Strongly correlated and strongly coupled s-wave superconductivity of the high entropy alloy Ta_1/6Nb_2/6Hf_1/6Zr_1/6Ti_1/6 compound

Abstract

High entropy alloy (HEA) is a random mixture of multiple elements stabilized by high mixing entropy. We synthesized a Ta_1/6Nb_2/6Hf_1/6Zr_1/6Ti_1/6 bulk HEA compound as a body-centered cubic structure with lattice parameter a = 3.38 Å based on arc melting. From the electronic and magnetic property measurements, we obtained the superconducting properties such as electron-phonon coupling constant λ_el-ph, electron-phonon potential V_el-ph, density of states at the Fermi level D(E_F), superconducting energy gap 2Δ(0)/k_BT_c, upper-critical field H_c2(0), coherence length ξ, and critical current density J_c. The compound showed a superconducting transition at T_c = 7.85 K. The compound has relatively sizeable specific heat jump (ΔC/γT_c), high effective mass of carrier (29 m_e), and high Kadowaki-Woods ratio (A/γ², which plays an important role in the heavy Fermi compounds), indicating that it resides within the strongly coupled s-wave superconductor within a dirty limit. Its vortex pinning force is described by the Dew-Huges double exponential pinning model, implying that there are two types of pinning mechanisms. The possible coexistence of strongly correlated behavior in s-wave superconductivity in HEA compounds is noteworthy because many of the strongly correlated superconductors, such as heavy-fermion and high T_c cuprate superconductors, have nodal gap symmetry. The HEA compound suggests exploiting different types of superconductivity with the current strongly correlated superconductors as well as metallic superconductors.

Introduction

High entropy alloys (HEAs) are multicomponent alloys that are formed by more than 5 different elements. HEAs are crystallized as simple crystallographic pseudo-lattices such as cubic and hexagonal structures by high mixing entropy [[1], [2], [3], [4]–5]. HEAs have many excellent physical properties, such as superior tensile strength (> 1 GPa), hardness, fracture-wear-corrosion-oxidation resistance (superior to 304 stainless steel), thermal and structural stability, compared to conventional alloys [[6], [7]–8]. Their novel physical properties have attracted much attention for various applications in structural materials.

There have been several recent reports on the superconducting properties of HEAs. For example, type-II bulk superconducting properties have been observed in the Ta-Nb-Hf-Zr-Ti system, exhibiting a critical temperature T_c = 7.3 K [9], and the superconducting state persists under high pressure up to 190 GPa [10]. Several other studies have reported various HEA superconductors, such as compositionally modified (TaNb)_1-x(HfZrTi)_x [11], Nb-Re-Hf-Zr-Ti (T_c = 5.3 K) [12], (ScZrNb)_1-x(RhPd)_x, and Sc-Zr-Nb-Ta-Rh-Pd (T_c = 9.3 K) [13]. All of these previous reports suggest that those HEAs are conventional s-wave phonon-mediated superconductors. The superconducting state is robust against disorder because the transition temperature is not sensitive to disorder in either the simple crystalline or amorphous metallic state [11].

Among intermetallic superconductors, Nb₃Ge has the highest T_c at 23.2 K, with a high critical field H_c = 37 T, in which a thin film is deposited on a sapphire substrate by a chemical transport reaction method [14]. Nb₃Sn is a commercially available superconductor (T_c = 18.3 K and H_c = 30 T) used in high-field magnet applications, such as thermonuclear fusion reactors, particle accelerator magnets, magnetic resonance imaging (MRI), and nuclear magnetic resonance (NMR) [15,16]. At present, the superconducting properties of critical temperature and critical current density of the HEAs are inferior to those of the Nb₃Sn superconductor with high critical current density (J_c = 3000 A/mm²). However, because of their extremely high mechanical strength, fracture-wear-corrosion-oxidation resistances, and high thermal and structural stability, HEAs have great potential for practical superconducting applications if their superconducting properties are enhanced by material design and process engineering. Because this research is in an early stage, HEAs have rarely been investigated on the fundamental understanding of the physical properties of HEA superconductors.

Recently, it has been suggested that the critical temperatures of HEA superconductors can be enhanced by increasing the valence electron count in crystalline as well as amorphous transition metal alloys [17]. However, this approach is controversial because it has not been demonstrated that critical temperature depends on valence electron count [18]. Currently, superconducting investigations of HEAs are limited to identifying the variation of superconducting properties with elemental composition.

In this study, we found unique properties of the superconducting compound Ta_1/6Nb_2/6Hf_1/6Zr_1/6Ti_1/6, which is nearly on the optimally doped by counting the valence electrons from measurements of the electronic properties in the normal and superconducting states of the compound. The temperature-dependent electrical resistivity ρ(T) showed parabolic temperature-dependency at the normal state near T_c. The parabolic temperature dependency is changed to linear behavior at the high-temperature region. Even though it was within the dirty limit, the compound exhibited a relatively large specific heat jump (ΔC/γT_c). We also found that the Kadowaki-Woods ratios (A/γ²) of the compound are close to the ones of heavy-fermion states, with a substantial effective mass (29 m_e), implying a strongly correlated system. The strongly correlated electron behavior in s-wave superconductivity is noteworthy because many superconductors in strongly correlated systems are heavy-fermion and high-Tc cuprate superconductors, making them nodal superconductors. This investigation addresses the improving understanding of unconventional superconducting and physical properties of the HEA Ta_1/6Nb_2/6Hf_1/6Zr_1/6Ti_1/6 compound and its potential applications as metallic superconductors.