Potential high-T_c superconductivity in ZrB₂ polymorph under pressure

Abstract

The clear proof of superconductivity in transition-metal diborides was rarely reported. In the current work, the recently developed particle swarm optimization structural search method was utilized to propose three ZrB₂ structures, namely, I41/amd-ZrB₂, P42/mmc-ZrB₂, and P4/nmm-ZrB₂. The structural stability of the three novel ZrB₂ phases was confirmed on the basis of elastic constant and phonon dispersion calculations. At ambient pressure, the mechanical properties of the I41/amd-ZrB₂ and P42/mmc-ZrB₂ phases are comparable to those of AlB₂–ZrB₂. Electron–phonon coupling (EPC) calculations revealed that the P4/nmm-ZrB₂ phase is predicted to be a potential high-T_c superconductor with a calculated T_c of 12.7 K at 20 GPa. Moreover, significant pressure-induced EPC enhancement can also be found in the P4/nmm-ZrB₂ phase. The maximum EPC constant λ and T_c under 600 GPa are 1.05 and 34.4 K, respectively.

Introduction

Since the discovery of the superconductivity of MgB₂ (T_c = 39 K) [1] in the AlB₂ structure (P6/mmm), considerable efforts [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] have been devoted to searching for new superconductors in related compounds with a structure and chemistry similar to that of MgB₂. Particularly some d-type transition-metal diborides (TMB₂) [4], which are claimed to combine average coupling constants with comparable phonon frequencies to those of MgB₂. The first superconductors reported in TMB₂ compounds were NbB₂ and MoB₂, whose experimentally determined superconductivity critical temperatures were 3.87 and 7.45 K [13], respectively. Gasparov et al. [14] reported an experimentally observed superconducting transition of polycrystalline ZrB₂ compounds with T_c = 5.5 K. However, these observations could not be confirmed in later studies [15], [16], [17]. Experimental studies [15], [18], [19] predicted that the occurrence of superconductivity is derived from the nonstoichiometry in TMB₂ compounds. Similar situations apply for TaB₂ and BeB₂ compounds, whose superconductivity critical temperatures were experimentally determined to be 9.5 [20] and 0.7 K [21], respectively. However, the follow-up studies had reached contradictory conclusions [6], [22], [23]. In summary, to date, there is no clear proof of superconductivity that could be established for the majority of TMB₂ materials.

Numerous studies concentrating on electronic structure [5], [24], [25], bond iconicity [26], Fermi surface [27], phonon spectra [28], and electron–phonon interaction [4], [6], [16] were performed to offer theoretical explanations for the lack of superconductivity in these TMB₂ materials. Several important aspects affecting the superconductivity of TMB₂ materials are summarized: (1) strong covalent interactions between boron and metal layers are enabled by the presence of d-electrons on metal; and (2) electron–phonon interaction plays an essential role in the occurrence of superconductivity for TMB₂ materials, whose electron–phonon interaction is fairly weak.

In general, pressure can effectively shorten the interatomic distance of materials, and consequently, significantly alter their electronic bonding states to modify the physical properties and/or induce the formation of new physical states. Experimental and theoretical research [29], [30], [31], [32], [33] confirmed that pressure can effectively regulate the phonon frequency and tune the electron–phonon coupling (EPC) in various materials. Therefore, pressure may be a promising method to acquire new superconductors or alter the superconducting properties of materials. In the case of ZrB₂, experimental compression up to 50 GPa revealed no obvious phase transition [34]. The theoretical research performed by Ma et al. [35] found no high-pressure phase transitions up to 300 GPa. Two new ZrB₂ structures were proposed by Pan et al. [36], but no superconductivity was reported.

As an exploratory study, extensive particle swarm optimization (PSO) structural searches up to 500 GPa were performed to uncover the high-pressure structures of ZrB₂. Three novel ZrB₂ structures were predicted in combination with the first-principle calculations. The structural characteristics, stability, electronic structure, electron–phonon interaction, and superconductivity under different pressure conditions were systematically investigated.