Chemical-Strain Induced Tilted Dirac Nodes in (BEDT-TTF) 2 X 3 (X = I, Cl, Br, F) Based Charge-Transfer Salts
R. Matthias Geilhufe, Benjamin Commeau, Gayanath W. Fernando
CChemical-Strain Induced Tilted DiracNodes in (BEDT-TTF) X (X = I, Cl,Br, F) Based Charge-Transfer Salts R. Matthias Geilhufe *,1 , Benjamin Commeau , Gayanath W. Fernando , Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden University of Connecticut, 2152 Hillside Road, U-3046 Storrs, CT 06269-3046, USA
Key words:
Dirac materials, Dirac type-II, Tilted Dirac, Charge Transfer Salts, (BEDT-TTF), Chemical Strain ∗ Corresponding author: e-mail [email protected], [email protected]
The identification of novel multifunctional Dirac materials has been an ongoing effort. In this connection quasi2-dimensional (BEDT-TTF)-based charge transfer salts are widely discussed. Here, we report about the elec-tronic structure of α -(BEDT-TTF) I and κ -(BEDT-TTF) I under a hypothetical substitution of iodine withthe halogens bromine, chlorine and fluorine. The decreasing size of the anion layer corresponds to applyingchemical strain which increases tremendously in the case of (BEDT-TTF) F . We performed structural op-timization and electronic structure calculations in the framework of density functional theory, incorporating,first, the recently developed strongly constrained and appropriately normed semilocal density functional SCAN,and, second, van der Waals corrections to the PBE exchange correlation functional by means of the dDsC dis-persion correction method. In the case of α -(BEDT-TTF) F the formation of over-tilted Dirac-type-II nodeswithin the quasi 2-dimensional Brillouin zone can be found. For κ -(BEDT-TTF) F , the recently reported topo-logical transition within the electronic band structure cannot be revealed. Organic charge transfer salts, espe-cially quasi two-dimensional (BEDT-TTF) X where Xrepresent a variety of acceptor molecules, have generatedgreat interest over the past few decades. Depending on thestructural phase, the acceptor molecules, and other fac-tors, these can be associated with a rich variety of physicalphenomena such as charge ordering, metal-insulator tran-sitions, unconventional superconductivity, antiferromag-netism and spin liquids. In these compounds, the molecu-lar units consisting of carbon atoms (i.e., donors) usuallypreserve their specific features and are separated by layersof anion atoms that act as acceptors. It is believed that theunpaired electrons (or holes) in the carbon π -orbitals areresponsible for the conducting properties.The α -phase with X=I represents a narrow band-gapsemiconductor at ambient pressure [1] showing chargeordering as investigated by synchrotron X-ray diffractionmeasurements [2]. Under high pressure, it was reportedthat α -(BEDT-TTF) I exhibits a transition to a semi-metallic phase exhibiting tilted Dirac-crossings within the band structure [3,4,5,6,7,8,9]. Although Dirac materi-als have been of major interest recently [10], α -(BEDT-TTF) I under high pressure is one of the few non-planarorganic Dirac materials known to date [11,12]. In general,organic compounds satisfying specific filling-constraints[13] favorable for exhibiting a semimetallic phase tend tobe susceptible to interaction instabilities which break theglobal symmetry of the system and with that eliminate theprotection of the semi-metallic phase [14]. However, forsufficiently high temperatures, above the transition temper-ature of the instability, and incorporating chemical strainwe argue that the quasi 2-dimensional material α -(BEDT-TTF) F is likely to host heavily tilted Dirac-cones atambient pressure.We have recently reported first principles-based bandstructure calculations for α - and β -phases with X=I and κ -phase with X=I, Br, Cl and F [15]. For the latter itwas found that the isovalent replacements of Iodine withBromine, Chlorine and Fluorine leads to a chemical-straininduced topological band crossing along the path Γ -Y a r X i v : . [ c ond - m a t . m t r l - s c i ] A ug : within the Brillouin zone, which is protected by the non-symmorphic symmetry present for the κ -phase.In the present work, we complement the previous studyby revising and extending this discussion for the κ - and α -phases incorporating very recently developed exchangecorrelation functionals within the framework of the den-sity functional theory (DFT). Here, α -(BEDT-TTF) X isfound to be of particular interest, due to emerging tilted(and over-tilted) Dirac crossings within the band structure.Furthermore, we rigorously discuss the structural changesand charge transfer connected to the incorporated chemi-cal strain. We point out that the chemically induced strainsmay not necessarily be similar to those due to hydrostaticpressure. Although the numerical values of charge trans-fer may depend on the selected appropriation scheme,the trends in charge transfer yield useful and consistentinsights into the donor-acceptor nature of various atomsbased on the DFT framework.The paper is structured as follows. First, we discuss thechange of the cell volume by inducing chemical strain me-diated by the substitution of the iodine layer by bromine,chlorine and fluorine. Second, we report about the chang-ing charge transfer observed by the chemical substitution.Afterwards, we discuss the change of the electronic struc-ture for α -(BEDT-TTF) X and κ -(BEDT-TTF) X due tothe decreased unit cell size. We have examined the effectsof changing the anion X in α -(BEDT-TTF) X and κ -(BEDT-TTF) X in the framework of the DFT by applyinga pseudopotential projector augmented-wave method [16,17,18,19], as implemented in the Vienna Ab initio Simula-tion Package (VASP) [20,21] and Quantum Espresso [22].The exchange correlation functional was approximated bythe recently developed semilocal meta-GGA functional(SCAN) [23,24]. Additionally, we performed calculationsin the framework of the generalized gradient approxima-tion (PBE) [25], incorporating Van der Waals correctionsin terms of the dDsC dispersion correction method (VdW)[26,27].The calculations were performed without spin-orbitcoupling, which is a reasonable approximation due to thelight elements within the (BEDT-TTF) I molecule. Forthe integration in k -space, a × × Γ -centered meshaccording to Monkhorst and Pack [28] was chosen dur-ing the self-consistent cycle. The precision flag was setto “normal”. A structural optimization was performed byallowing the ionic positions, the cell shape, and the cellvolume to change ( ISIF = 3 ).Quantum ESPRESSO was applied to estimate the as-sociated irreducible representations of the energy levelswithin the band structure. The cut-off energy for the wavefunction was chosen to be 48 Ry and the cut-off energyfor the charge density and the potentials was chosen to be316 Ry. The charge transfer for the κ -phase was computed a) b)c)d) Figure 1
The crystal structures with the respective a -, b -, and c -axes are shown in (a) for α -(BEDT-TTF) X and(b) for κ -(BEDT-TTF) X . Volume, c/a , and c/b ratiochanges under chemical substitution I → Br, Cl, Fr (c) α -(BEDT-TTF) X and (d) κ -(BEDT-TTF) X .using projected wavefunctions onto orthogonalized atomicwavefunctions, which calculates the Lowdin charges. The basic structural parameters of α -(BEDT-TTF) I and κ -(BEDT-TTF) I were taken from the CambridgeStructural Database (CSD) [29,30,31]. An illustration ofthe molecular ordering as well as the chosen unit cellsfor α -(BEDT-TTF) X and κ -(BEDT-TTF) X is shownin Figure 1 (a), (b). The (BEDT-TTF) layers and the anionlayer are stacked alternately in these materials and the latteris thought to be insulating. The bands near the Fermi levelare mostly originating from (BEDT-TTF) layers, with themain contributions originating from the C and S p -orbitals[15]. In the κ -phase, there is a set of bonding (occupied)and antibonding (partially occupied) bands in the vicinityof the Fermi level. We have examined the role of the anionlayer as follows. The α - and κ -phases of (BEDT-TTF) I were studied by replacing all the iodine atoms with an-other halogen atom, namely bromine, chlorine, and fluo-rine. These atoms are isovalent and smaller in size com-pared to iodine and hence can induce “chemical strains”,giving rise to a compression of the original unit cell.We have monitored the relaxed volumes of the unit cellunder such substitutions and found a steady decrease inthe volume of the unit cell under the progressive substitu-tions I → Br → Cl → F. Figures 1 (c) and (d) show the relativechange of the unit cell volume and c/a and c/b ratios withrespect to the experimentally observed values [30,31] for α -(BEDT-TTF) I and κ -(BEDT-TTF) I . In the α -phase,under the above progressive substitution, c/a and c/b ra-tios also show an almost steady decrease. In this case, the c -axis is the long axis of the crystal, while ˆ a and ˆ b vectorsspan a plane almost perpendicular to the c -axis. The steadydecrease of the c/a and c/b ratios is due to a relativelylarge contraction along the c axis compared to somewhatsmaller changes in the plane spanned by ˆ a and ˆ b vectors.This change can be directly attributed to the decrease of theatom size in the insulating (acceptor) layers under the sub-stitution I → Br → Cl → F. The induced chemical strain maybe designated as an almost uniaxial strain. The analogouschanges in the κ -phase look more subtle. Note here thatthe long axis in this case is the a -axis while the b -axis isthe special axis in this monoclinic structure (which is per-pendicular to both a - and c -axes), according to our choiceof axes shown in Fig. 1 (d). Note that the c/a ratio remainssteady during the above progressive substitution althoughboth a and c parameters decrease. Also noteworthy is thefact that the parameter b does not show changes compara-ble to those associated with c and a . This case may be inter-preted as indicating a biaxial strain. The results are consis-tent for both exchange correlation functionals SCAN andVdW corrected PBE. For the α -(BEDT-TTF) I , the struc-tural information obtained incorporating the SCAN func-tional is in almost perfect agreement with the experimen-tal values, whereas the cell volume is underestimated byabout 5 % using the VdW method. However, both function-als underestimate the cell volume for κ -(BEDT-TTF) I byabout 7% for SCAN and 8% for VdW. O O O O^ ^ ^ ^ - - - -+ + + +
X S C H - - electronselements O κ -( BEDT - TTF ) I ^ κ -( BEDT - TTF ) Br - κ -( BEDT - TTF ) Cl + κ -( BEDT - TTF ) F a) Kappa Phase O O O O^ ^ ^ ^ - - - -+ + + +
X S C H - - electronselements O α -( BEDT - TTF ) I ^ α -( BEDT - TTF ) Br - α -( BEDT - TTF ) Cl + α -( BEDT - TTF ) F b) Alpha Phase Figure 2
Charge transfer under chemical substitution forthe halogen atoms (X=I,Br,Cl,F). The charge transfer is thenet electron charge displaced with respect to the atom’svalence electrons averaged over all atoms of the same el-ement type. The valence electron numbers of each atomare (7,6,4,1) for (I,S,C,H) respectively. For example, κ -(BEDT-TTF) F gained an additional 0.65 electron chargeto each of its six fluorine atoms on average, giving it a totalaverage of 7.65 electron charge to its valence electrons. Figure 2a and 2b illustrate thecharge transfer for α -(BEDT-TTF) X and κ -(BEDT-TTF) X , respectively. Both sets of data have consistentcharge transfer behavior. Charge is transfered from the sul-fur and hydrogen atoms to the carbon and halogen atoms.Fluorine gains twice as much charge compared to the otherhalogens.Figure 3a illustrates a gradual movement of the halo-gens I → Br → Cl under chemical substitution ion relaxationin the kappa phase, and a large displacement in the loca-tion of 3 of its fluorine atoms. To our knowledge, thereare no publications related to the synthesis of (BEDT-TTF) F . Fluorine, as a single atom, has shown in ourrelaxation calculations to be very electronegative and at-tempts to form strong charge transfer bonds with the otheratoms in the crystal. However, we note here that organiccrystals with an isolated anion fluorine atom can be syn-thesized in general[32]. α -phase The α -phases of (BEDT-TTF) X crystallize in a triclinic crystal structure, havingthe (symmorphic) space group P ( α -(BEDT-TTF) I is a narrow band-gap insula- : a) b) Figure 3
Halogen movement under chemical substitu-tion for κ -(BEDT-TTF) X for X=(I,Br,Cl,F) in the b - c -plane, spanned by lattice vectors b and c . (a) Top downview of normalized b - c -plane (lattice vectors normalizedto equal length). Circles’ centers are the halogen locationsfor κ -(BEDT-TTF) X for X=(I,Br,Cl,F). (b) b - c -planecut where halogens (purple atoms) exist in 3D crystal unitcell for κ -(BEDT-TTF) X .tor as shown in Figure 4a. The “tilted Dirac cone” reportedin α -(BEDT-TTF) I under high pressure is centered at aninterior k-point in the Brillouin zone [3,4,5,6,7,8,9]. Theplacement of the Dirac point in k-space is similar to whatis observed in strained graphene where the Dirac points inunstrained graphene get dragged away from the high sym-metry K and K (cid:48) points. The “tilt parameter” in this casehas been shown to depend linearly on the strain [33]. Thelinear (and tilted) bands, if placed near the Fermi level, cangive rise to distinct transport properties.The substitution of I with Br and Cl, does not changethe band structure qualitatively. However, the decreas-ing unit cell size lowers the energy of several high-lyingbands and additionally decreases the band gap along thepath S − Γ − S . Interestingly, the situation dramaticallychanges for a substitution I → F , leading to a huge in-crease of the band gap along S − Γ − S and over-tiltedband crossings along S − Γ − S , as can be seen in Fig.4b. As each band additionally carries a spin-degeneracy,the total degeneracy at the crossing points is four. Suchmaterials are referred to as Dirac type-II semimetals. Thesame tilted crossings are revealed incorporating the PBEfunctional and Van der Waals corrections.Recently, Dirac type-II and Weyl type-II materials haveattracted a lot of attention, as they are discussed to effec-tively mimic the behavior of Dirac or Weyl fermions inthe vicinity of a strong gravitational field [34,35,36,37].The influence of the effective gravitational field leads toa curved metric and a tilted light or Dirac cone in thecase of massless fermions. In this picture, an over-tiltedDirac-cone refers to Fermions beyond the event-horizonof a black hole, where the particle momentum is com- S Γ S − . − . . . . . . E n e r g y ( e V ) S Γ S a) S Γ S − . − . . . . . . E n e r g y ( e V ) S Γ S b) Figure 4
Band structure of (a) α -(BEDT-TTF) I and (b) α -(BEDT-TTF) F calculated using VASP and the SCANmeta-GGA functional. The high symmetry points repre-sent the corners of the quasi-2D Brillouin zone givenby S = (0 . , . , . , S = (0 . , − . , . , S =( − . , . , . , and S = ( − . , . , . .pletely suppressed away from the origin of the gravitationalfield. Thus, the investigation of materials like α -(BEDT-TTF) F with effective excitations given by Dirac type-II fermions can lead to important insights of black holephysics by means of condensed matter systems. κ phase The κ -phase crystal-lizes in a monoclinic crystal structure having the spacegroup G ≡ P ( G = T ∪ ( { C y | (0 , / , } (cid:12) T ) . (1) Here, { C y | (0 , / , } denotes a two-fold screw symme-try, represented by a two-fold rotation about the y -axistogether with a non-primitive shift along the lattice vec-tor a . The nonsymmorphic nature of the space groupleads to degenerate line-nodes along the Brillouin zoneboundary. Nonsymmorphic symmetries were widely dis-cussed in protecting Dirac nodes [38,39,40,41]. In gen-eral, it is possible to distinguish between crossings pro-tected by the crystalline symmetry, i.e., crossings which areassociated with higher dimensional irreducible representa-tions or pairs of complex-conjugate irreducible representa-tions, and crossings protected by band topology, where thebands belong to different irreducible representations (acci-dental crossings), but where the crossing is forced to occurdue to the connectivity of the bands [11,12,42,43,44].The band structure of κ -(BEDT-TTF) I close to theFermi level is shown in Fig. 5a. Within the energy rangeof [ − . , . two pairs of two bands can clearly be re-vealed. Here, the bands occur pair-wise as the nonsym-morphic symmetry protects the degeneracy at the Brillouinzone boundary. As discussed in [15], each pair consists ofone band transforming even (irrep A at the Γ -point) andone band transforming odd (irrep B at the Γ -point) under C y . Here, the four bands illustrated in Fig. 5a correspondto an ordering of A , B , A , B , from the lowest to the highestband. However, in Ref. [15] it was reported that a substitu-tion of I → F leads to a shift upwards of the bands, and, inaddition to that, to a change of the ordering of the levels atthe Γ point to A , A , B , B . This ordering introduces a topo-logically protected crossing along the path Γ − Y . How-ever, the present calculations performed using the SCANfunctional do not support this change of the ordering, butreveal a band touching along Γ − Y (see Fig. 5b). A similarbehavior is also found for the calculations performed usingthe VdW-corrected PBE functional. Universal phase dia-grams summarizing the rich physics of the α and κ -phaseshave been presented following the work of Refs. [45,46]. The κ -phase diagram, which was published first inRef. [45] for (BEDT-TTF) Y where Y=Cu(NCS) com-bined with selected halogens, has been compared to thewell-known (and strongly correlated) V O phase dia-gram. It was noted there that, for this phase, the chemicalpressure and the strength of correlations act in the oppositedirection to the hydrostatic pressure. To our knowledge,the BEDT-TTF compound corresponding to fluorine sub-stitution has not been synthesized. If it can be synthesized,its placement in such a phase diagram will be quite inter-esting. This is due to our calculated results which showa behavior somewhat different from the trends seen forCl and Br substitutions. In the latter cases, the changesin the electronic and lattice structures are gradual andpredictable. However, the changes in the lattice constantratios as well as volume are relatively significant underfluorine substitution. The induced chemical strains are not X Γ Y V − . − . − . − . . . . E n e r g y ( e V ) ABAB a) X Γ Y V − . . . . . . . E n e r g y ( e V ) ABAB b) Figure 5
Band structure of (a) κ -(BEDT-TTF) I and(b) κ -(BEDT-TTF) F calculated using VASP and theSCAN meta-GGA functional. The high symmetry pointsare X = (0 . , . , . , Y = (0 . , . , . , and V =(0 . , . , . .necessarily isotropic and may not resemble those due tohydrostatic pressure. The phase diagram indicates that thefluorine compound is likely to lead to equally or morerich physical properties, if it can be synthesized. However,any other small set of atoms as the insulating layers (eventhough not chemically similar) may give rise to fascinatingphysical properties. Organic materials based on (BEDT-TTF) X (X=I, Br, Cl, F) show great potential for fine tun-ing specific band structures near the Fermi level due to theirsoftness. Our research shows that applying chemical strainto the α - and κ - phases creates significant changes in thevolume and ratios of their lattice constants. From the struc-tural optimization it follows that the mutual replacementof iodine with bromine, chlorine and fluorine correspondsto an almost uniaxial strain applied to the sample. Thestructural optimization also give insights into the accuracyof the recently developed exchange-correlation function-als SCAN and VdW-corrected PBE. For SCAN we find avery good agreement with the experimental unit cell for α -(BEDT-TTF) I . However, for the κ -phase, both function-als underestimate the cell volume. As a result of the chem-ical strain, we observe over-tilted Dirac-type-nodes in the α -phase for α -(BEDT-TTF) F . These crossings exhibit afour-fold degeneracy. For the nonsymmorphic κ -phase, theexistence of a topological transition has been examined andquestioned throughout this work. This research highlightsthe promise and importance of tuning the band structureusing chemical or other strains that could lead to creatingmulti-functional Dirac materials. Additionally, our calcu- : lations can be used as a starting point to probe strong cor-relations known to exist in such compounds. We thank Dr. A. V. Balatskyfor his support and helpful discussions concerning thisstudy. We are grateful for support from the Swedish Re-search Council Grant No. 638-2013-9243, the Knut andAlice Wallenberg Foundation, and the European ResearchCouncil under the European Union’s Seventh Frame-work Program (FP/2207-2013)/ERC Grant AgreementNo. DM-321031. The authors acknowledge computationalresources from the Swedish National Infrastructure forComputing (SNIC) at the High Performance ComputingCenter North (HPC2N), the High Performance Comput-ing (HPC) cluster at the University of Connecticut, and thecomputing resources provided by the Center for FunctionalNanomaterials, which is a U.S. DOE Office of Science Fa-cility, at Brookhaven National Laboratory under ContractNo. de-sc0012704.
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