Mapping superconductivity in high-pressure hydrides: The Superhydra project

The discovery of high-$T_c$ conventional superconductivity in high-pressure hydrides has helped establish computational methods as a formidable tool to guide material discoveries in a field traditionally dominated by serendipitous experimental search. This paves the way to an ever-increasing use of data-driven approaches to the study and design of superconductors. In this work, we propose a new adaptive method to generate meaningful datasets of superconductors, based on element substitution into a small set of representative structural templates, generated by crystal structure prediction methods—adapted high-throughput approach. Our approach realizes an optimal compromise between structural variety and computational efficiency and can be easily generalized to other elements and compositions. As a first application, we apply it to binary hydrides at high pressure, realizing a database of 880 hypothetical structures, characterized with a set of electronic, vibrational, and chemical descriptors. In our Superhydra Database, 139 structures are superconducting according to the McMillan-Allen-Dynes approximation. Studying the distribution of $T_c$ and other properties across the database with advanced statistical and visualization techniques, we are able to obtain comprehensive material maps of the phase space of binary hydrides. The Superhydra database can be thought as a first step of a generalized effort to map conventional superconductivity.

Figure 1

Template structures used for adapted high-throughput data generation, classified by H-H bond distance into short (S), medium (M), and long (L). The label $XN\text{−}\text{SPG}\text{−}{\mathrm{A}}_m{\mathrm{H}}_n$ indicates the H-H distance type ($X$), the structure number ($N$), space group number of the system (SPG), and the generic composition of the structure (${\mathrm{A}}_m{\mathrm{H}}_n$). Details of the crystal structures are provided in the Supplemental Material [23].

Figure 2

Distribution of data points in DB1 with respect to minimum H-H distance $d_{\text{HH}}$ and atomic number $Z$. Dark brown, orange, and light orange dots correspond to cluster TMs, HTC, and ${\mathrm{H}}_2$, respectively.

Figure 3

Heat map of different properties (color) of all the hydride structures for different elements ($y$ axis) and different templates ($x$ axis). All quantities are estimated for pressure of 200 GPa. (a) Average Bader charge on the H atom in arb. units; (b) formation enthalpy $\mathrm{\Delta }\mathrm{H}$ (eV/atom) estimated w.r.t. stable elemental phases; (c) average quasi-bulk modulus (see the SM [23]) in GPa, and (d) critical superconducting temperature $T_c$ in K. Red represents high-$T_c$ and blue low-$T_c$; the threshold is set to $T_c$ = 77 K, corresponding to ${\mathrm{N}}_2$ boiling temperature. The methodology used to estimate different quantities are provided in the SM [23].

Figure 4

Histograms of four quantities in DB2: (a) quasi-bulk modulus ${\mathrm{BM}}_q$, (b) average nearest-neighbor H-H distance $d_{\text{HH}}$, (c) average residual Bader charge on the H atom (${\rho }_H$), and (d) partial H DOS at the Fermi level HDOS (see text). Compounds are divided into low-$T_c$ (blue) and high-$T_c$ (red) structures. Inset: distribution of $T_c$'s in DB2 where the red dashed line indicates the threshold for high-$T_c$ superconductivity, given by liquid nitrogen boiling temperature (77 K).

Figure 5

Total (solid black line) and atom-projected (colored filled lines) Éliashberg function, along with the electron-phonon coupling $\lambda \left(\omega \right)$ (dashed black line) of ${\mathrm{AsH}}_2$ (S2-166-${\mathrm{A}}_1{\mathrm{H}}_2$) (top panel) and ${\mathrm{SiH}}_3$ (M5-221-${\mathrm{A}}_1{\mathrm{H}}_3$) (bottom panel) at 200 GPa. Projections onto As, H, and Si are shown in red, blue, and orange, respectively.