镁硼二元化合物中的超导性：金属硼在MgB2中的层状结构与电子-声子耦合

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在2001年的一篇研究论文《Superconductivity of metallic boron in MgB2》中，作者们探讨了镁硼合金(MgB2)中的超导现象。硼在MgB2中形成了一种类似于蜂窝状的晶格结构，其中镁作为填充物，起到了关键作用。电子结构分析表明，镁原子被显著离子化，而能带主要由硼的价电子轨道构成。这种强的化学键合，包括离子成分，以及丰富的金属态密度导致了显著的电子-声子耦合。通过采用刚性原子球近似法，并参考铝（Al）的情况，研究人员估计了电子-声子耦合常数λ大约为1。这是超导转变的重要参数，它与材料的临界温度密切相关。通过冻结波函数中心的区中心振动计算，他们预测了MgB2中的声子频率范围在300到700厘米^-1之间，这些较高的频率进一步提高了材料的超导性能。这一发现意味着MgB2具有高临界温度，这与当时的实验结果相一致。该研究将MgB2类比于长期以来寻找但尚未实验证明的超导金属氢，即一种理论上预期拥有极高超导性的物质。这一发现对于理解金属间化合物的超导机制以及探索新的超导体材料具有重要意义，因为它揭示了一种新颖的电子-声子相互作用模式，可能适用于其他类似的复合体系。在2001年前的超导材料研究中，MgB2的出现打破了传统超导体的局限，为设计新型高效、高温超导材料开辟了新的途径。

arXiv:cond-mat/0101446v2 [cond-mat.supr-con] 18 Feb 2001

Superconductivity of metallic boron in MgB

J. Kortus

†

, I.I. Mazin

†

, K.D. Belashchenko,

‡

V.P. Antropov

‡

, L.L. Boyer

†

Center for Computational Materials Science, Code 6390, Naval Research Laboratory, Washington, DC 20375

‡

Ames Laboratory, ISU, Ames, IA, 50011

(February 1, 2008)

Boron in MgB

forms layers of honeycomb lattices with magnesium as a space ﬁller. Band struc-

ture calculations indicate that Mg is substantially ionized, and the bands at the Fermi level derive

mainly from B orbitals. Strong bonding with an ionic component and considerable metallic density

of states yield a sizeable electron-phonon coupling. Using the rigid atomic sphere approximation

and an analogy to Al, we estimate the coupling constant λ to be of order 1. Together with high

phonon frequencies, which we estimate via zone-center frozen phonon calculations to be between

300 and 700 cm

−1

, this produces a high critical temperature, consistent with recent experiments.

Thus MgB

can be viewed as an analog of the long sought, but still hypothetical, superconducting

metallic hydrogen.

Before the discovery of high-temperature supercon-

ductors much eﬀort was devoted to boosting the criti-

cal temperature of conventional, BCS-Eliashberg super-

conductors [1]. An exo tic and appealing idea go ing

back to the early 60’s, was that of metallic hydrogen

[2]. The arguments were very simple: due to the light

mass, the phonon frequencies in metallic hydrogen would

be very high, of the o rder of several thousand K, and

the prefactor in the BCS formula would be very lar ge,

so that even a moderate coupling constant would pro-

vide a size able T

. This idea can be quantiﬁed as fol-

lows: for monoatomic solids, the electr on-phonon cou-

pling (EPC) constant, λ, which enters the BCS equation,

can be wr itten in the so-called McMillan-Hopﬁeld form

[3], λ = N(0)









, where N(0) is the density

of states (DOS) at the Fermi level per spin per atom,





is the pr operly averaged electron-ion ma trix ele-

ment squared, M is the atomic mass and





is (again,

properly averaged) the phonon frequency. The product





does not depend on the mass, but on the force

constants only [1], while η = N(0)





, also known as

the Hopﬁeld factor, is a purely elec tronic property. Cor-

respondingly, light elements, everything else being the

same, are beneﬁcial for superconductivity.

Lacking metallic hydrogen, attention was focused upon

compounds with light elements: car bides , nitrides (ar-

guably, the superconductivity in fullerenes was a discov-

ery along this road). Indeed, many of them were ‘high-T

supe rconductors’ on the contemporary scale: 10-15 K. It

was pointed out [4] tha t





is rather large in these ma-

terials due to the relatively high ionicity (although not as

high as in MgB

), but N (0) is rather small. This led to

the suggestion of cubic MoN, which would have a larger

N(0) than existing nitrides and carbides, as a hypothet-

ical superconductor with T

> 30 K [5].

The recently discovered medium-T

supe rconductor

MgB

[6] with T

∼

39 K is clearly a c ontinuation of the

same idea. The main component, B, is even lighter than

C and N. Furthermore, electronic structure c alculations

show tha t the co mpound is not only quite ionic with a

reasonable DOS, but als o has strong covalent B-B bond-

ing (the bonding-antibonding splitting due to in-plane

B-B hopping is about 6 eV) and thus exhibits strong

electron-phonon interactions. Interestingly, unlike car-

bides and nitrides , and similar to metallic hydrogen, elec-

trons at the Fermi level (and below) are predominantly B-

like. Mg s-states are pushed up by the B p

orbitals and

fully donate their electrons to the boron-derived conduc-

tion bands. In the following we will describe the physics

of such ‘metallic’ boron in detail, pr e sent an estimate of

the EPC constant, and propose some routes for optimiz-

ing T

in this kind o f compound.

MgB

occurs in the so-called AlB

structure. Borons

form a primitive honeycomb lattice, consisting of

graphite-type s hee ts stacked with no displacement. The

borons form hexagonal pr isms with the base diameter

of 3.5

A nearly equal to the height. This creates large,

nearly spherical pores for Mg. As in graphite, the intra-

planar B-B bonds are much shorter than the distance be-

tween the planes, and hence the B-B bonding is strongly

anisotropic. However, the interplane bonds are only twice

as long a s the intraplane ones, as compared to the ratio

of 2.4 in graphite, allowing for a signiﬁca nt interplane

hopping.

We have calculated the electronic structure of MgB

using a general potential LAPW code [7]. For the

Rigid Atomic Spheres calculations we used the Stuttgart

LMTO-TB code [8]. For the exchange-correlation poten-

tial, the Generalized Gradient Approximation of Ref. [9]

was employed. Despite the rather simple crystal struc-

ture, very few electronic structure calculations for MgB

have been rep orted (a model TB calculation of Burdett

and Miller [10] and a recent full-potential LMTO study

[11]), and these have concentrated mainly on chemical

bonding, paying hardly any attention to transport and

electronic prop e rties. The results of our LAPW calcula-

tions ar e shown in Figs. 1 and 2. We note ﬁrst that there

is almost no valence charge inside the Mg MT sphere (less

than 0.2 e). About half of the total valence charge resides

inside the B spheres, and about the same amount in the

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