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Molecular Physics An International Journal at the Interface Between Chemistry and Physics
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Structural and electronic properties of potassium- doped 1,2;8,9-dibenzopentacene superconductor: comparing with doped [7]phenacenes
Guo-Hua Zhong, Chao Zhang, Xunwang Yan, Xiaoguang Li, Zheng Du, Gexin Jing & Cencen Ma
To cite this article: Guo-Hua Zhong, Chao Zhang, Xunwang Yan, Xiaoguang Li, Zheng Du, Gexin Jing & Cencen Ma (2017) Structural and electronic properties of potassium-doped 1,2;8,9- dibenzopentacene superconductor: comparing with doped [7]phenacenes, Molecular Physics, 115:4, 472-483, DOI: 10.1080/00268976.2016.1274439
To link to this article: http://dx.doi.org/10.1080/00268976.2016.1274439
Published online: 04 Jan 2017.
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RESEARCH ARTICLE Structural and electronic properties of potassium-doped ,;,-dibenzopentacene superconductor: comparing with doped []phenacenes
Guo-Hua Zhong a, Chao Zhangb,XunwangYanc, Xiaoguang Lid, Zheng Due, Gexin Jinge and Cencen Maf aShenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, P.R.China; bDepartment of Physics, Yantai University, Yantai,P.R.China;cSchool of physics and electrical engineering, Anyang Normal University, Henan, P.R.China; dInstitute for Advanced Study, Shenzhen University, Shenzhen, P.R. China; eNational Supercomputing Center in Shenzhen, Shenzhen, P.R.China; fShenzhen Energy Guangming Gas Turbine Power Plant Construction Planning and Development Office, Shenzhen, P.R. China
ABSTRACT ARTICLE HISTORY Polycyclic aromatic hydrocarbons doped by metal have exhibited the potential of high temperature Received October superconductivity. Understanding the basic properties of materials is the key to reveal the super- Accepted December conductivity. Here, a systemically theoretical study has been done to explore crystal structures and KEYWORDS electronic properties of pristine and potassium-doped 1,2;8,9-dibenzopentacene, compared with Polycyclic aromatic [7]phenacenes case. We determined that vdW-DF2 functional is more suitable to describe the non- hydrocarbons; hydrocarbons; local interaction in a molecular crystal. Based on this functional, we predicted the crystal structures organic superconductor; and investigated in detail the K atomic positions in a system. It was found that the intralayer doping dibenzopentacene leads to lower total energy. From the calculated formation energy, for each 1,2;8,9-dibenzopentacene molecule, the doping of two electrons is more stable under the relatively K-poor condition while the doping of four electrons is more stable under the K-rich condition. Between these two phases, the three-electron doping phase stabilises in a narrow region of K chemical potential. Combining with the electronic states at Fermi level, we analysed the reasons of superconductivity enhancement in doped 1,2;8,9-dibenzopentacene. This work further deepens the understanding of 1,2;8,9-dibenzopentacene superconductor.
1. Introduction to the Tc enhancement near 40 K. The research of the superconductivity in PAHs renews the interest in organic Organic based compounds are believed to be potential superconductors. As a new kind of superconducting high temperature or room temperature superconductors materials with intriguing properties, the magnetism [10– based on the idea of V. L. Ginsburg that the interac- 12], electronic correlation effects [12–14] and pressure tion of electrons with much higher excitation energy effects15–19 [ ] have received much attention. The fea- than the phonon energy can result in a substantially ture of armchair edge type, which is regarded as a key higher critical temperature T [1]. The recent discovery c factor of superconductivity in such a system, is shared of superconductivity in metal doped polycyclic aromatic in hydrocarbon superconductors in contrast to the zigzag hydrocarbons (PAHs) [2–9]seeminglysupportsthisidea edge type [20]. It has been experimentally observed that because increasing the number of benzene rings has led all of the doped phenanthrenes (C14H10) exhibit the
CONTACT Guo-Hua Zhong [email protected] © Informa UK Limited, trading as Taylor & Francis Group MOLECULAR PHYSICS 473 superconductivity of Tc ∼ 5 K, though the dopant is bytheprojectoraugmentedwave(PAW)method,while selectable among K, Rb, Sr, Ba and Sm [4,6,7]. The the monoelectronic valence electrons were expanded in superconductivity is as high as Tc ∼ 15 K in K-doped plane waves with an cutoff energy of 600 eV. For the coronene [3] while only 7 K in K-doped [6]phenacene optimisation, a conjugate-gradient algorithm was used to [9]. The superconductivity reaches to Tc ∼ 18 K in K- relax the ions into their instantaneous ground state. The doped picene (C22H14)[2], even 33 K in K-doped 1,2;8,9- Monkhorst-Pack k-point grids were generated according −1 dibenzopentacene [C30H18(I)] [5]. Combining with the to the specified k-point separation 0.02 A˚ .Andthecon- geometrical shape of these organic molecules, these find- vergence thresholds were set as 10−5 eV in energy and ings above indicate that Tc changes with the number and 0.005 eV/Ainforce.InthestandardDFT,thelocalden-˚ the arrangement of benzene rings. Thus, a new avenue in sity approximation (LDA) [24] and the generalised gra- the quest for organic superconductors has been opened. dient approximation (GGA) of Perdew-Burke-Ernzerhof The higher superconducting transition temperature is version [25]wereadoptedtodescribetheelectronic expected in this kind of materials. exchange-correlation interactions. As a comparison, the So far, the highest Tc of 33.1 K was observed in K- vdW density functional (vdW-DF) [26], the second ver- doped 1,2;8,9-dibenzopentacene [KxC30H18(I), x = 3.45] sion of vdW-DF (vdW-DF2) [27] and the semi-empirical for PAH superconductors [5]. Actually the obtained high- DFT method of Grimme (DFT-D2) [28]wereadoptedto est Tc is far less than the room temperature. One of its investigate the influence of the dispersion interactions to main limitations is that the kind of compound is diffi- the optimisation of crystal structures. cult in fabricating experimentally. The ideal crystalline sample for measurement is lack. However, for C30H18(I) with the long-benzene-ring chain, the result of elec- 3. Results and discussion tron energy-loss spectroscopy [21]hasconfirmedthe 3.1. Functional analysis formation of K-doped phases. Moreover, [n]phenacenes as large as [11]phenacenes have been synthesised [22], In order to obtain the accurate crystal structures of pris- which implies more choices to realise the higher super- tine and doped C30H18(I), we first tested the precision conducting transition temperature in PAHs. Interestedly, of different functionals by comparing optimised crys-
multi-T phases exist in PAHs with the long-benzene- c tal parameters of pristine naphthalene (C10H8), C14H10, ring chain such as 6.5, 6.9, 7, 7.4, 8, 17 and 18 K in K- chrysene (C18H12)andC22H14 with their experimen- doped C22H14 [2] as well as 5, 7, 7.4, 28.2 and 33.1 K tal values. The calculated results are summarised in in KxC30H18(I) [5]. Besides the number and the arrange- Table 1, comparing with experimental and previous the- ment of benzene rings, we point out that the supercon- oretical values [29–35]. From the calculated data listed ductivity is related to the doping content and the position in Table 1, we can conclude that vdW-DF2 functional of K atoms which also determines the different electronic produces the crystal parameters closer to experimen- properties of doped system. It is important for under- talones.InthecaseofC14H10,ourdatabasedon standing this fascinating superconductivity to reveal the LDA/GGA is consistent with the previous LDA/GGA crystal and electronic structures of KxC30H18(I). Unfor- calculation [31,32]. However, the optimised lattice con- tunately, the research on basic properties of KxC30H18(I) stantsbasedonLDAarecorrespondinglysmallerthan is still lacking. In this work, therefore, we present a the experimental ones [30]. The contraction of cell vol- detailed theoretical study on the structures and elec- ume reaches 10.8% or over this. Contrary to LDA, GGA tronic properties of KxC30H18(I) using the first-principles leads to the larger lattice constants than experiment [30]. study with van der Waals density functional, which is In particular, the expansions of the lattice constant in simultaneously compared with those of [7]phenacenes b direction and the volume of unit cell reach to ∼ 9% [C30H18(II), which is used to distinguish from C30H18(I)] and ∼ 15%, respectively. As a result, both LDA and GGA with the different armchair edge type. functionals are unsuited to obtain the reasonable crystal parameters. Based on the consideration of vdW interac- tions, the calculation results listed in Table 1 imply the 2. Computational details importance of the dispersion interactions in this kind of Within the framework of the density functional the- molecular crystal. Differing from the previous theoreti- ory (DFT), the Vienna ab initio simulation package cal study [32]inwhichvdW-DFistheoptimalscheme, (VASP) [23]wasemployedtocarryoutthecalculations the lattice constants and the cell volume optimised with of full optimisation and electronic structures of all of the help of vdW-DF2 in our calculations are in excellent the designed structures. Inner electrons were replaced agreement with experimental values. The biggest errors 474 G.-H. ZHONG ET AL.
Table . Optimised lattice constants a, b and c (in A),˚ angle Table . Optimised lattice constants a, b and c (in A˚ ), angle β β between a and c axes, and volume V of a unit cell for the between a and c axes, and volume V of a unit cell for the pristine pristine CH,CH,CH and CH molecular crystals, CH(I) and CH(II), with the P symmetry and two molecules with the P symmetry and two molecules per cell, obtained per cell, obtained by the vdW-DF scheme, compared with the with different approximations, compared with experiment results from other functionals. and previous theoretical results. System Source ab cβ V System Source abcβ V LDA . . . . . Expt. [] . . . . . GGA . . . . . LDA . . . . . CH(I) vdW-DF . . . . . vdW-DF . . . . . CH GGA . . . . . vdW-DF . . . . . DFT-D . . . . . vdW-DF . . . . . DFT-D . . . . . LDA . . . . . GGA . . . . . Expt. [] . . . . . CH(II) vdW-DF . . . . . LDA [] . . . . . vdW-DF . . . . . GGA [] . . . . . DFT-D . . . . . vdW-DF [] . . . . . vdW-DF [] . . . . . CH DFT-D [] . . . . . LDA . . . . . provides a key contribution to obtain the accurate crystal GGA . . . . . vdW-DF . . . . . parameters. vdW-DF . . . . . DFT-D . . . . . 3.2. C30H18 and C30H18II Expt. [] . . . . . LDA . . . . . With the help of the analysis above, we predicted geo- CH GGA . . . . . vdW-DF . . . . . metrical configurations of the pristine30 C H18(I), which vdW-DF . . . . . has not been reported. Crystal parameters optimised by DFT-D . . . . . vdW-DF2 are listed in Table 2, compared with the results Expt. [] . . . . . from other functionals. Under P21 symmetry,wepropose LDA [] . . . . . = ˚ = ˚ LDA . . . . . that the lattice constants are a 6.745 A, b 7.613 A CH GGA . . . . . and c = 18.495 A,˚ and the angle is β = 97.13° between vdW-DF . . . . . vdW-DF . . . . . a and c axes, leading to the volume of unit cell of 942.5 DFT-D . . . . . A˚ 3. Crystal parameters induced by LDA and GGA obvi- ously deviate from those from vdW-DF2 functional. Geo- metrical configurations viewing from different directions are shown in Figure 1(a). Noticeably, the angle formed by in lattice constants and cell volume are only 0.7% and two molecular layers in herringbone structure becomes 1.3%, respectively. For other forms of vdW functionals, smaller than those in pristine C14H10 and C22H14,which vdW-DF (DFT-D2) overestimates (underestimates) the is possibly caused by the different arrangements of ben- lattice constants and the cell volume. zene rings. For C30H18(II) with the same armchair-edge For pristine C22H14, although the previous LDA cal- type as C14H10 and C22H14, the predicted lattice constants culation [35] has led to lattice constants close to experi- of solid C30H18(II) with P21 symmetry are a = 8.613 A,˚ b = = β = ° mental ones [34], the smaller cell volume of C22H14 was 6.144 Aand˚ c 17.644 Aandtheangleis˚ 86.32 obtained by LDA. GGA still overestimates lattice con- between a and c axes. The geometry shown in Figure 1(b) stants. Comparing with other functionals, vdW-DF2 is exhibitsthesimilarstructuralshapetopristineC14H10 still an effective functional in the optimisation of pristine and C22H14.However,thelatticeconstantinthec direc- β C22H14. Theoretically obtained lattice constants and the tion gradually becomes larger and the angle becomes cell volume are in good agreement with the experimental smaller from C14H10 to C22H14 and to C30H18(II). Addi- ones under considering the correction of vdW forces in tionally, the total energies implies the stronger stability the scheme of vdW-DF2. The biggest error in all of the in C30H18(II) than C30H18(I)withthedifferenceofabout lattice constants in Table 1 is only 0.7%. Moreover, the 0.45 eV/f.u.. optimised lattice constants and the cell volume of pristine C10H8 and C18H12 also exhibit the similar phenomenon 3.3. K-doped C30H18 and C30H18II to C14H10 and C22H14 as shown in Table 1.Thus,vdW forces can not be ignored in the investigations on crys- To study the doped structures, we respectively put tal structures of PAHs. Especially, vdW-DF2 functional different number of K atoms into C30H18(I), namely MOLECULAR PHYSICS 475
P Figure . (Colour online) Optimised crystal structures of undoped CH(I) (a) and CH(II) (b) with the symmetry and two molecules per cell, based on the vdW-DF scheme. The solid blue line represents the unit cell size. Big brown and small grey balls represent C and H atoms, respectively. Seen along the b direction, benzene rings in a organic molecule are distinguished by the digit of , , … .
KxC30H18(I) (x = 1, 2, … 7), and performed the full experiment, from K3C30H18(I) to K4C30H18(I), optimisation using the vdW-DF2 functional. Kosugi the expansion along a direction is in the range of et al. [36] and Vergés et al. [37] have verified that the 19.1%−21.6%. Along b direction, on the contrary, the systemic energy is lower when K atoms are intercalated lattice constant has a small contraction when doping K into the intralayer region. Based on this viewpoint, we atoms. the contraction ratio is about 0.7%−5.8%. Near considered dozens of initial configurations induced thedopinglevelofK3C30H18(I), the contraction along b by the differences of K atomic positions and angles of direction is the smallest as shown in Figure 2(a). Notice- herringbone structure for each doping concentration. ably, except for K5C30H18(I) and K7C30H18(I), the lattice ThesameprocesswasalsocarriedoutforK-doped constant along c direction is shrunk for other doping lev- C30H18(II), namely KxC30H18(II) (x = 1, 2, … 7). In els of K atoms comparing with undoped case. However, Table 3,welistoutthecrystalparametersbyselecting thevolumeofunitcellofKxC30H18(I) is monotonously the most stable structure at each doping level. And we increased with increasing K atoms. The expansion of present the evolutions of lattice constants in Figure 2.For volume is about 14.7% for K3C30H18(I) and 17.0% for C30H18(I), the K doping results in the obvious expanding K4C30H18(I). of lattice constant along a direction though the varia- Differing from KxC30H18(I), as shown in Figure 2(b), tion is not monotonous. The expansion ratio along a the lattice constant along a (b) direction in KxC30H18(II) direction reaches to 17.8% in K1C30H18(I) even 26.4% has the opposite variation tendency. Except for the doping in K6C30H18(I). Corresponding to doping levels in level of K7C30H18(II), the K doping in C30H18(II) results 476 G.-H. ZHONG ET AL.
in the lattice constant along a direction contracting. And Table . Optimised lattice constants a, b, c (in A˚ ), angle β in these doping levels of K3C30H18(II) and K4C30H18(II), between a and c axes, and volume V ofaunitcellforKxCH(I) the contraction is the strongest. Along b direction, the and KxCH(II), with the P symmetry and two molecules per lattice constant obviously increases when intercalating K cell, based on the vdW-DF scheme. atoms into C30H18(II).Specially,thelatticeconstantalong System ab c β V c direction has an expansion after initial contraction with theincreaseofdopingconcentrationinC30H18(II). How- C H (I) . . . . . ever, the volume variation induced by the doping in KCH(I) . . . . . KCH(I) . . . . . C30H18(II)isthesameasthatinC30H18(I). The K dop- K C H (I) . . . . . ingleadstotheincreaseofvolumebothinC30H18(I) KCH(I) . . . . . KCH(I) . . . . . and C30H18(II), which is different from the experimental K C H (I) . . . . . observations on doped C H [4]andC H [2]. K C H (I) . . . . . 14 10 22 14 The change of lattice parameters comes from the vari- C H (II) . . . . . ationofinteractionsamongKatoms.Wealsofoundthat KCH(II) . . . . . KCH(II) . . . . . the K atoms moving into the intralayer area makes the KCH(II) . . . . . system more stable which is according with K-doped K C H (II) . . . . . other PAHs [36,37]. Figure 3 clearly exhibits crystal struc- KCH(II) . . . . . KCH(II) . . . . . tures of KxC30H18(I). Combining with the label of ben- K C H (II) . . . . . zene ring marked in Figure 1,wecancarefullyobserve the distribution of K atoms on ac-plane for different dop- ing levels. For the doping concentration of one K atom per organic molecule, K1C30H18(I), this K atom is at the cen- treofring-5.ForK2C30H18(I), one of two K atoms is in ring-2 but near the edge of benzene ring, while the other isonthebridgeofring-4andring-5.ForK3C30H18(I), oneofthreeKatomsisonthebridgeofring-4andring-
5, while the other two respectively lie in ring-2 and ring-7 anddeviatefromtheeofbenzenering.ForK4C30H18(I), four K atoms occupy ring-1, ring-3, ring-5 and ring-7, respectively. But they all are near the edge of benzene ring. For K5C30H18(I), the doped five K atoms are sym- metrically distributed in the organic molecular layer. One is localised at the centre of ring-4, the centre of organic molecule. Two are respectively on the bridges of ring-2 and ring-3 and of ring-5 and ring-6. In particular, two of five K atoms are pushed to the end of organic molecule as shown in Figure 3.Forthesedopinglevelsabove,the relaxation calculation of atomic positions indicated that Katomsaremorelikelytostayintheintralayerregion of organic molecules. When adding up to six K atoms per organic molecule, K6C30H18(I), four of six K atoms are situated in the intralayer region of organic molecules, while two of six K atoms are close to the interlayer region. In K7C30H18(I), two of seven K atoms completely move into the interlayer region of organic molecules. This enhancement of K interatomic repulsion results in the ris- ing of systemic energy. As a comparison, crystal structures of KxC30H18(II) are shown in Figure 4. Seen from the projection on ac a b c Figure . The evolutions of lattice constants in , and direc- plane, K1C30H18(II) is similar to K1C30H18(I), the K atom tions with the change of the doping level. (a) and (b) represent is located in ring-5. In K2C30H18(II), two K atoms occupy KxCH(I) and KxCH(II), respectively. on ring-3 and ring-6, respectively. In K3C30H18(II), MOLECULAR PHYSICS 477
× × Figure . Optimised crystal structures of KxCH(I) based on the vdW-DF scheme, showed in form of supercell and projected at ac plane. Brown, grey and purple balls represent C, H and K atoms, respectively.
ac Figure . Optimised crystal structures of KxCH(II) based on the vdW-DF scheme, projected at plane. Brown, grey and purple balls represent C, H and K atoms, respectively. 478 G.-H. ZHONG ET AL.
k Figure . Calculated electronic band structures along high symmetrical -path of KxCH(I), where zero energy denotes the Fermi level. The position variation of LUMO in CH(I) is highlighted by red letters.
three K atoms are in ring-2, ring-4 and ring-6, respec- 3.4. Electronic structures tively. The same as K C H (I), in K C H (II), four 4 30 18 4 30 18 The difference of doping contents results in not only the K atoms are also in ring-1, ring-3, ring-5 and ring-7, variation of crystal configurations but also the change of anddeviatefromthecentreofbenzenering.Similar electronic properties. It has been well known that all of to K C H (I), K atoms are favourably staying in the x 30 18 these metal-doped PAHs are charge-transfer compounds intralayer region of organic molecules. When, adding up with the electrons transferring from metal to organic to six K atoms per organic molecule in C H (II), some 30 18 molecule. Although the rigid-band model is not enough of K atoms will move into the interlayer region of organic to describe the electronic structures of doped PAHs, the molecules as shown in Figure 4,duetotheincreaseof visible feature is the shift of Fermi level under the elec- Coulomb repulsion interaction. Thus, the high doping tron doping. As shown in Figure 5,thepristineC H (I) concentration will drive a stronger structural change, 30 18 is an indirect band-gap semiconductor with the band- which implies the possible instability at the high doping gap (E ) of 1.03 eV. Under P2 symmetry, the lowest levels. g 1 MOLECULAR PHYSICS 479
k Figure . Calculated electronic band structures along high symmetrical -path of KxCH(II), where zero energy denotes the Fermi level. The position variation of LUMO in CH(II) is highlighted by red letters. unoccupied molecular orbital (LUMO) evolves into two semiconductor feature with the Eg of 0.91 eV. Similarly, conduction bands above 1.0 eV, and the highest occu- there are three electrons transferring from K to molecule pied molecular orbital (HOMO) forms these two valence in K3C30H18(I). LUMO will be full-filled by two of these bands below Fermi level. After doping, conduction bands three electrons, and LUMO+1withhigherenergyishalf- become much fatter. Doping one K atom for each organic filled by the other electron. Thus,3 K C30H18(I) becomes molecule will result in one electron transferring from into a metal again. At the doping level of x = 3, the K atom to organic molecule and push Fermi level to variation of electronic conductive properties of K-doped higher energy. But LUMO is half-filled because of only C30H18(I) is according with that of K-doped C22H14 [38]. one electron transferring. Two conduction bands formed However, this theoretical prediction is different from by LUMO almost are degenerated and cross Fermi level. the measurement of electron energy-loss spectroscopy As a result, K1C30H18(I) behaves as a metal. Two elec- basedonafilmsamplewhereK1C30H18(I) is a semi- trons transfer from K to organic molecule in K2C30H18(I), conductor while K2C30H18(I) is metallic [21]. This rea- which makes two bands to be full-filled. LUMO trans- son possibly comes from the difference between thin forms a new HOMO, thus K2C30H18(I) exhibits a film and bulk crystal. Comparing with K3C30H18(I), in 480 G.-H. ZHONG ET AL.
Figure . Calculated electronic density of states of KCH(I), K.CH(I) and K.CH(I), where zero energy denotes the Fermi level.
principle, one additional electron will fully fill LUMO+1 LUMO+1inC30H18(I). Introducing electrons by dop- in K4C30H18(I). But, there are degenerated energy levels ing K atoms, as shown in Figure 6,K1C30H18(II) behaves along some k paths between LUMO+1andLUMO+2, as a metal, K2C30H18(II) becomes back a semiconduc- as shown in Figure 5. The degeneracy in energy results in tor with a small Eg of 0.03 eV, and K3C30H18(II) trans- this additional electron occupying not only LUMO+1but fers to metal again. In K4C30H18(II), there is a big also LUMO+2, which means that neither LUMO+1nor energy gap between LUMO+1andLUMO+2sothat LUMO+2isfilled.SoK4C30H18(I) has the metallic char- the exotic electrons occupy first LUMO+1. K4C30H18(II) acter, which differs from picene doped by four K atoms exhibits the semiconductor characteristic with the Eg of [38]. Furthermore, more K atoms doping into C30H18(I) 0.19 eV, distinguishing from the metallic K4C30H18(I). repeats the transition between metal and semiconductor. K5C30H18(II) displays the metallic feature, abiding the Noticeably, in K7C30H18(I), more K atoms will cause the electronic occupancy principles on orbital. However, nei- largervariationofbandstructureduetotheincreaseof ther K6C30H18(II) nor K7C30H18(II) has the band nature energy bands from K component, as shown in Figure 5. of molecular crystal, similar to K7C30H18(I). More K The crystalised C30H18(II) is direct band gap semi- atoms are intercalated into the system, which breeds a conductor with the larger Eg of 2.0 eV than C30H18(I). stronger density of itinerant electrons. The band struc- The valence band maximum and the conduction band ture tends to the style of bulk metal instead of molecular minimum are both at Zk-point, but the bands along crystal. Z − direction are very fat. Under P21 symmetry, For K-doped 1,2;8,9-dibenzopentacene, K3C30H18(I) each orbital of C30H18(II) is also split into two bands. only exhibited the superconductivity of Tc = 7K[5]. But the energy levels of orbitals in C30H18(II) are dif- The high Tc phases of 33 and 28.2 K [5] were observed ferent from those in C30H18(I), due to the distinc- in K3.45C30H18(I) and K3.17C30H18(I) samples, respec- tion of the arrangement of benzene rings. For instant, tively. The doping levels of high Tc phases in KxC30H18(I) LUMO is close to LUMO+1inC30H18(II), while LUMO deviate from x = 3, which is similar to those in K-doped is isolated with a energy gap of 0.5 eV distant from C22H14 [2]. These doping levels, x = 3.17 and x = 3.45, MOLECULAR PHYSICS 481 mean that more electrons transfer from K to organic molecule, comparing with x = 3. Fermi level will be pushed up to the higher energy level. In order to under- stand these three different superconducting phases, we have calculated the electronic structures by the virtual crystal approximation. Figure 7 presents the electronic densityofstates(DOS)ofK3C30H18(I), K3.17C30H18(I) and K3.45C30H18(I). We find that the electronic states nearFermilevelsplitintothreesharppeaks.Withthe increase of injected electrons, Fermi level shifts towards the higher energy level. The variation of doping concen- trationinducesthechangeoftheDOSvalueatFermi level (NEF). From K3C30H18(I) to K3.17C30H18(I) and to K3.45C30H18(I), the NEF is respectively 13.1, 19.8 and 22.9 states/eV, which is corresponding to the variation of superconducting critical temperatures of these phases. Namely, one reason of higher Tc origins from the higher NEF value. Of course, the mechanism of superconduc- tivity in metal-doped PAHs is still complicated. Simi- lar to metal-doped fulleride [39,40], the narrow band- width less than 0.5 eV indicates that the strong electronic correlation effects exist in doped PAHs. Only electron– phonon coupling is not enough to explain the high Tc phenomenon such as 18 K in K-doped C22H14 and 33 or 28.2 K in KxC30H18(I), though it can match the low Tc (7 K) case well [41,42]. However, from the aspect of elec-
tronic structures, the physical picture of superconductiv- ity of KxC30H18(I) has been understood further.
3.5. Stability
In this study, we have investigated the structural and elec- tronic properties of seven doping concentration cases of Figure . Formation energy of K-doped system as a function of the KxC30H18(I). But only three doping concentrations were K chemical potential. Upper and lower panels represent K C H (I) observed in this experiment. To determine which dop- x and K C H (II), respectively. ing concentration is easy to be fabricated in the experi- x ment,wehavealsocalculatedtheformationenergy(Ef) ofthedopedsystemtoanalysethethermodynamicstabil- ity. Referring to previous studies on the formation energy theupperpanelshowninFigure 8,focusingonthesitua- tion of E < 0forK C H (I), we find that K C H (I) of doped system [43–45], the Ef for the doping level x is f x 30 18 2 30 18 defined as the function of K chemical potential: has stronger stability than other phases in the large range of chemical potential, while K4C30H18(I) is more sta- ble under K-rich condition. Between K2C30H18(I) and Ef = Edoped − Epristine − xμK(bulk) − x[μK − μK(bulk)] K4C30H18(I), K3C30H18(I) phase only forms in a narrow (1) rangeofchemicalpotential.Fromthecalculatedresults, these phases with higher doping concentrations are diffi- where Edoped and Epristine arethetotalenergyofthedoped cult to be fabricated due to the condition of higher for- and host crystal, respectively. μK(bulk) can be obtained mation energy, which also indirectly confirms that the from the energy per K atom in the K metal with the bcc intercalating K atoms into the intralayer region of organic structure. x is the doped concentration. μK is the chemical molecules is perfect on the system stability. In a whole potentialoftheKspecie.μK = μK(bulk) means the ele- rangeofchemicalpotential,however,thesethreephases ment is so rich that the pure element phase can form. Ef < of K2C30H18(I), K3C30H18(I) and K4C30H18(I) are eas- 0 indicates that the doped compound can stably exist. As ily fabricated in the experiment. As mentioned earlier, 482 G.-H. ZHONG ET AL.
− Table . Calculated relative total energy (E[KxC30H18 (I)] E[KxC30H18 (II)]) in unit of eV. System x = x = x = x = x = x = x = x =
KxCH(I) . –. –. –. –. –. –. –. KxCH(II)
K2C30H18(I) is a semiconductor. Hence, the supercon- superconducting phases observed experimentally. For ductivity should be discovered in KxC30H18(I) (2 < x < K-doped [7]phenacenes, K3C30H18(II) and K4C30H18(II) 4) such as experimental investigations with samples cor- phases are more stable from the calculated formation responding x = 3, 3.17 and 3.45 [5]. energy. Because K4C30H18(II) exhibits a semiconductor For KxC30H18(II) as lower panel shown in Figure 8 feature,wesuggestthatthesuperconductivityshould the doping phase only exists in the K-rich situation, and also appears in the doping range of 2 < x < 4, if existing K3C30H18(II) and K4C30H18(II)phasesaremorestable. superconducting phase. This study is helpful for under- Sowepredictthatthepossiblesuperconductivityshould standing the 1,2;8,9-dibenzopentacene superconductor appear in this phase of doping level in the range of 2 < as well as the superconductivity of PAHs. x < 4, since x = 2 and 4 corresponds to the semicon- ducting phase. Undoped C30H18(II) is more stable than Acknowledgements undoped C30H18(I). However, from the calculated total energy listed in Table 4,dopedC30H18(I) has higher sta- The work was supported by the National Natural Science Foun- dation of China [Grant nos. 11274335, 11474004, 61274093, bility than doped C30H18(II). 61574157 and 11504398], the Research Program of Guang- dong under Grant no. 503169657054 and the Research Pro- 4. Conclusions gram of Shenzhen under Grant nos. JCYJ20150521144320993, JCYJ20160331193059332 and JCYJ20150529143500956. The We have systematically studied crystal and electronic calculation was supported by the Special Program for Applied structures of pristine and potassium-doped 1,2;8,9- Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase). dibenzopentacene compared with [7]phenacenes, based on the DFT first-principles calculations plus the vdW correction. The calculations of full optimi- Disclosure statement sations fitting experimental crystal parameters suggest No potential conflict of interest was reported by the authors. that the vdW-DF2 functional is perfect to describe the nonlocal interaction. With the help of vdW-DF2, Funding we have predicted crystal structures of pristine and doped 1,2;8,9-dibenzopentacene and [7]phenacenes, National Natural Science Foundation of China [Grant and investigated the K atomic positions after dop- Numbers 11274335, 11474004, 61274093, 61574157 and ing. In this kind of material, K atoms are favourably 11504398]; the Research Program of Shenzhen [Grant Num- bers JCYJ20150521144320993, JCYJ20150529143500956, staying in the intralayer region of organic molecules. JCYJ20160331193059332]; the Research Program of Guang- For undoped cases, [7]phenacenes is more stable than dong [Grant Number 503169657054]; Special Program for 1,2;8,9-dibenzopentacene. However, doped 1,2;8,9- Applied Research on Super Computation of the NSFC- dibenzopentacene has higher stability correspondingly Guangdong Joint Fund. than doped [7]phenacenes. From the evolution of elec- tronic structures, the doping realises the transition ORCID from semiconductor to metal or from metal to semi- conductor. Due to the difference of aromatic edge, Guo-Hua Zhong http://orcid.org/0000-0003-0673-8738 the electronic band structures near Fermi level in K- doped 1,2;8,9-dibenzopentacene are clearly different References from those in K-doped [7]phenacenes. For K-doped 19 1,2;8,9-dibenzopentacene, K2C30H18(I) and K4C30H18(I) [1] V.L. Ginzburg, Sov. Phys. Usp. , 174 (1976). [2] R. Mitsuhashi, Y. Suzuki, Y. Yamanari, H. Mitamura, T. areeasilyfabricatedintheexperiment.K3C30H18(I) can also form in a narrow range of chemical potential. Kambe, N. Ikeda, H. Okamoto, A. Fujiwara, M. Yamaji, N. Kawasaki,Y.Maniwa,andY.Kubozono,Nature(London) Amongthree,K2C30H18(I) is a semiconductor; on the 464,76(2010). contrary, both K3C30H18(I) and K4C30H18(I) are metal- [3] Y. Kubozono, M. Mitamura, X. Lee, X. He, Y. Yamanari, lic, which are just corresponding to the doping range of Y. Takahashi, Y. Suzuki, Y. Kaji, R. Eguchi, K. Akaike, T. MOLECULAR PHYSICS 483
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