Excitation spectrum and superconductivity in diamond-type compounds
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ONIC PROPERTIES OF SOLID
Excitation Spectrum and Superconductivity in DiamondType Compounds R. O. Zaitsev Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia email: [email protected] Received June 11, 2013
Abstract—The occurrence of superconductivity in a diamondtype lattice is investigated. For each integer interval of electron concentration np, narrow concentration regions are discovered in which the supercon ducting transition temperature has the highest possible value. Analysis is carried out under the assumption that the energy of strong electron–electron correlations is the largest energy parameter. The results are in qualitative agreement with experimental data. DOI: 10.1134/S1063776113140069
1. INTRODUCTION The problem of the possibility of the occurrence of superconductivity in compounds with partly filled p shell is directly related to the existence of strong Cou lomb interaction between electrons belonging to the same atom. Analysis of this interaction for p electrons leads to values of U *p ranging from 8 to 17 eV [1, 2], which considerably exceeds the integrals of hopping to
has the following form in the simplest case of hoppings to the nearest neighbors:
+
∑
† ba bˆ i, σ ( r 1 )aˆ k, σ ( r 2 )t i, k ( r 1 – r 2 )
(1)
i, k, r 1, r 2, σ
–μ
∑ aˆ
† ˆ k, σ ( r )a k, σ ( r )
k, r, σ
–μ
∑ bˆ
† ˆ k, σ ( r )b k, σ ( r ).
k, r, σ
Passing to the atomic representation, we can write the creation and annihilation operators as linear combi nations of Hubbard X operators † aˆ k, σ ( r ) =
∑g α
k, σ ˆ α α Xr ,
† bˆ p, σ ( r ) =
∑g
p, σ ˆ γ γ Yr .
(2)
γ
k, σ
For the lowest highspin states, coefficients g α can be expressed in terms of the products of the spin and orbital coefficients of vector summation, which corre spond to the separation of a particle (see below), and α
X r are the X operators of the Fermi type, which satisfy the nonFermiliquid commutation relations
2. GENERAL RELATIONS
np nm kp km { Xˆ r , Xˆ r' } = δ r, r' ( δ mk Xˆ + δ pn Xˆ r ).
The Hamiltonian of the system can be written in terms of the creation and annihilation operators and 1 According
† ab aˆ i, σ ( r 1 )bˆ k, σ ( r 2 )t i, k ( r 1 – r 2 )
i, k, r 1, r 2, σ
1
the nearest neighbors. For this reason, we can assume that the Hubbard model is applicable to all com pounds with an unfilled 2p shell, and the correspond ing values of the Coulomb matrix elements can be set at infinity. It is well known that the energy levels of 2s elec trons in carbon compounds lie much lower than the levels of 2p electrons [1]. For this reason, we will assume that the 2s states are filled and will analyze the population of triply degenerate 2p shell in a diamond type lattice. Analysis will be carried out based on the general results obtained by the author in [3]. It will be shown that the superconducting state for each integer interval of concentrations can exist only when one lowest band of antibinding states is filled, which corresponds to a small interval of electron concentrati
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