Pis’ma v ZhETF, vol. 109, iss. 6, pp. 392 - 393

March 25

Interplay between Coulomb interaction and hybridization in Ca and

anomalous pressure dependence of resistivity

D. Y. Novoselov^+∗1), D. M. Korotin⁺, A. O. Shorikov^+∗, A. R. Oganov^×◦, V. I. Anisimov^+∗

⁺M. N. Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences, 620108 Yekaterinburg, Russia

^∗Department of theoretical physics and applied mathematics, Ural Federal University, 620002 Yekaterinburg, Russia

^×Skolkovo Institute of Science and Technology, 143026 Moscow, Russia

^◦Moscow Institute of Physics and Technology, 141701 Dolgoprudny, Russia

Submitted 30 November 2018

Resubmitted 25 December 2018

Accepted 26

December 2018

DOI: 10.1134/S0370274X19060092

Metallic Ca exhibits unusual growth of electrical re-

der high pressure is due to an interplay of hybridiza-

sistivity with an increase of pressure [1]. Moreover Ca

tion and correlation effects. Furthermore, it was found

has a very complex phase diagram and in the high-

that the Coulomb repulsion can explain the experi-

pressure phase it has the superconductivity with critical

mentally observed anomalous growth of the resistiv-

temperature of 25 K, the highest among all chemical

ity with pressure in the simple cubic phase of cal-

elements [2]. The explanation of all this behavior can

cium.

originate from a specific electronic structure character-

We have found that both the transfer of electrons

istic of the high-pressure phase(s). Despite large effort

from 4s to 3d states with increasing pressure and

achieved recently in developing computational meth-

Coulomb correlations play an important role in the for-

ods based on DFT (Density Functional Theory), re-

mation of the ground electronic state of the system un-

searchers failed to reproduce the full phase diagram

der pressure. The former leads to the localization of the

of Ca.

electron density in the interstices and the existence of

We start with DFT calculations, which give the crys-

partially filled bands, rendering the cubic phase of cal-

tal structure with relaxed atomic positions for a se-

cium an electride and the latter is responsible for the

ries of cell volumes and provide the electronic struc-

opening of the energy gap.

ture of Ca. The pseudopotential VASP package [3] was

The idea of taking electronic correlations into ac-

used for optimization of crystal structures and band

count for electride states allowed us to describe and

structure calculations which was used as the starting

explain the experimentally observed structural transi-

point for construction of a correlated states Hamiltonian

tion to the simple cubic phase, as well as the anoma-

in Wannier function (WF) basis. For the constructed

lous behavior of resistivity as a function of compression.

Hamiltonian the Coulomb correlations were taken into

Quantitative description of this transition requires more

account within DFT + U method using so-called “re-

accurate charge self-consistent theoretical techniques

stricted Hartree-Fock” approach.

such as dynamical mean-field theory (DFT + DMFT)

An increase of external pressure gives rise to s-

or DFT + U.

d electron transfer in calcium that results in the lo-

Authors thank M. A. Korotin for his CPA (Coherent-

calization of the charge density in the interstices of

Potential Approximation) computer code used in our

the crystal cell, i.e., the formation of an electride.

calculations.

The corresponding electronic states are partially filled

This work was supported by Russian Science Foun-

and localized and, hence, strong electronic correlations

dation (Project 19-72-30043).

could arise. We have carried out theoretical calcula-

Full text of the paper is published in JETP Letters

tions for the high-pressure phases of Ca taking into

journal. DOI: 10.1134/S0021364019060043

account the Coulomb interactions between the elec-

1. T. Yabuuchi, Y. Nakamoto, K. Shimizu, and

tronic states centered on the interstitial sites. The

T. Kikegawa, J. Phys. Soc. Jpn. 74, 2391 (2005).

results of our calculations and proposed microscopic

2. H. Fujihisa, Y. Nakamoto, K. Shimizu, T. Yabuuchi, and

model showed that the structural phase transition un-

Y. Gotoh, Phys. Rev. Lett. 101, 095503 (2008).

3. G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169

¹⁾e-mail: novoselov@imp.uran.ru

(1996).

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