of the moreelusive features of the electronic structure of these materialsuntil recently, when Kartsovnik et al.14 proposed that thoseof b-(BEDT-TTF)2IBr2 originate from the warping of thecylindrical FS. But no high-level first-principles character-ization of the FS of the material is available. The tight-binding FS for this material is in reasonable agreement withexperiment as far as the anisotropy in the conducting plane isconcerned.6,15 This method is, however, unable to treat theinterlayer interactions properly, a major drawback in thepresent context. First-principles calculations of the aug-mented spherical-wave type were used to study the isostruc-tural and physically related b-(BEDT-TTF)2I3 salt,16 whichafter all @with b-(BEDT-TTF)2IBr2] is the simplest BEDT-TTF based salt. The results concerning the Fermi surfacediffered dramatically from experiment. Later, another first-principles study using the pseudofunction method was ap-plied to b-(BEDT-TTF)2IBr2.17 However, except for theband dispersion along a few selected directions of reciprocalspace no detailed information was reported. Thus, no com-putational data can be confronted with the recent work byKartsovnik et al.14RAPID COMMUNICATIONSPHYSICAL REVIEW B 67, 180505~R! ~2003!0163-1829/2003/67~18!/180505~4!/$20.00 ©2003 The American Physical Society67 180505-1The present calculations were carried out by the densityfunctional theory ~DFT! ~Refs. 18 and 19! using a numericalatomic orbital approach,20 which has been recently devel-oped and designed for efficient calculations in large systemsand implemented in the SIESTA code.20,21 We have used thegeneralized gradient approximation for the exchange-correlation energy and, in particular, the functional of Per-dew, Burke, and Ernzerhof.22 Only the valence electrons areconsidered in the calculation, with the core being replaced bynorm-conserving scalar relativistic pseudopotentials23 factor-ized in the Kleinman-Bylander form.24 The nonlinear core-valence exchange-correlation scheme25 is used for all ele-ments with the exception of the hydrogen atom. We haveused the following type of basis set: triple-z for the s orbitalsof I, Br, S, and C atoms; triple-z plus single polarizationfunctions for the s orbital of H; triple-z plus double polariza-tion functions for the p orbitals of I and Br; and triple-z plussingle polarization functions for the p orbitals of S and C, asobtained with an energy shift of 2 meV.20,21 The integrals ofthe self-consistent terms of the Kohn-Sham Hamiltonian areobtained with the help of a regular real space grid in whichthe electron density is projected. The grid spacing is deter-mined by the maximum kinetic energy of the plane wavesthat can be represented in that grid. In the present work, weused a cutoff of 250 Ry. The Brillouin zone was sampledusing a grid of 43332 Monkhorst-Pack26 k points for thedetermination of density matrix and projected density ofstate and a set of 20000 k points for the determination of FSand density of states.The conducting donor layers of b-(BEDT-TTF)2IBr2 ex-tend in the (a ,b) plane and are built from parallel chains ofBEDT-TTF along the (a1b) direction. The calculated bandstructure and density of states ~DOS! near the Fermi level areshown in Figs. 2 and 3. As shown there, the anion contribu-tions are practically nil in the region displayed ~Fig. 3!. Thetwo bands of Fig. 2 are almost exclusively built from thehighest occupied molecular orbital ~HOMO! of BEDT-TTF.There are two such bands because the unit cell ofb-(BEDT-TTF)2IBr2 contains two donor molecules.As shown in Fig. 1, there are different types of S and Catoms in the BEDT-TTF donor. The analysis of the DOSshows that the H and the outer C3 atoms practically do notcontribute to the two bands and thus to the DOS at the Fermilevel ~Fig. 3!. The largest contribution is that of the inner S1atoms followed by that of the inner C1 atoms. Note that thereare four S1 atoms but only two C1 atoms per molecule, soFIG. 1. ~Color! Crystal structure of b-(BEDT-TTF)2IBr2 show-ing the alternation of layers along the c direction. The differenttypes of C and S atoms in the BEDT-TTF donor molecule arelabeled. The energy is relative to the Fermi level.FIG. 2. ~a!, ~b!, and ~c! Calculated band structures, and ~d!density of states ~DOS! for b-(BEDT-TTF)2IBr2 . G5(0,0,0), X5(1/2,0,0), Y5(0,1/2,0), and Z5(0,0,1/2) in units of the triclinicreciprocal lattice vectors. The energy is relative to the Fermi level.FIG. 3. ~Color! Projected density of states ~PDOS! ofb-(BEDT-TTF)2IBr2 in terms of the different types of atoms. Thedifferent contributions plotted refer to the total contribution for agiven type of atom.RAPID COMMUNICATIONSY. J. LEE, R. M. NIEMINEN, P. ORDEJON, AND E. CANADELL PHYSICAL REVIEW B 67, 180505~R! ~2003!180505-2that the DOS per atom is only a little bit larger for the S1atoms. The contributions of the S2 atoms are approximatelythree times smaller than those of the inner S1 atoms, andthose of the C2 atoms approximately two times smaller thanthose of the inner C1 atoms ~recall that there are two C1atoms but four C2 atoms per molecule!. The relative contri-butions of the carbon atoms are in excellent agreement withthose derived from a 13C high-resolution NMR study of theisostructural b-(BEDT-TTF)2I3.27 The contributions of theS1, S2, C1, and C2 atoms are almost exclusively due to thep-type orbitals ~i.e., the pz orbitals!. The band dispersions ofFig. 2 are typical of a Q2D metal and are very close to thoseobtained by the tight-binding methods.15 To the best of ourknowledge there is not a precise experimental estimation ofthe band width but from a Drude analysis of the reflectancespectra it was estimated that the dispersion along the chaindirection (a1b) is 0.63 eV.28The calculated DOS at the Fermi level is 4.65 electronsper eV and per unit cell. Again, we have not found data tomake a direct comparison, but for the isostructuralb-(BEDT-TTF)2I3 superconductor a value of 13.6 electronsper eV and per unit cell was reported from spin susceptibilitymeasurements.29 On the basis of comparison between thespin susceptibility and optical data it was proposed that therewas a susceptibility enhancement factor of 3 at room tem-perature and ambient pressure. Our result provides confirma-tion for this proposal assuming that the DOS at the Fermilevel is very similar in the two salts, something which isexpected from structural reasons. The previous analysis ofthe DOS provides a basis to understand the success of tight-binding methods as far as the in-plane band structure is con-cerned. The relative weight of the different contributions isvery similar in the region of the two bands, giving evidencethat only the HOMO of the BEDT-TTF is implicated in thesebands. The shape of the HOMO of BEDT-TTF provided bythese methods is in close agreement with the relative atomiccontributions to the DOS near the Fermi level, and thus therelative anisotropy of the electronic interactions is satisfac-torily described by these methods.In Fig. 4 we report a detailed characterization of the FS ofb-(BEDT-TTF)2IBr2. As expected from the band structure itis a typical Q2D FS with a cylinder like shape @Fig. 4~a!#.The transverse cross-section of the FS cylinder is howeversomewhat distorted from a purely elliptical shape @Fig. 4~b!#.The calculated transverse cross-section is in excellent agree-ment with that reconstructed from the magnetoresistancedata.6,30 As shown by the chart of the eigenvalues of the kpoints in the (a*,c*) plane passing through the G point @Fig.4~c!#, the cylinder like FS must be warped. This warping isnot uniform but changes along the closed line of the trans-FIG. 4. ~Color! Calculated Fermi surface for b-(BEDT-TTF)2IBr2. ~a! Three-dimensional FS. ~b! FS and Brillouin zone viewed alongthe c* direction. ~c! Eigenvalues of the k points in the (a*, c*) plane passing through the G point. The numbers in the color scale are in eV.~d! Band dispersion along the lines parallel to the c* direction passing through the points A and B marked in ~b!. The energies in ~c! and ~d!are relative to the Fermi level. ~e! and ~f! Graphical representations of the FS warping ~see text!.RAPID COMMUNICATIONSFIRST-PRINCIPLES CHARACTERIZATION OF THE . . . PHYSICAL REVIEW B 67, 180505~R! ~2003!180505-3verse cross section as shown in Fig. 4~d! for two differentpoints marked A and B in Fig. 4~b!. The dispersion along thec* direction reaches values around 9 meV and varies con-siderably. This warping leads to a FS as depicted in Figs.4~e! and 4~f!. In order to clarify the kind of warping, theregion of k space giving negative values of de/dc* ~e is theeigenvalue at c*! is encoded by a bright color and the regionof k space giving positive values is encoded by a dark color.It is clear that the striped bands of colors are inclined withrespect to the c* direction @see Figs. 4~e! and 4~f!# a featurewhich harmonizes with the results of the magnetoresistancereconstruction of the FS.6,30 The present study shows withoutany ambiguity that the FS of b-(BEDT-TTF)2IBr2 does notcontain any small closed pockets of carriers which could bethe origin of the slow oscillations. It also suggests that thedispersion along the interlayer direction is of the order of0.8–1.7 % of that in the conducting plane. Let us note thatslow oscillations have not been found for other BEDT-TTFsalts exhibiting cylinder like features in their FS suchas those of the a-(BEDT-TTF)2MHg(XCN)4 family(M5K, Tl, Rb; X5S, Se).1 We have carried out computa-tions of the same quality for a-(BEDT-TTF)2KHg(SCN)4,and found a considerably smaller warping along the inter-layer direction.The two facts, together, the absence of additional closedpockets of carriers and the warping as reported here providea firm computational basis to a very recent proposal14 thatthe slow oscillations in b-(BEDT-TTF)2IBr2 originate fromthe warping of its cylindrical FS. In addition, the presentwork opens the way towards a more in depth characterizationof the electronic structure of b-(BEDT-TTF)2IBr2 by allow-ing the comparison of the calculated and experimental finedetails of the FS and band structure.The work at HUT was supported by the Academy of Fin-land through the Center of Excellence Program ~2002-2005!.Work at Bellaterra was supported by DGI-Spain ~Project No.BFM2000-1312-C02-01!, Generalitat de Catalunya ~ProjectNo. 2001 SGR 33!, and by grants for computer time from theCESCA-CEPBA.1 J. M. Williams, J. R. Ferraro, R. J. Thorn, K. D. Carlson, U.Geiser, H. H. Wang, A. M. Kini, and M.-H. Whangbo, OrganicSuperconductors ~Prentice-Hall, Englewood Ciffs, NJ, 1992!.2 T. Ishiguro, K. Yamaji and G. Saito, Organic Superconductors,2nd ed. ~Springer-Verlag, Berlin, 1998!.3 M. V. Kartsovnik, in Molecular Low Dimensional and Nanostruc-tured Materials for Advanced Applications, edited by A. Graja,V. M. Agranovich and F. Kajzar, NATO-ARW Series, ~Kluwer,Dordrecht, 2002! and references therein.4 M.V. Kartsovnik and V.N. Laukhin, J. Phys. I 6, 1753 ~1996!.5 J. Wosnitza, Fermi Surfaces of Low-Dimensional Organic Metalsand Superconductors ~Springer-Verlag, Berlin, 1996!.6 J. Wosnitza et al., J. Phys. I 6, 1597 ~1996!.7 S.J. Blundell and J. Singleton, J. Phys. I 6, 1837 ~1996!.8 C. Rovira, J.J. Novoa, J.L. Mozos, P. Ordejon, and E. Canadell,Phys. Rev. B 65, 081104 ~2002!.9 J.M. Williams et al., Inorg. Chem. 23, 3839 ~1984!.10 M.V. Kartsovnik, V.N. Laukhin, V.I. Nizhankovski, and A.A.Ignat’ev, Pis’ma Zh. E´ ksp. Teor. Fiz. 47, 302 ~1988! @JETP Lett.47, 363 ~1988!#; M.V. Kartsovnik, P.A. Kononovich, V.N.Laukhin, and I.F. Schegolev, ibid. 48, 498 ~1988! @48, 541~1988!#.11 M.V. Kartsovnik, P.A. Kononovich, V.N. Laukhin, S.I. Pesotskii,and I.F. Schegolev, Pis’ma Zh. E´ ksp. Teor. Fiz. 49, 453 ~1989!@JETP Lett. 49, 519 ~1989!#; J. Wosnitza, D. Beckmann, G. Goll,and D. Schweitzer, Synth. 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Froyen, and M.L. Cohen, Phys. Rev. B 26, 1738~1982!.26 H.J. Monkhorst and J.D. Pack, Phys. Rev. B 13, 5188 ~1976!.27 A.M. Vainrub, I.A. Kheinmaa, and E.B. Yagubskii, Pis’ma Zh.E´ ksp. Teor. Fiz. 44, 247 ~1986! @JETP Lett. 44, 317 ~1986!#.28 T. Sugano and G. Saito, J. Phys. C 19, 5471 ~1986!.29 B. Rothaemel et al., Phys. Rev. B 34, 704 ~1986!; R.C. Haddon,A.P. Ramirez, and S.H. Glarum, Adv. Mater. ~Weinheim, Ger.! 6,316 ~1994!.30 M.V. Kartsovnik, V.N. Laukhin, S.I. Pesotskii, I.F. Schegolev, andV.M. Yakovenko, J. Phys. I 2, 89 ~1991!.RAPID COMMUNICATIONSY. J. LEE, R. M. NIEMINEN, P. ORDEJON, AND E. CANADELL PHYSICAL REVIEW B 67, 180505~R! ~2003!180505-4

First-principles characterization of the electronic structure of the molecular superconductor beta-(BEDT-TTF)2IBr2

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First-principles characterization of the electronic structure of the molecular superconductor beta-(BEDT-TTF)2IBr2

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