Pis’ma v ZhETF, vol. 109, iss. 9, pp. 627 - 628

May 10

Electron-phonon interaction, phonon and electronic structures

of layered electride Ca₂N

B.N.Mavrin⁺, M.E.Perminova⁺, Yu.E.Lozovik^+∗×1)

⁺Institute of Spectroscopy of Russian Academy of Sciences, 142190 Troitsk, Moscow, Russia

^∗Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russia

^×Dukhov Research Institute of Automatics (VNIIA), 127055 Moscow, Russia

Submitted 27 March 2019

Resubmitted 27 March 2019

Accepted 27

March 2019

DOI: 10.1134/S0370274X1909011X

The phonon and electronic properties, the Eliash-

which is smaller than that of pure Ca metal [7]. The

berg function and the temperature dependence of resis-

temperature dependence of resistivity indicated that

tance of electride Ca₂N are investigated by the DFT-

the electron-electron interaction could be much stronger

LDA (density functional theory in local density approx-

than the electron-phonon interaction even in the high-

imation) plane-wave method. The phonon dispersion,

temperature region [7].

the partial phonon density of states and the atomic

In this Letter we calculate the Eliashberg function

eigenvectors of zero-center phonons are studied. The

of Ca₂N from first principles (DFT) to estimate the

electronic band dispersion and partial density of states

electron-phonon interaction (EPI) and its contribution

conclude that Ca₂N is a metal and the Ca 3p, 4s and

to resistance as well as a temperature dependence of

N 2p orbitals are hybridized. For the analysis of an

resistance caused EPI.

electron-phonon interaction and its contribution of the

We start our calculations from the study the phonon

Eliashberg function to resistance was calculated and a

and electronic properties of the Ca₂N crystal in order

temperature dependence of resistance due to electron-

to compare with calculations [11, 12] of these properties

phonon interaction was found.

in the isolated layer Ca₂N and to obtain the density of

There is considerable interest in layered electrides in

phonon states F (ω) that is necessary to compute EPI.

bulk and monolayer forms in which playing anionic role

Besides, in distinct from previous calculations [11,12],

electrons form two-dimensional planes separated from

we had to use the relativistic pseudopotentials [13, 14]

positively charged layers of ions [1-6]. In view of their

in first-principles calculations of EPI. The frequencies

promising properties such as high electrical conductiv-

of phonon branches have been calculated within den-

ity, low work function, and significant catalytic activity

sity perturbation theory [15]. There was no an energy

in their ideal form, electrides are perspective for use in

gap between acoustic and optic branches in the phonon

next-generation electronics.

dispersion. If the main contribution of the N atoms in

Sub-nitride Ca₂N belongs to this new class of

phonon density F (ω) locates above 285 cm^-1, the Ca

layered-structure electrides with the two-dimensional

atom gives a contribution at lower frequencies except for

delocalized layers of electrons [7, 8]. The rhombohedral

acoustic modes in which a participation of both atoms is

unit cell of Ca₂N contains more electrons than it is ex-

noticeable. We have found, the electron density of states

pected from the simple electron counting rules. It is sup-

at the Fermi level is finite, that is, Ca₂N is a metal.

posed that excess electrons are localized between posi-

The role of different phonon branches in electron-

tively charged layers [Ca₂N]⁺. The physical properties

phonon interactions can be characterized by the spec-

of Ca₂N were studied by photoelectron spectroscopy

tral Eliashberg function α²F (ω) [16, 17] where α² is

[7, 9], optical reflectance spectroscopy [7], electrical con-

the squared effective EPI. The calculations of α²F (ω)

ductivity [7, 10], by study of magnetic susceptibility [10]

were performed by the method [18]. The main peaks in

and magnetoresistance [7]. It was found that single crys-

phonon density F (ω) are seen also in function α²F (ω),

tal Ca₂N exhibits metallic transport with resistivity,

confirming a contribution of almost all phonons to the

Eliashberg function in Ca₂N. We calculate the resis-

¹⁾e-mail: lozovik@isan.troitsk.ru

tance only due to electron-phonon interactions. In this

Письма в ЖЭТФ том 109 вып. 9 - 10

2019

627

4^∗

628

B.N.Mavrin, M.E.Perminova, Yu.E.Lozovik

case the temperature dependence of electrical resistiv-

P. Cudazzo and M. Gatti, Phys. Rev. B 96, 125131

ity can be calculated in the lowest-order variational ap-

(2017).

proximation [18] using the calculated function α²F (ω),

D. L. Druffel, K. L. Kuntz, A. H. Woomer, F. M. Alcorn,

density of the electronic states at the Fermi level and

J. Hu, C. L. Donley, and S. C. Warren, J. Am. Chem.

Soc. 138(49), 16089 (2016).

average square of the Fermi velocity for electrons. The

calculated resistance ρ of Ca₂N turned out to be highly

M. Hiraishi, K. M. Kojima, I. Yamauchi, H. Okabe,

S. Takeshita, A. Koda, R. Kadono, X. Zhang, S. Mat-

anisotropic, and it is visibly higher along the axis z. This

suishi, H. Hosono, K. Hirata, S. Otani, and N. Ohashi,

result is consistent with experimental estimates. The

Phys. Rev. B 98, 041104(R) (2018).

small value of ρ_x is in agreement with idea of presence of

L. Zhang, W. Yu, J.-Y. Ou, Q. Wang, X. Cai, B. Wang,

a two-dimensional layer of electrons between positively

X. Li, R. Zhao, and Y. Liu, Phys. Rev. B 98, 075434

charged layers [Ca₂N]⁺ [7, 8] and with our calculated

(2018).

electronic structure, from which it follows that Ca₂N

Ch. Park, S. W. Kim, and M. Yoon, Phys. Rev. Lett.

should have a metallic character along the plane of the

120, 026401 (2018).

layers.

Y. Zhang, H. Wang, Y. Wang, L. Zhang, and Y. Ma,

In summary, we have presented a first-principles

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study of phonon and electronic structures and resis-

K. Lee, S. W. Kim, Y. Toda, S. Matsuishi, and

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H. Hosono, Nature 494, 336 (2013).

account semi-core electrons for the Ca atom and using

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the plane-wave pseudopotential method. The phonon

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10.

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in Ca₂N. The calculated resistance of Ca₂N turned out

11.

C. M. Fang, G. A. de Wijs, R. A. Groot, M. T. Hintzen,

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and G. de With, Chem. Mater. 12, 1847 (2000).

plane of the layers.

12.

S. Guan, S. A. Yang, L. Zhu, J. Hu, and Y. Yao, arXiv:

We would like to thank Dr. T. A. Ivanova for assis-

1502.02321.

tance.

13.

C. Hartwigsen, S. Godecker, and J. Hutter, Phys. Rev.

The use of facilities of the Joint Supercomputer Cen-

B 58, 3641 (1998).

ter of Russian Academy of Sciences is greatly appreci-

14.

H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188

ated. The work was supported by Russian Foundation of

(1976).

Basic Research grants #17-02-01134 and 18-52-00002.

15.

S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Gian-

Yu. E. Lozovik was supported by the Program of Ba-

nozzi, Rev. Mod. Phys. 73, 515 (2001).

sic Research of Higher School of Economics.

16.

G. M. Eliashberg, Sov. Phys. JETP 11, 696 (1960).

17.

P. B. Allen, Phys. Rev. B 17, 3725 (1978).

Full text of the paper is published in JETP Letters

18.

S. Y. Savrasov and D. Y. Savrasov, Phys. Rev. B 54,

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2019