${\text{BaPtSi}}_3$: A noncentrosymmetric BCS-like superconductor

By investigations of phase relations in the alloy system Ba-Pt-Si at $900°\text{C}$ we observe the formation of the compound ${\text{BaPtSi}}_3$, which crystallizes in the noncentrosymmetric ${\text{BaNiSn}}_3$ structure type. Its space group is $I4mm$ with the tetragonal lattice parameters $a=0.44094\left(2\right)\text{nm}$ and $c=1.0013\left(2\right)\text{nm}$ for the arc-melted compound annealed at $900°\text{C}$. The characterization of the physical properties of ${\text{BaPtSi}}_3$ reveals a superconducting transition at 2.25 K with an upper critical field at $T=0\text{K}$ of $\approx 0.05\text{T}$. For analyzing the electronic structure, density-functional theory calculations are performed yielding very good agreement between theory and experiment for the structural properties. From relativistic electronic-structure calculations, Fermi surface nesting features are found for two characteristic double sets of bands. The spin-orbit splitting of the relativistic electronic bands is in general rather small at Fermi energy and, therefore, superconductivity adheres to an almost undisturbed BCS state.

Figure 1

(Color online) Sketch of the crystal structure of ${\text{BaPtSi}}_3$. Note the loss of centrosymmetry due to the arrangement of Pt and Si atoms.

Figure 2

(Color online) Panel (a) shows the temperature-dependent electrical resistivity $\rho$ of ${\text{BaPtSi}}_3$. The dashed line denotes a least-squares fit according to the Bloch-Grüneisen law resulting in the Debye temperature of ${\theta }_D=345\text{K}$. The inset shows the field response of the superconducting transition as measured at various externally applied magnetic fields. Panel (b) shows the temperature-dependent electrical resistivity $\rho$ of ${\text{BaPtSi}}_3$ measured at various applied pressures. The inset shows the pressure dependence of the superconducting transition temperature $T_c$, initially varying as $\partial T_c/\partial p=-0.06\text{K}/\text{kbar}$.

Figure 3

(Color online) Temperature-dependent specific heat $C_p$ of ${\text{BaPtSi}}_3$, plotted as $C_p/T$ vs $T$. The inset shows low-temperature details of the superconducting transition for various values of externally applied magnetic fields. The solid line represents the temperature-dependent specific heat of a spin-singlet fully gapped superconductor according to the model of Mühlschlegel, Ref. 25.

Figure 4

(Color online) Temperature-dependent specific heat $C_p$ of ${\text{BaPtSi}}_3$, plotted as $\left(C_p-\gamma T\right)/T^3$ vs $\text{ln}T$. The solid line is a least-squares fit of the experimental data using the model described in the text and the dashed-dotted line represents a simple Debye contribution with ${\theta }_D=370\text{K}$. The essential parameters of the model used to construct the spectral function $F\left(\omega \right)$ (dotted lines, right axis), are ${\theta }_D=370\text{K}$, ${\omega }_{E1}=43\text{K}$ with a width of 5.3 K and ${\omega }_{E2}=128\text{K}$ with a width of 37 K. The DFT derived function $F_{\text{DFT}}\left(\omega \right)/{\omega }^2$ ($F_{\text{DFT}}$ being the phonon density of states as calculated by DFT) is shown as a dashed line, referring to the second axis on the right-hand side.

Figure 5

(Color online) Temperature-dependent upper critical field ${\mu }_0{H}_{c2}$ and thermodynamic critical field ${\mu }_0{H}_c$ of ${\text{BaPtSi}}_3$ as obtained from resistivity and specific-heat measurements. The dashed-dotted line represents the WHH model. The solid line is an extrapolation of the thermodynamic critical field towards zero and the dashed line serves as a guide to the eyes.

Figure 6

(Color online) Section of total and atom-projected densities of states (DOS; in states ${\text{eV}}^{-1}$) for ${\text{BaPtSi}}_3$ in the energy range $\pm 2.5$ around the Fermi energy $E_F$. Energy scale is defined relative to $E_F$. Upper panel: DOS with SO coupling; lower panel: DOS for scalar relativistic calculation. Total DOS (solid lines) split into Ba like (dotted lines), Pt like (dashed-dotted lines), and Si like (dashed lines) DOS summed over all three Si atoms.

Figure 7

Section of electronic band structure along high symmetry directions for ${\text{BaPtSi}}_3$ in the energy range $\pm 2.5$ around the Fermi energy $E_F$. Upper panel: spin-orbit coupling included; lower panel: scalar relativistic only. Brillouin zone, see Fig. 8.

Figure 8

(Color online) Fermi surface of band 1 (see text). (a) view in direction $Z\text{−}\Gamma$; (b) view in direction [100]; (c) view in direction $X\text{−}\Gamma$. Top left panel: Brillouin zone of the body-centered tetragonal lattice for $c>a$.

Figure 9

(Color online) Fermi surface of band 4 (see text). (a) view in direction $Z\text{−}\Gamma$; (b) view in direction [100]; and (c) view in direction $X\text{−}\Gamma$.

Figure 10

(Color online) DFT-derived phonon dispersions and density of states. The PDOS is split into contributions of local modes attributed to Ba, Pt, and Si atoms.