Pressure-induced superconductivity at 32 K in MoB2

ABSTRACT Since the discovery of superconductivity in MgB2 (Tc ∼ 39 K), the search for superconductivity in related materials with similar structures or ingredients has never stopped. Although about 100 binary borides have been explored, only a few of them show superconductivity with relatively low Tc. In this work, we report the discovery of superconductivity up to 32 K, which is the highest Tc in transition-metal borides, in MoB2 under pressure. The Tc of MoB2 in the α phase can be well explained by theoretical calculations in the framework of electron-phonon coupling. Furthermore, the coupling between the d electrons of Mo and the out-of-plane Mo-phonon modes are the main driving force of the 32 K superconductivity of MoB2. Our study sheds light on the exploration of high-Tc superconductors in transition metal borides.


Sample synthesis, structural and composition characterizations. Single crystals of
MoB2 were grown by the Al flux method. Mo (99.5 %), B (99.9 %) and Al (99.99 %) with a molar ratio of Mo : B : Al = 1 : 2.5 : 73.3 were loaded in an alumina crucible.
The mixture was heated up at 1773 K for 10 h, then it was cooled down to 1173 K with the rate of 30 K/h. The single crystal growth process was performed under high-purity argon atmosphere in the furnace. Finally, the MoB2 single crystals were obtained by means of sodium hydroxide solution to remove the Al flux.
Experimental details of high-pressure measurements. In situ high pressure XRD measurements were performed at the beamline 15U at Shanghai Synchrotron Radiation Facility (λ = 0.6199 Å). Symmetric diamond anvil cell (DAC) with anvil culet sizes of 200 μm as well as Re gaskets were used. Mineral oil was used as pressure transmitting medium (PTM) and pressure was determined by the ruby luminescence method [1].
CeO2 was used to calibrate the sample-detector distance and the orientation parameters of the detector. The two-dimensional diffraction images were analyzed using the FIT2D program [2]. Rietveld refinements on crystal structures under high pressure were performed by General Structure Analysis System (GSAS) and graphical user interface EXPGUI package [3,4].
High pressure resistivity measurements were performed in a nonmagnetic diamond anvil cell. A cubic BN/epoxy mixture layer was inserted between BeCu gaskets and electrical leads. Electrical resistivity was measured using the dc current in van der Pauw technique in Physical Property Measurement System (Dynacool, Quantum Design, Tmin = 1.8 K). Pressure was measured using the ruby scale by measuring the luminescence from small chips of ruby placed in contact with the sample [1].
An in situ high-pressure Raman spectroscopy investigation of MoB2 was performed using a Raman spectrometer (Renishaw inVia, UK) with a laser excitation wavelength of 532 nm and low-wavenumber filter. A symmetric DAC with anvil culet sizes of 200 μm was used, with silicon oil as the PTM.
Theoretical calculations. We employed the swarm-intelligence-based CALYPSO structure prediction method [5] to find the energetically stable structures of MoB2 under high pressure. Six independent searching missions at 90 GPa, which were respectively limited to 1, 2, 3, 4, 6, and 8 chemical formulae per unit cell, were carried out. The underlying enthalpy calculations were performed with the Vienna Ab-initio Simulation Package (VASP) [6]. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) type was adopted for the exchange-correlation functional [7]. A kinetic energy cutoff of 360 eV was used for the plane-wave basis. A Monkhorst-Pack k-point mesh with a grid spacing of 0.1 Å -1 was adopted for the Brillouin zone (BZ) sampling. The Gaussian smearing method with a width of 0.05 eV was used for the Fermi surface broadening. We also checked the enthalpy differences between different structures of MoB2 (Supplemental Information Fig. S3a) by using the Quantum ESPRESSO (QE) package [8]. The consistent results were obtained, which insures the reliability of our calculations.
The electronic structure, phonon spectrum, and electron-phonon coupling (EPC) of AlB2-type α-MoB2 at 90 GPa were studied based on the density functional theory (DFT) [9,10] and density functional perturbation theory (DFPT) [11,12] calculations as implemented in the Quantum ESPRESSO (QE) package [8]. The interactions between electrons and nuclei were described by the norm-conserving pseudopotentials [13]. The GGA-PBE exchange-correlation functional was adopted. The kinetic energy cutoff of the plane-wave basis was set to be 80 Ry. A 24×24×24 k-point mesh was used for the sampling of Brillouin zone (BZ). The Gaussian smearing method with a width of 0.004 Ry was employed for the Fermi surface broadening. In the structural optimization, both lattice constants and internal atomic positions were fully relaxed until the forces on all atoms were smaller than 0.0002 Ry/Bohr.
The EPC constant λ can be calculated either by the summation of the EPC strength λ qν in the full BZ for all phonon modes or by the integral of the Eliashberg spectral function [16] α 2 F(ω) as following, where N(εF) is the density of states at the Fermi level εF, ω qν is the frequency of the νth phonon mode at the wave vector q, and γ qν is the phonon linewidth. The superconducting transition temperature Tc can be calculated by substituting the EPC constant λ into the McMillan-Allen-Dynes formula [17,18], where ωlog is the logarithmic average frequency defined as [17,18], and μ * is the effective screened Coulomb repulsion constant setting to an empirical value [19,20]