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Sep 19, 2016 - Samarium is a magnetic element due to its unfilled f shell in electronic configuration [Xe]4f65d06s2. Usually, there are large spin mom...
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Magnetic and Electronic Properties of Samarium-Doped Phenanthrene from First-Principles Study Xun-Wang Yan,*,†,‡ Yanyun Wang,† Miao Gao,§ Dongwei Ma,† and Zhongbing Huang∥ †

School of Physics and Electrical Engineering, Anyang Normal University, Henan 455000, China Beijing Computational Science Research Center, Beijing 100084, China § Faculty of Science, Ningbo University, Zhejiang 315211, P. R. China ∥ Faculty of Physics and Electronic Technology, Hubei University, Wuhan 430062, China ‡

ABSTRACT: Based on the van der Waals density functional theory (DFT), we have studied the crystal structure and magnetic and electronic properties of samarium-doped phenanthrene, a newly discovered aromatic superconductor. For Sm1phenanthrene, we found that the magnetism in the ground state is antiferromagnetic, in good agreement with the experimental measurement. When Hubbard U of 6 eV is considered, the Sm1-A structure becomes an atomic force microscopy (AFM) semiconductor with a gap of 0.12 eV. Including the spin−orbit coupling, the orbital moment of the Sm atom is 2.28 μB with the opposite direction to the spin moment of 5.99 μB. The total moment of 3.7 μB around Sm atoms in Sm-doped phenanthrene is quite distinct to the divalent and trivalent Sm ions in monochalcogenides and samarium hexaboride. The hybridization of Sm 5d and C 2d states results in a relatively strong interaction of metal and molecule in Sm-doped phenanthrene compared with the interaction in K-doped picene and phenanthrene. Our results provide the fundemental magnetism and electronic properties of the Sm-doped phenanthrene superconductor.

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INTRODUCTION The search for a novel superconductor is one of the most challenging tasks in condensed matter physics and material science. The recent discovery of superconductivity in potassium-doped picene (C22H14) with the superconducting transition temperature Tc of 18 K has excited great interest in organic superconductors.1 At the beginning, alkali metal K and Rb were doped into picene, phenanthrene, coronene, and dibenzopentacene to synthesize the superconducting samples.2−5 Thereafter, alkali-earth metal Ba, Sr, and Ca were used to replace the alkali metal to act as the dopant.3,6 Still later, Chen’s group chose rare-earth metal La and Sm to synthesize the La1phenanthrene and Sm1phenanthrene with Tc ∼ 6 K superconductors.7 Artioli et al. discovered the superconductivity in Sm-doped picene and chrysene with Tc of 4 and 5.4 K and confirmed a Sm-doped phenanthrene superconductor.8 Recently, the experimental studies of Kintercalated polyacenes and coronene were reported by S. Heguri’s group and X. Xiao’s group9,10 These superconductors based on the aromatic hydrocarbons have some common structural features. The molecules consist of several benzene rings fused together along a zigzag line, and in crystal the molecules are arranged in a herringbone pattern to form the molecular layer and then stacked layer by layer. The metal dopants are intercalated into the interstitial space among molecules in a layer. The charge is transferred from metal dopant to molecule and delocalized on the whole crystal to © XXXX American Chemical Society

induce the metallic state, similar to the Bechgaard salt superconductors.11−13 The mechanism of the superconducting pair in these metaldoped aromatic hydrocarbons is in debate. Within the framework of Bardeen−Cooper−Schrieffer (BCS) theory, T. Kato and co-workers think that strong intramolecular electron− phonon coupling in trianionic picene3− can explain the Tc = 18 K superconductivity,14 and M. Casula et al. emphasize that intercalant and intermolecular phonons have a great contribution to the superconductivity.15 However, there exist some hints to manifest the unconventional nature of superconductivity, such as the obvious positive pressure dependence of Tc and the existence of local magnetic moment in K-, Ba-, Sr-, La-, and Sm-doped phenanthrene superconductors.2,6,7 K3picene was suggested to be a strongly correlated system, and the ratio between the effective Coulomb repulsion and the bandwidth was estimated from the first-principle calculations.16,17 The insulating phase of K-doped picene multilayers was observed and confirmed by the Caputo group and Ruff group.5,18 Magnetic instability and electron−electron correlation are also suggested to play an important role in pair binding in aromatic hydrocarbon superconductors.19 Samarium is a magnetic element due to its unfilled f shell in electronic configuration [Xe]4f65d06s2. Usually, there are large spin moments and orbital moments around Sm ions in Received: August 18, 2016

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contains two phenanthrene molecules and two holes, shown in Figure 1(a). Since the P21 group symmetry is still kept in Sm-

compounds. In experiment, the magnetic susceptibility of Sm1phenanthrene takes on an obvious antiferromagnetic transition at 15 K,7 which was not observed in other metaldoped phenanthrene and picene, including alkali metal, alkali earth metal, and nonmagnetic rare earth metal lanthanum. Therefore, Sm-doped phenanthrene is a unique aromatic superconductor with magnetic ground state, quite different from those aromatic superconductors doped by nonmagnetic metals. The superconductivity in Sm-doped phenanthrene has been confirmed recently as well as Sm-doped chrysene, and picene superconductors have been discovered by the Lorenzo Malavasi group.8 This has revived the discussion on the magnetism and correlation effect in Sm-doped aromatic hydrocarbon superconductors. Since there are no theoretical research reports so far, it is an urgent issue to clarify the magnetic and electronic structure of Sm-doped phenanthrene, chrysene, and picene, which is the key basis to discuss the relation among magnetism, correlation, and superconductivity in this class of materials. In this paper, we focus on Sm-doped phenanthrene to study its electronic and magnetic properties from the first-principles method.

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COMPUTATIONAL DETAILS Our calculations have been performed using the plane-wave pseudopotential method as implemented in the Vienna ab initio simulation package (VASP) program.20,21 The generalized gradient approximation (GGA) with Perdew−Burke−Ernzerhof (PBE) formula22 for the exchange-correlation potentials and the projector-augmented wave method (PAW)23 for ionic potential were used to model the electron−electron and electron−ion interactions. The C, H, and K pseudopotentials are from the subfolder C_s, H_s, and Sm_3 in the pseudopotential package potpaw_PBE.52 supplied by the VASP Web site. The plane-wave basis cutoff is set to 500 eV, and a mesh of 4 × 4 × 4 k-points was sampled for the Brillouinzone integration. Also, the Gaussian broadening technique was used. The convergence thresholds of the total energy, force on atom, and pressure on cell are 10−5 eV, 0.005 eV/Å, and 0.1 KBar, respectively. The van der Waals (vdW) interaction is included, and the van de Waals functional we used is the vdWDF2 scheme, proposed by Langreth and Lundqvist et al.24−27 We have included the strong Coulomb repulsion in the Sm4f orbitals on a mean-field level using the GGA + U approximation with an effective Ueff of 6.0 eV. Because the orbital magnetic moments have a substantive contribution to the total moment of Sm ion, the spin−orbit coupling (SOC) is included in our calculations.

Figure 1. (a) Crystal structure of pristine phenanthrene with a monoclinic unit cell containing two molecules. Left panel: a side view along the b axis to show the molecular layer. Right panel: a front view along the c axis to show the herringbone-type arrangement of molecules. (b), (c), and (d) are the crystal structures of Sm1-A phase, Sm1-B phase, and Sm2phenanthrene.

doped phenanthrene samples in experiment,7,8 the unit cells of Sm1phenanthrene and Sm2phenanthrene constructed in our calculations hold the P21 symmetry. Namely, each of two holes has one Sm atom for Sm1phenanthrene and two Sm atoms for Sm2phenanthrene, shown in Figure 1(b) and (d). Another Sm1phenanthrene structure without P21 symmetry is considered, as shown in Figure 1 (c), which was mentioned in previous reports on La1phenanthrene.28 We first performed the structural optimization of pristine phenanthrene. After full relaxations, the lattice parameters along a, b, and c axes are 8.494, 6.087, and 9.363 Å. The β angle between a and c axes is 97.86°. All these parameters are in a good agreement with the experimental ones. This indicates the C and H pseudopotentials and the selected computational scheme are reasonable and reliable. Crystal Structure of Sm 1 phenanthrene and Sm2phenanthrene. The detailed crystal structures of metal-

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RESULTS AND DISCUSSION The phenanthrene molecule is a polycyclic aromatic hydrocarbon which is composed of three fused benzene rings in the shape of the letter V. Phenanthrene crystal has the monoclinic symmetry with space group P21 (Z = 2), and the lattice parameters are a = 8.453 Å, b = 6.175 Å, c = 9.477 Å, and β = 98.28°.2 The molecules in the solid are arranged in a herringbone-type pattern to form each molecular layer, and the layers are stacked one by one along the c axis to form the crystal. That leaves the enough interstitial space among molecules in the layer to accommodate the dopant. The interstitial space among molecules in a layer can be considered as a hole enclosed by four neighbor molecules. A unit cell B

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exhibits the valence state +2 or +3 in samarium compounds, such as SmS and Sm2O3. By the Hund’s rule, a divalent Sm2+ ion with 4f6 has the spin of S = 3, the orbital angular momentum of L = 3, and total angular momentum of J = |L − S| = 0. So, the divalent Sm2+ ion is nonmagnetic, as reported for samarium monochalcogenides in ref 35. For trivalent Sm3+ ion with a 4f 5 configuration, total angular momentum of 5 5 J = |L − S| = |5 − 2 | = 2 ; meanwhile, Hund’s rule ground state is predicted to have a small total moment of 0.84 μB. In first-principle results of the SmN compound, the spin moment is 4.99 μB, and the orbital moment is −4.53 μB.36 The two moment directions are antiparallel, which leads to a small net moment of 0.46 μB according to spin moment and orbital moment canceling each other. Namely, Hund’s rule is valid for Sm3+ and Sm2+ ions in samarium compounds. What about the Sm atom in Sm-doped phenanthrene? To inspect the Sm moment, we put a Sm atom in the middle of a hole in a unit cell to perform the GGA calculations including spin−orbit coupling. Quite distinct to the above situations, the orbital moment of the Sm atom is −2.28 μB with an antiparallel direction to spin moment. The orbital moment is so small that it can not effectively cancel the spin moment, which is 5.99 μB around the Sm atom in Sm-doped phenanthrene. The spin moment comes from the Sm 4f and 5d electrons with the contribution of ∼5.7 μB and ∼0.3 μB, respectively. To sum up, there still exists a large net moment of 3.71 μB around the Sm atom. As we know, the crystal field effect has a significant influence on electron occupation and the atomic orbital alignment. In Sm-doped phenanthrene, the bonding between Sm and the molecule is not as strong as the bonds in ionic and covalent samarium compounds, and the crystal field around the Sm atom in this material is very different from that in other samarium compounds. Hence the Hund’s rule is expected to be unreliable in this system. The charge transfer from the Sm atom to molecule in Smdoped phenanthrene is about 1.3 electrons, and the valence state of the Sm atom is close to +1, instead of +2 or +3. The Sm 4f states have 5.6 electrons, distributed among seven atomic orbitals, i.e., fy(3x2−y2), fz(x2−y2), fyz2, fz3, fzx2, fxyz, and fx(3y2−x2), with the charge of 0.73, 0.64, 0.86, 0.87, 0.76, 0.74, and 0.97 electrons, respectively. The projected density of states of 4f states on seven partial orbitals are displayed in Figure 2. One feature is that these DOS peaks of seven orbitals are all located in the energy range from −0.3 to 0.1 eV around the Fermi level. Another feature is that Sm 4f states have a homogeneous distribution among seven orbitals which leads to the roughly uniform occupation of electrons in these orbitals. It is noted that the electronic states on seven orbitals are located in the same energy range and are nearly degenerate, which is very different from the 4f-multiplet splitting by the crystal field in samarium ionic or covalent compounds. Magnetic Ground State of Sm-Doped Phenanthrene. A superconductor whose parent compound takes a magnetic ground state usually has a nonconventional superconducting mechanism, such as iron arsenide superconductor and copperoxide superconductor. In K-doped picene and phenanthrene, localized spin was detected in experiments.1,7 Theoretical researches have pointed out that electron−electron correlation and magnetism played an important role in the formation of Cooper pairs in metal-doped aromatic superconductors.18,19 In the above section, we have mentioned that there is a large local

doped phenanthrene and picene are not determined in experiment, especially the metal atom positions, due to the sample quality and the limit of measurement techniques. The Kosugi,29,30 Vergés,31,32and Tosatti groups28,33have systematically investigated the crystal structures of metal-doped picene and phenanthrene with different dopant concentrations, and the results indicated that the dopants in the interstitial space in the molecular layer are more energetically favorable than in the region between two molecular layers. For rare earth metal lanthanum-doped phenanthrene, the two structural phases, the best metallic structure with P21 symmetry and the lowest energy structure with P1 symmetry, are found after a crystal structure search in ref 28. We also obtained the identical two structural phases by the full relaxation of the unit cell of Ladoped phenanthrene after inserting La atoms into the intralayer space in our previous work.34 For samarium-doped phenanthrene, the similar two structural phases are found in this paper. In the experiment, the amount of spurious phases was very low in the Sm1phenanthrene sample, and no impurities were detected, suggesting that nominal and experimental stoichiometries could be close; namely, the ratio of Sm and molecule is 1:1.7,8 We first construct the unit cell of Sm1phenanthrene consisting of two Sm atoms and two molecules. Two Sm atoms are intercalated into the two holes separately to form the Sm1-A phase with P21 symmetry shown in Figure 1(b). After full relaxation we obtain that the z coordinations of two Sm atoms are about 0.33c and 0.66c. If two Sm atoms are placed in one hole without regard for P21 symmetry, the resulting structure is the Sm1-B phase in which the z coordinations of two Sm atoms are 0.35 c and 0.73 c. The above Sm1-A and Sm1-B phases are very similar to those of La-doped phenanthrene in previous reports.28,34 In the relaxation calculation, the spin polarization is considered with the ferromagnetic order (FM) and the antiferromagnetic order (AFM). The optimized lattice parameters for Sm1-A and Sm1-B phases have been listed in Table 1. As can be seen, there exist great discrepancies of lattice parameters between Sm1-A and Sm1-B, but the parameters have a small change from FM order to AFM order for each phase. Table 1. Optimized Lattice Parameters for the Sm1-A Phase, Sm1-B Phase, and Sm2phenanthrene in Ferromagnetic (FM) Order and Antiferromagnetic (AFM) Order Sm1-A FM AFM Sm1-B FM AFM Sm2 FM AFM

α (deg)

β (deg)

γ (deg)

a (Å)

b (Å)

c (Å)

8.79 8.83

6.54 6.53

9.42 9.47

90 90

105.7 106.7

90 90

9.19 9.14

5.96 5.95

9.85 9.88

86.9 86.7

104.2 105.0

87.6 87.6

7.86 7.68

6.77 6.92

9.96 10.04

90 90

105.7 107.5

90 90

The Sm2phenanthrene is involved as well in our calculation, though the experiments support that the sample stoichiometry is Sm1phenanthrene. The Sm2phenanthrene structure is displayed in Figure 1(d), and the optimized constants are also listed in Table 1. Compared to Sm1-A, the a axis becomes shorter, and the b axis becomes longer. Magnetic Moment of the Sm Atom in Sm-Doped Phenanthrene. As a magnetic element, samarium has a unfilled f shell in electron configuration. In general, samarium C

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Table 2. Energy Difference of FM and AFM States with GGA, GGA + SOC, and GGA + U Calculations for Each Structure Phase of Sm-Doped Phenanthrene EAFM − EFM (meV)

a

structure

GGA

GGA + SOC

GGA + U

Sm1-A Sm1-B Sm2

−75 −29 0.4

−155 −42 9

−15 −16 −52

EAFM − EFM denotes AFM energy minus FM energy.

FM order for Sm1-A and Sm1-B phases. Consequently, according to the calculational results with the GGA method and GGA + U method, we can draw the conclusion that antiferromagnetism is the magnetism in the ground state of Sm1phenanthrene, which is consistent with the measurement in experiment.7 For Sm2phenanthrene, FM order and a kind of AFM order are shown in Figure 3(c) and (d), and the energy differences are listed in Table 2. The values indicate that FM order is more favorable than AFM order in GGA and GGA + SOC calculations, but almost degenerated with AFM order. However, GGA + U calculation displays a different result that AFM energy is lower than FM energy, similar to Sm1phenanthrene situations. There are three AFM orders in total when the four spin moments are arranged in a unit cell of Sm2phenanthrene. We also checked two other AFM orders and found they have more high energies than the AFM order shown in Figure 3(d). Hubbard Ueff = 6.0 eV is not a precise value in our calculations since the electronic correlation strength is not clear in this system. The aim to include the Hubbard U is to exhibit the influence of on-site Coulomb repulsion on the electronic properties of Sm-doped phenanthrene. Electronic Properties of the Sm1-A Phase in AFM Order. We choose the Sm1-A phase as an example to illustrate the electronic properties of Sm-doped phenanthrene systems. The total and atomic orbital-resolved partial density of states in the majority spin channel for Sm1-A in AFM order are presented in Figure 4(a). By comparing the middle two panels in Figure 4(a), we find that the distribution of C 2d states is consistent with Sm 5d states because their DOS peak positions have a perfect overlap, which denotes a relatively strong hybridization between C 2d and Sm 5d states. The Sm 4f states are very localized, situated in a narrow energy region from −0.3 to 0.1 eV, especially a few very sharp peaks in the range of 0.2 eV below Fermi energy. In the bottom panel of Figure 4(a), total DOS displays that the Sm1-A phase is metallic, and the DOS value at the Fermi level is mainly from Sm 4f, 5d, and C 2d orbitals. To inspect the effect of on-site Coulomb repulsion on the electronic properties of Sm-doped phenanthrene, the GGA + U method with Hubbard U of 6 eV was adopted in our calculations. The value of Ueff = 6 eV was used in SmX (X = S, Se, and Te) in ref 37. As seen from Figure 4(b), Sm 4f DOS peaks are shifted to −2.0 ∼ −1.5 eV below the Fermi level. A small DOS peak of C 2d at −1.5 eV has been induced by Sm 4f states, shown in the third panel of Figure 4(b). Besides, C 2d and Sm 5d DOS spectra with Hubbard U have no large change with respect to those spectra in Figure 4(a). In this case, the Sm1-A phase in AFM order becomes semiconducting with a gap of 0.12 eV, and the states in the vicinity of Fermi level only come from C 2d and Sm 5d orbitals.

Figure 2. Projected density of states of Sm 4f states on seven partial orbitals for the Sm atom embedded in the phenanthrene crystal. The x and y axis in the Cartesian coordinate system are along the a and b crystal axis shown in Figure 1.

moment around the Sm atom resulting from the 4f electrons in Sm-doped phenanthrene. As a key basis to understanding the superconducting mechanism, it is necessary to clarify the magnetic ground state of Sm-doped phenanthrene. There are two Sm atoms in a unit cell of the Sm1-A or Sm1-B phase. The two spin moments around Sm atoms can be aligned parallel to each other to form FM order or antiparallel to form AFM order. The schematic drawings of AFM order in the Sm1A phase and Sm1-B phase are shown in Figure 3(a) and (b).

Figure 3. Schematic view of magnetic order in Sm-doped phenanthrene. (a) AFM order in the Sm1-A phase. (b) AFM order in the Sm1-B phase. (c) FM order in Sm2phenanthrene. (d) AFM order in Sm2phenanthrene. The red arrows denote the direction of spin moment.

The energies in FM order and AFM order are denoted as EFM and EAFM, and EAFM − EFM means the difference between AFM energy and FM energy. Apart from the standard GGA and GGA + SOC calculations, we also include on-site Coulumb repulsion with Hubbard Ueff = 6.0 eV in Sm 4f states in the energy calculations. The energy differences EAFM − EFM for Sm1-A and Sm1-B are presented in Table 2. The negative values mean the energy in AFM order is lower than the energy in FM order, which indicate that AFM order is more favorable than D

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Figure 4. Total density of state in the majority spin channel and the atomic orbital-resolved partial density of state for Sm 4f, 5d, and C 2d per one atom in the majority spin channel for Sm1-A in AFM order. The Fermi level is set to zero. (a) Standard GGA calculations; (b) GGA + U calculations with the Hubbard Ueff = 6.0 eV. (c) GGA + SO calculation. Note that the values for total DOS and C 2p DOS in GGA + SO calculations are divided by 2 for comparing with the DOS of the majority spin channel. The DOS values of Sm 4f and 5d keep unchanged for their full spin polarization.

discovered aromatic superconductor. For Sm2phenanthrene, the energy in FM order is lower than AFM order within GGA and GGA + SOC calculations but higher than AFM order within GGA + U calculation. The magnetic moment of the Sm atom in this class of materials is an interesting and significant issue. Quite different from divalent and trivalent Sm ions in ionic and covalent compounds such as monochalcogenides and samarium hexaboride, there exists a large local moment of 3.7 μB around Sm atoms in Sm-doped phenanthrene because its orbital moment is about 2.3 μB which only can cancel the small fraction of Sm spin moment of 6.0 μB. Due to the hybridization between Sm 5d and C 2d states, there is a stronger interaction between Sm and phenanthrene in Sm-doped phenanthrene than the interaction of K and molecule in K-doped picene and phenanthrene. Our results provide the fundemental magnetism and electronic properties of Sm-doped phenanthrene superconductor.

Including the spin−orbit coupling effect, we performed the noncollinear magnetism calculations of the Sm1-A phase with the GGA + SOC method. The orbital-resolved partial DOS and total DOS are displayed in Figure 4(c). Compared to the DOS spectra in Figure 4(a), the striking change is that the Sm 4f peaks become broader with energy range extending to −0.75− 0.1 eV. The DOS peaks of Sm 5d and C 2d around the Fermi level also become more dispersive, while the DOS peaks far below Fermi energy are unaffected by the spin−orbit coupling. The overlap of Sm 5d and C 2d states in the same energy range indicates a strong hybridization between them, which can enhance the interaction of the Sm atom and phenanthrene molecule and strengthen their binding. This is another notable difference between Sm-doped phenanthrene and K-doped picene and phenanthrene. To describe quantitatively the difference, we calculate the formation energy in terms of the formula

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ΔE = (ESm1phenanth − Ephenanth − 2*ESm)/2

where ESm1phenanth, Ephenanth, and ESm are the energies of Sm1phenanthrene, pristine phenanthrene, and the Sm atom in the bulk phase, respectively. The formation energy is −0.67 eV per Sm atom, which is about two (three) times as much as that in K-doped picene (Ba-doped phenanthrene) in our previous studies.38,39 From the viewpoint of formation energy, the bonding between the Sm atom and phenanthrene is stronger than that between alkali (or alkali earth metals) and phenanthrene due to the relatively strong hybridization between Sm 5d and C 2d orbitals. Hence, we can deduce that Sm metal is more easy to be doped into aromatic hydrocarbons to synthesize the experimental samples than alkali and alkali earth metals.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the National Natural Science Foundation of China under Grants Nos. 11404383, U1504108, 91221103, 11474004, and U1204108, China Postdoctoral Science Foundation under Grant No. 2014M550597, and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase).

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CONCLUSIONS In summary, the atomic structure, magnetism, and electronic properties of Sm-doped phenanthrene are investigated by the first-principles simulation method for the first time. Two structural phases of Sm1phenanthrene are obtained, Sm1-A with P21 group symmetry and Sm1-B with P1 symmetry, similar to the La1phenanthrene reported previously. By the standard GGA, GGA + SOC, and GGA + U calculations for Sm-doped phenanthrene in FM order and AFM order, we draw the conclusion that the antiferromagnetism is the magnetic ground state for Sm1phenanthrene, which is the important foundation for further investigation of superconductivity in this new

(1) Mitsuhashi, R.; Suzuki, Y.; Yamanari, Y.; Mitamura, H.; Kambe, T.; Ikeda, N.; Okamoto, H.; Fujiwara, A.; Yamaji, M.; Kawasaki, N.; et al. Superconductivity in alkali-metal-doped picene. Nature 2010, 464, 76−79. (2) Wang, X. F.; Liu, R. H.; Gui, Z.; Xie, Y. L.; Yan, Y. J.; Ying, J. J.; Luo, X. G.; Chen, X. H. Superconductivity at 5 K in alkali-metal-doped phenanthrene. Nat. Commun. 2011, 2, 507. (3) Kubozono, Y.; Mitamura, H.; Lee, X.; He, X.; Yamanari, Y.; Takahashi, Y.; Suzuki, Y.; Kaji, Y.; Eguchi, R.; Akaike, K.; et al. Metalintercalated aromatic hydrocarbons: a new class of carbon-based superconductors. Phys. Chem. Chem. Phys. 2011, 13, 16476−16493.

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DOI: 10.1021/acs.jpcc.6b08373 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.6b08373 J. Phys. Chem. C XXXX, XXX, XXX−XXX