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arXiv 1608.07937cond-mat.mtrl-scicond-mat.mes-hallquant-ph
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Cu $_2$ O中$1S$邻位激子的$K$依赖的交换相互作用

$K$ dependent exchange interaction of the $1S$ ortho exciton in Cu$_2$O

Frank Schweiner, Jörg Main, Günter Wunner, Christoph Uihlein

备注：
Accepted for publication in Phys. Rev. B
发表信息：
Phys. Rev. B 94, 115201 (2016)
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摘要：

在处理Wannier激子的交换相互作用时，通常只考虑解析和非解析交换相互作用的主导项。然而，更高阶项可导致激子态的分裂，为此，Dasbach等人[Phys.Rev.Lett.2009]将取决于其总动量$\hbar K$的氧化亚铜$\left(\mathrm{Cu_{2}O}\right)$中的$1S$ ~激子的分裂归因于$K$依赖的分析交换相互作用[Phys.Rev.Lett.2009]。91，107401（2003）]。超越交换相互作用的共同治疗，我们得到正确的表达式，这些$K$依赖于高阶项使用$\boldsymbol{k}\cdot\boldsymbol{p}$微扰理论。我们证明了依赖于$K$的交换相互作用的出现与$P$和$D$激子的独立于$K$的交换相互作用密不可分。我们估计这些条款的大小为$\mathrm{Cu_{2}O}$从微观计算，并表明，他们是太小，无法解释所观察到的$K$依赖分裂。相反，这种分裂必须根据激子的色散来处理。此外，我们还证明了由于$K$依赖的非解析交换作用，在$\mathrm{Cu_{2}O}$中存在纵向激子和横向激子之间的耦合.

英文摘要：

When treating the exchange interaction of Wannier excitons, usually only the leading terms of the analytic and the nonanalytic exchange interaction are considered. However, higher order terms can lead to a splitting of exciton states, for which reason a splitting of the $1S$~exciton in cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ depending on its total momentum $\hbar K$ has been attributed to a $K$ dependent analytic exchange interaction by Dasbach et al [Phys. Rev. Lett. 91, 107401 (2003)]. Going beyond the common treatment of the exchange interaction, we derive the correct expressions for these $K$ dependent higher order terms using $\boldsymbol{k}\cdot\boldsymbol{p}$ perturbation theory. We prove that the appearance of a $K$ dependent exchange interaction is inseparably connected with a $K$ independent exchange interaction of $P$ and $D$ excitons. We estimate the magnitude of these terms for $\mathrm{Cu_{2}O}$ from microscopic calculations and show that they are far too small to explain the observed $K$ dependent splitting. Instead, this splitting has to be treated in terms of the dispersion of the excitons. Furthermore, we prove the occurence of a coupling between longitudinal and transverse excitons in $\mathrm{Cu_{2}O}$ due to the $K$ dependent nonanalytic exchange interaction.

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