Solid State Communications 142 (2007) 536–540www.elsevier.com/locate/ssc

First-principles investigation of pressure-induced changes in structural andelectronic properties of Y2C3 superconductor

Chun Yu, Junyan Liu, Hao Lu∗, Peilin Li, Ruizhi Fan, Junyan Xiao

School of Materials Science and Engineering, Shanghai Jiaotong University, Shanghai 200030, PR China

Received 14 January 2007; received in revised form 14 March 2007; accepted 15 March 2007 by J.R. ChelikowskyAvailable online 24 March 2007

Abstract

The structural and electronic properties of Y2C3 superconductor under different external pressures were calculated by employing the first-principles method. This shows that the lattice constants as well as the lengths of C–C dimers decrease with the pressure. Results of band structurecalculations indicate that the Fermi level advances to the bonding zone with an increase in pressure; meantime, the valence and conduction bandsintersect more deeply with the Fermi level. Moreover, the Fermi level is found to shift from the valley bottom of the density of states (DOS) curveto the shoulder, which means an increase in N (EF ), and therefore the critical temperature, Tc. The calculations verify that the critical temperatureis directly related to the electronic structure.c© 2007 Elsevier Ltd. All rights reserved.

PACS: 74.25.Jb; 74.70.Ad

Keywords: A. Y2C3; D. Electronic structure; E. First-principles

1. Introduction

The yttrium carbide family has now attracted considerableattention, for the superconducting critical temperatures (Tc)

of the compounds belonging to this family are comparablewith those of A15 compounds [1,2]. Y2C3 is a representativesuperconductor in the yttrium carbide family that crystallizeswith the body-centered cubic (bcc) Pu2C3 structure. It has ahigh superconducting transition temperature of over 10 K [3].Recently, Amano et al. [4] reported a new undoped Y2C3superconductor with a high Tc of 18 K, which was synthesizedunder high pressure. This high-Tc superconductor was thenreproduced by Nakane et al.; the synthesis process wasperformed in a cubic-anvil-type high-pressure apparatus [5–7].It is reported that the experimental samples had the same Pu2C3structure as the previous one obtained at atmospheric pressure,but a slight difference occurred in the lattice parameters.Moreover, the lattice parameters as well as Tc were found tobe sensitive to the sintering conditions. For instance, the lattice

∗ Corresponding author.E-mail addresses: yuchun1980@sjtu.edu.cn (C. Yu), shweld@sjtu.edu.cn

(H. Lu).

0038-1098/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.ssc.2007.03.020

parameters were found to change from 8.181 to 8.226 A, withthe reported Tc spanning the range 15–18 K at pressures of4–5.5 GPa, and from 8.214 to 8.251 A with a Tc of about 11 Kat pressures of 1.5–2.5 GPa [3]. That is, Tc increases with andecrease in the lattice parameter, or a increase in the externalpressure. Therefore, the change in Tc of Y2C3 was believed tobe correlated to the structural properties [6], which also led tochanges in electronic structure and phonon mode.

Many theoretical works have been performed to investigatethe electronic and superconducting properties of Y2C3 [8,9].The electronic structure of Y2C3 was calculated by Sheinand Ivanovskii [8]. This shows that the hybridization of C–Cdimer anti-bonding and the Y 4d states are dominant atthe Fermi level. Singh and Mazin [9] also found that theelectronic structure could have substantial C–C anti-bondingcharacter near the Fermi level. Such states may be expectedto have extremely high deformation potentials, reflecting thesevery strong C–C triple bonds. Moreover, the electron–phononcoupling of Y2C3 was calculated by Singh and Mazin [9]. Theyfound that the electron–phonon coupling λ is dominated byphonons other than the C–C bond stretching.

Surprisingly, there has been no serious calculation of theelectronic structures of this compound in order to explain the

C. Yu et al. / Solid State Communications 142 (2007) 536–540 537

Fig. 1. Crystal structure of Y2C3. Large balls denote Y and small ones are C.

generally observed change in Tc with external pressure. In thispaper, the structural and electronic properties with pressurewere calculated by employing the first-principles method.Considering that the synthesis processes of Y2C3 were underconditions of high temperature (1400 ◦C) and high pressure(about 5 GPa), the applied iso-pressures ranged from 0 to50 GPa at 0 K. This work is expected to give deep insight intothe mechanism of superconductivity in Y2C3.

2. Methods

Yttrium sesquicarbide Y2C3 crystallizes in a bcc structurewith a space group of T 6

d = I 43d and eight formula units perunit cell, Y on site 16c (0.05, 0.05, 0.05) and C on site 24d(0.2821, 0, 0.25). The lattice constant is 8.226 A, taken fromthe experimental results of Amano et al. [4]. This parameterwas also used by Shein [8] and Singh [9] to perform theoreticalcalculations. The crystal structure of Y2C3 is shown in Fig. 1.In this paper, our supercell model was based on the primitiveunit cell, which has four formula units, as seen in Fig. 1, wherethe coordinates were in terms of the bcc lattice vectors.

The calculations were performed by employing the CASTEPcode, which was developed by Payne et al. based on aplane-wave basis first-principles pseudopotential method [10,11]. The pseudopotential used in the present study to de-scribe the electron–core interaction is the ultrasoft pseudopo-tential (USPP) generated by the scheme of Vanderbilt [12].This potential is known to require less kinetic cutoff energyfor plane-wave expansion of wave functions to obtain well-converged results compared to the norm-conservation non-local potential. Brillouin-zone sampling was performed us-ing a Monkhorst–Pack [13] mesh of 8 × 8 × 8 special kpoints. Also, energy smearing of 0.1 eV was chosen for allthe calculations. As for the method of approximation to theexchange–correlation term of the density-functional theory(DFT) [14] in describing the electron–electron interaction, thegeneralized gradient approximation (GGA) [15,16] was used.A series of cutoff energies was used to check the convergenceof these calculations; it is found that the lattice parameters, aswell as the shape of the density of states (DOS) and the rela-tive position of the Fermi level in the DOS curve, agree well if

the cutoff energy was not less than 300 eV. Therefore, the cut-off energy was 320 eV. Structure relaxations were performedup to forces on each atom below 0.02 eV/A. Pseudo-atomiccalculations performed for C are 2s and 2p states, while thosefor Y are 4s, 4p, 4d, and 5s states. Hydrostatic pressure, cou-pled with the variable cell approach, was applied within theParrinello–Rahman method [17,18] to perform a full optimiza-tion of the cell structure for each target external pressure.

3. Results and discussions

Table 1 shows the lattice constants and interatomic distancescalculated at pressures of 0, 5, 10, and 50 GPa, as well asthe experimental results. It is seen that the calculated latticeconstant, a, is underestimated by only 0.15% at ambientatmosphere. We also found significant changes in the C–Cdimer bond lengths relative to the experimental results; thediscrepancy may be generated due to the general gradientapproximation, which overestimates or underestimates theresults. In addition, the original lattice constant chosen for thecalculations is also less than that observed in Ref. [6], whichalso accounts for this difference. However, our results are ingood agreement with Singh’s calculations: a C–C bond distanceof 1.33 A and a Y–C distance of 2.51 A at 0 GPa. After a seriesof external iso-pressures was applied, the interatomic distanceswere found to decrease, as well as the lattice parameter. But thedecrease rate of C–C dimmer bond lengths is obviously slowerthan that of other bond distances. However, the experimentshows that a higher-TcY2C3 has a longer C–C bond [6]. Thisdifference is unclear. Kim et al. [19] believed that the shrunkenC–C double bond distance in the rare-earth sesquicarbides wasdue to the charge transferring from antibonding C2-π∗ orbitalsto Y d orbitals. In our calculations, it is also found that thenumber of transferring charges increases with pressure.

To investigate the effects of changes in lattice structureon the electronic properties, the band structures and densityof states (DOS) of Y2C3 crystal were also calculated underdifferent external pressures ranging from 0 to 50 GPa. Thecalculated band structures of Y2C3 crystal under the conditionsof 0 and 50 GPa are displayed in Fig. 2. It is seen that ourcalculated electronic band structure agrees qualitatively withthe recent reports by Shein and Ivanovskii [8] and Singh andMazin [9]. Since the band structure near the Fermi level ismore important for investigating the electronic properties, theband structure near the Fermi level is also shown in Fig. 2, inorder to probe deeply into the mechanism of higher Tc withhigher pressure. It is worth noting that the band structuresnear the Fermi level are quite different under the two pressureconditions. There are two valence bands and one conductionband crossing the Fermi level (EF , indicated by a dashedline, which locates at 0 eV) near the G point. As the pressureis increased to 50 GPa, the Fermi level is found to shiftto the bonding states and results in a widening of the anti-bonding states, as seen in Fig. 2. Meanwhile, the valence andconduction bands intersect with the Fermi level much moredeeply. This behavior is expected to account for the bettersuperconductivity at higher pressure. Since the crystal structure

538 C. Yu et al. / Solid State Communications 142 (2007) 536–540

Table 1Interatomic distances and lattice parameters at different conditions, in A

0 GPa 5 GPa 10 GPa 50 GPa High-Tc [6] Low-Tc [6]

Y–C1 2.511 2.474 2.449 2.311 2.510 2.507Y–C2 2.623 2.590 2.555 2.387 2.641 2.647Y–C3 2.813 2.778 2.752 2.610 2.810 2.806Y–Y1 3.381 3.345 3.306 3.281 3.391 3.395Y–Y2 3.562 3.517 3.479 3.456 3.5668 3.5669C–C 1.320 1.319 1.317 1.302 1.298 1.290a 8.214 8.122 8.034 7.577 8.2372 8.2374

Fig. 2. Electronic band structures of Y2C3, (a) for 0 GPa and (b) for 50 GPa, as well as the corresponding amplified parts near the Fermi level.

changes with external pressure, this means that the crystalstructure is important for superconductivity. This result is ingood agreement with the experimental and theoretical results.

Fig. 3 shows the total DOS and site-projected DOS curvesof Y2C3 at pressures of 0, 10, and 50 GPa, respectively. Itis seen that the valence zone of Y2C3 contains five separatedzones. However, the previous calculations carried out byShein et al. [11] with the first-principles full-potential linearmuffin-tin generalized gradient approximation (FLMTO-GGA)method show that the valence zone of Y2C3 contains fourseparated band groups. This difference may be induced by thatthe electron–core interaction in our calculations was describedby using pseudopotentials. The valence zone between −43.48and −41.62 eV is offered by Y s states, whereas Y p stateswith a weak hybridization of C s and p orbitals contribute to thevalence zone at energies ranging from −23.82 to −21.33 eV.Likewise, C s and p states contribute mostly to the valence zone

between −16.06 eV and −13.61 eV, with a weak hybridizationeffect from Y d states. Valence zones between −8.51 and−2.43 eV are contributed to by Y d and C s and p states. Nearthe Fermi level of energies ranging from −2.15 to 5.39 eV, themixture of Y d and C p states is dominant. The possibility ofcovalent bonding between the constituent atoms is due to thefact that the DOSs of Y d and C p are energetically degeneratefrom the bottom of the valence band to the Fermi level.

The Fermi level resides on the valley of a narrow peakat 0 and 10 GPa; this phenomenon is also found in previouscalculations [8,9]. However, it shifts to the shoulder of the peakas the external pressure is raised to 50 GPa, which gives riseto a higher value of N (EF ). The calculated N (EF ) values,as well as the contributions from each state of Y and C, arelisted in Table 2, corresponding to external pressures of 0, 5,10, and 50 GPa, respectively. It is seen that the N (EF ) ismostly contributed to by Y d states and C p states, and that the

C. Yu et al. / Solid State Communications 142 (2007) 536–540 539

Fig. 3. The total and site-projected density of states (DOS) curves for Y2C3 calculated at 0, 10, and 50 GPa, respectively.

contributions from Y s, p and C s states is too small and can beignored, which is comparable to the results calculated by Sheinand Ivanovskii [8]. It is worth noting that the DOS value for Cp states is enhanced with pressure, while it is the reverse for Yd states. Due to the increased rate in DOS of the C p states withexternal pressure being slightly larger than the decreased rate inDOS of Y d states, the DOS at the Fermi level, i.e. N (EF ), performula unit, increases with pressure. The N (EF ) calculatedby Singh and Mazin [9] was 1.88 states/eV, per formulaunit. Their work was performed using the general potentiallinearized augmented planewave (LAPW) method [20]; thelattice parameter was also a = 8.226 A at 0 GPa, and the modelwas a 20-atom primitive cell. However, the value of N (EF )

at 0 GPa was 1.211 states/eV, per formula unit, which wascalculated by Shein and Ivanovskii [8]. In their calculations, thelattice constant was also 8.226 A. The difference between theprevious results of N (EF ) is possibly caused by the calculationmethods. Also, our results can maintain good agreement withboth methods.

It is worth noting that many works have been undertaken toinvestigate the relationship between the external pressure andTc, as well as N (EF ). It is found that N (EF ) is not boundto increase with the pressure [21,22]. The superconductingtransition temperature, Tc, of MgB2 was studied underhydrostatic and quasi-hydrostatic pressures up to 12 GPaaccording to Razavi et al. [23], who found that N (EF )

Table 2Total and site-projected DOS at the Fermi level (states/eV, formula unit)

DOS 0 GPa 5 GPa 10 GPa 50 GPa

C s states 0.004 0.004 0.004 0.005C p states 0.198 0.203 0.207 0.241Y s states 0.020 0.019 0.019 0.017Y p states 0.065 0.065 0.065 0.064Y d states 0.397 0.394 0.393 0.384N (EF ) 1.569 1.577 1.592 1.685

decreases with the pressure, and therefore so does Tc. Thisresult was in good agreement with what has been found byShao et al. [24] and Zheng and Zhu [25]. Meanwhile, thesuperconducting properties of o-MoRuP was investigated byNg et al. through experimental and ab initio methods [26]; theyfound that the high Tc in o-MoRuP is directly related to thehigher level of the DOS at the Fermi level. Same conclusionswere drawn by Li et al. [27].

Actually, in the BCS theory of metallic superconductivity, Tcis directly related to N (EF ) and the electron–phonon couplingconstant based on McMillan formula [28] is given by

Tc =〈ωlog〉

1.2× exp

[−1.04(1 + λ)

λ − µ∗ − 0.62λµ∗

](1)

where, 〈ωlog〉 represents the logarithmically averaged phononfrequency, µ∗ is the renormalized Coulomb pseudopotential

540 C. Yu et al. / Solid State Communications 142 (2007) 536–540

which describes the repulsive interaction between electrons,and λ = N (EF )/V is the electron–phonon coupling constant,where V stands for the electron–phonon coupling strength.However, the McMillan formula is only valid in the λ ≤

1 regime. If we take Tc = 18 K, µ∗= 0.1, and ω =

175 cm−1 [9], we obtain λ = 1.35. The correct Eliashberg Tcformula [28] for large λ is

Tc ∼√

λ〈ωlog〉 (2)

which is unbounded in λ and potentially much larger than〈ωlog〉. According to this equation, Moussa and Cohen [29]advanced an expression to describe the relationship between Tcand N (EF ) which fits to the materials containing C–C bonds;it is

Tc ∼

√N (EF )

∑i

FFSi

√Mi

(3)

where FFSi is the average root-mean-square force on atom i

from electrons on the Fermi surface, and Mi is the atomic mass.This relation reflects the common wisdom, based on the BCSmodel, that a large density of states at EF and light elements arewhat lead to a high Tc. Therefore, according to Eq. (3), we candeduce that the Tc of Y2C3 increases with N (EF ), or pressure.This conclusion is in good agreement with experimentalresults.

4. Conclusions

The changes in structural and electronic properties of Y2C3were examined by employing the first-principles method. Itis found that the lattice constants decrease with pressure, aswell as the Y–C, Y–Y and C–C bond lengths. Meanwhile,the Fermi level was found to shift toward the bonding regionat high pressure, and also the valence and conduction bandscross the Fermi level deeply. These findings are relevant for thephenomenon of high Tc at high pressure for Y2C3. Moreover,the density of states at the Fermi level is mainly contributed bya mixture of C p and Y d states; although C p states increase andY d states decrease with external pressure, the total DOS valueis found to increase. This leads directly to a higher Tc at higherpressure. These results are consistent with the experimental andtheoretical results.

Acknowledgement

This work was supported by National Natural ScienceFoundation of China under grant no. 50475021.

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