Table 1 Electronic, vibrational, and superconducting properties of dynamically stable phases at 270 GPa.

From: Dilute carbon in H3S under pressure

Structure

ΘD

NF

\({\omega }_{\ln }\)

λ

\({T}_{{{{\rm{c}}}}}^{{{{\rm{ME}}}}}\)

\({T}_{{{{\rm{c}}}}}^{{{{\rm{AD}}}}}\)

Pstab

\(Im\bar{3}m\) H3S

1288

0.050

1626

1.24

175–162

166–148

N/A

R3m H3S

1330

0.044

1652

1.02

135–115

125–107

N/A

\(Im\bar{3}m\) Oh-CS7H24

1366

0.030

    

260–270

\(Pm\bar{3}m\) Oh-CS15H48

1382

0.040

    

255–270

\(Pm\bar{3}m\) Oh-CS53H162

1368

0.048

    

200–270

Amm2 Td-CS3H12

1752

0.028

1370

0.85

80–67

76–63

160–270

Amm2 Td-CS7H24

1824

0.039

    

250–270

Fmm2 Td-CS7H24

1525

0.039

    

200–270

Pm Td-CS7H24

1701

0.033

    

140–270

Amm2 Td-CS15H48

1623

0.033

    

180–270

Amm2 Td-CS53H162

1678

0.046

    

200–270

Cmcm CSH7

1821

0.026

    

140–270

R3m CSH7

1780

0.028

1703

1.10

156–140

147–129

140–270

Cm CS3H13

1810

0.025

1704

1.01

142–121

128–110

140–270

R3m CS3H13

1664

0.028

1250

1.02

111–98

96–83

140–270

Cm CS7H25

1832

0.031

1551

0.94

115–100

104–88

140–270

R3m CS7H25

1729

0.038

    

160–270

R3m CS15H49

1760

0.034

    

140–270

R3m CS53H163

1792

0.043

    

200–270

  1. Debye temperature (ΘD, in K), density of states at the Fermi level (NF, in states eV−1 A−3), logarithmic average of phonon frequencies (\({\omega }_{\ln }\), in K), electron–phonon coupling constant (λ), and superconducting critical temperature (Tc, in K) obtained via numerical solution of the Migdal–Eliashberg equations (ME) and the Allen–Dynes equation for strongly coupled systems (AD) using μ* = 0.1−0.13 at 270 GPa. The pressure range where dynamic stability was confirmed in this study (phonon calculations were carried out between 140 and 270 GPa, see Section S2.4, S3.4, and S4.4) is also provided in GPa.
  2. Calculated strong coupling and shape dependence correction factors, f1 and f2, used in the AD equation are: \(Im\bar{3}m\) H3S: f1 = 1.067, f2 = 1.022, R3m H3S: f1 = 1.052, f2 = 1.017, Td-CS3H12: f1 = 1.039, f2 = 1.016, R3m CSH7: f1 = 1.058, f2 = 1.022, Cm CS3H13: f1 = 1.046, f2 = 1.013, R3m CS3H13: f1 = 1.047, f2 = 1.019, Cm CS7H25: f1 = 1.047, f2 = 1.017.