Upper magnetic field in superconducting Dirac semi-metal

Temperature dependence of the upper critical field $H_{c 2}$ of the Dirac semi

metal (DSM) with phonon mediated pairing is considered within semi - classical approximation. The low temperature dependence deviates from conventional BCS superconductor with parabolic dispersion relation\cite{WHH} even for large adiabaticity parameter, $\gamma =\mu /\left( \hbar \Omega \right) $., w h e r e$ \mu $i s t h e c h e m i c a l p o t e n t i a l a n d$ \Omega $ - Debye frequency. In particular the “reduced field”, ratio of zero temperature $% H_{c2} $t o d e r i v a t i v e a t c r i t i c a l t e m p e r a t u r e,$ h^{\ast }=H_{c2}\left( 0\right) /\left( -T\frac{dH_{c2}}{dT}\right) |{T{c}} $, d e p e n d s o n$ \gamma $ and can be extended beyond the adiabatic limit. The reduced magnetic field ratio is universal (independent of the chemical potential, interaction strength etc.) and smaller than the Werthamer ratio for clean superconductors: $h^{\ast }=0.55 $f o r D S M,$ h^{\ast }\left( 0\right) =0.69$ for parabolic band. The results are in good agreement compared with recent experiments on $T a P$ .

Temperature dependence of the upper critical field $H_{c 2}$ of the Dirac semi

metal (DSM) with phonon mediated pairing is considered within semi - classical approximation. The low temperature dependence deviates from conventional BCS superconductor with parabolic dispersion relation\cite{WHH} even for large adiabaticity parameter, $\gamma =\mu /\left( \hbar \Omega \right) $., w h e r e$ \mu $i s t h e c h e m i c a l p o t e n t i a l a n d$ \Omega $ - Debye frequency. In particular the “reduced field”, ratio of zero temperature $% H_{c2} $t o d e r i v a t i v e a t c r i t i c a l t e m p e r a t u r e,$ h^{\ast }=H_{c2}\left( 0\right) /\left( -T\frac{dH_{c2}}{dT}\right) |{T{c}} $, d e p e n d s o n$ \gamma $ and can be extended beyond the adiabatic limit. The reduced magnetic field ratio is universal (independent of the chemical potential, interaction strength etc.) and smaller than the Werthamer ratio for clean superconductors: $h^{\ast }=0.55 $f o r D S M,$ h^{\ast }\left( 0\right) =0.69$ for parabolic band. The results are in good agreement compared with recent experiments on $T a P$ .

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