High-entropy alloy superconductors: Status, opportunities, and challenges

High-entropy alloys (HEAs) are a recently opened research area in materials science and condensed matter physics. Although $3d$-metal-based HEAs have already been the subject of many investigations, studies of HEA superconductors, which tend to be based on $4d$ metals, are relatively fewer. Here we provide a short update of the progress made in studies of superconducting HEAs. We aim to summarize their current status and describe some of the key factors that appear to influence their superconducting transition temperatures and properties, including crystal structure, atomic makeup, valence electron count, molar volume, and mixing entropy. Many opportunities and challenges remain for expanding our knowledge of HEA superconductors, finding new types of HEA superconductors, and their potential for applications; these are also briefly discussed.

Figure 1

(a)–(d) Schematic representation of the bcc, CsCl, fcc, and hcp lattices with randomly distributed atoms. (e) Schematic phase diagram of a multicomponent alloy system showing conventional and HEA phase regions.

Figure 2

Ambient-pressure properties of the superconducting HEA ${\mathrm{Ta}}_{34}{\mathrm{Nb}}_{33}{\mathrm{Hf}}_8{\mathrm{Zr}}_{14}{\mathrm{Ti}}_{11}$. (a) Resistivity as a function of temperature in zero magnetic field, showing the superconducting transition at 7.3 K. The inset displays the magnetic-field dependence of the resistivity in the region of the superconducting transition for fields up to 9 T. (b) The magnetic susceptibility in the region of the superconducting transition. The inset shows the isothermal magnetization in the low-field range. (c) Low-temperature specific heat $C$($T$) for selected magnetic fields. (d) Specific heat in zero field and 9 T in a $C$/$T$ vs $T^2$ plot. Reproduced with permission from [15].

Figure 3

Valence electron count (VEC) dependence of the superconducting transition temperatures for type-A (orange region), type-B (cyan and blue regions), and type-C (red region) HEA superconductors compared to amorphous alloys (orange dashed line) and classic crystalline alloys (green dashed line). The data were taken from Refs. [7, 17, 23].

Figure 4

Plot of mixing entropy and Nb content vs superconducting transition temperature for HEA superconductors. The data were taken from Ref. [7].

Figure 5

Schematic universal pressure-$T_C$ phase diagram of ${\left(\mathrm{TaNb}\right)}_{0.67}{\left(\mathrm{HfZrTi}\right)}_{0.33}$ (type-A HEA superconductor) and ${\left(\mathrm{ScZrNbTa}\right)}_{0.6}{\left(\mathrm{RhPd}\right)}_{0.4}$ (type-C HEA superconductor). $T_C^{{}^{\mathrm{am}}}$ and $T_C^{\mathrm{const}}$ represent ambient-pressure $T_C$ and the $T_C$ which stays almost constant, respectively. $P_C$ and $P_{\max }$ stand for the critical pressure where $T_C$ starts to be saturated and the highest pressure investigated, respectively. SC represents the superconducting phase. The insets display the real data.