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arXiv 1602.05797cond-mat.supr-concond-mat.mtrl-sci
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$s$波超导体附近强自旋轨道耦合半导体量子阱中的能隙三重态$p$波超导性

Gapped triplet $p$-wave superconductivity in strong spin-orbit-coupled semiconductor quantum wells in proximity to $s$-wave superconductor

T. Yu, M. W. Wu

摘要:

我们证明了{ \it gapped}三重态超导电性,即,具有三重态序参量的三重态超导体,可以在接近于$s$波超导体的强自旋轨道耦合量子阱中实现。结果表明,在超导邻近效应诱导的单重态序参量作用下,量子阱中不仅由于自旋-轨道耦合可以产生三重态对,而且由于电子-电子之间的有效相互作用(包括电子-电子库仑相互作用和电子-声子相互作用)也可以诱导出三重态序参量.这是de Gennes工作的自然延伸,在de Gennes工作中,排斥相互作用诱导的单重态序参量出现在接近$s$波超导体的正常金属中[Rev. Mod. Phys. { \bf 36},225(1964)]。具体来说,我们推导出有效的Bogoliubov-de Gennes方程,其中由于有效的电子-电子相互作用的自能有助于单重态和三重态序参量。结果表明,对于单重态序参量,由于自能重整化,它被有效地抑制;而对于三重态序参量,由于自旋轨道耦合,它是具有平行于有效磁场的${\bf d}$矢量的$p$波($p_x\pm ip_y$).最后,我们对InSb(100)量子阱进行了数值计算。具体地说,我们揭示了库仑相互作用是更重要的比电子-声子相互作用在低温下。此外,它表明,适当的电子密度,重整化单重态的最小值和诱导的三重态序参量的最大值是可比的,因此可以在实验上区分。

英文摘要:

We show that the {\it gapped} triplet superconductivity, i.e., a triplet superconductor with triplet order parameter, can be realized in strong spin-orbit-coupled quantum wells in proximity to $s$-wave superconductor. It is revealed that with the singlet order parameter induced from the superconducting proximity effect, in quantum wells, not only can the triplet pairings arise due to the spin-orbit coupling, but also the triplet order parameter can be induced due to the repulsive effective electron-electron interaction, including the electron-electron Coulomb and electron-phonon interactions. This is a natural extension of the work of de Gennes, in which the repulsive-interaction-induced singlet order parameter arises in the normal metal in proximity to $s$-wave superconductor [Rev. Mod. Phys. {\bf 36}, 225 (1964)]. Specifically, we derive the effective Bogoliubov-de Gennes equation, in which the self-energies due to the effective electron-electron interactions contribute to the singlet and triplet order parameters. It is further shown that for the singlet order parameter, it is efficiently suppressed due to this self-energy renormalization; whereas for the triplet order parameter, it is the $p$-wave ($p_x\pm ip_y$) one with the ${\bf d}$-vector parallel to the effective magnetic field due to the spin-orbit coupling. Finally, we perform the numerical calculation in InSb (100) quantum wells. Specifically, we reveal that the Coulomb interaction is much more important than the electron-phonon interaction at low temperature. Moreover, it shows that with proper electron density, the minimum of the renormalized singlet and the maximum of the induced triplet order parameters are comparable, and hence can be experimentally distinguished.

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