半导体量子点电子-核自旋系统的长期动力学
Long-term Dynamics of the Electron-nuclear Spin System of a Semiconductor Quantum Dot
摘要：
对电子自旋极化的任意机制，发展了一个准经典理论描述单电子量子点中核自旋的极化和弛豫。本文分析了在核超精细场中电子自旋进动的关联时间$τ_c$与电子自旋进动频率$Ω$的关系。它表明，最高的核极化实现的相关时间接近的电子自旋旋进期间在核领域。对于这些和更大的相关时间，间接超精细场，这对核自旋的作用，也达到最大值。这个最大值是原子核相互作用产生的偶极-偶极磁场的量级。即使平均电子极化为零，该值也不为零。结果表明，从短关联时间到$Ωτ_c>1$的转变并不影响Knight场中核自旋温度和核极化方程的一般结构，但改变了参数的值，使之成为$Ωτ_c$的函数.当关联时间大于电子超精细场中原子核的进动时间时，发现极化电子-原子核自旋系统具有三种热力学势（$χ$，$\bmξ$，$ς$）.这些电位的值计算假设从短到长的相关时间的急剧转变，这些电位的弛豫机制进行了讨论。数值模拟了核自旋势的弛豫过程，结果表明，高的核极化降低了弛豫速率。
英文摘要：
A quasi-classical theoretical description of polarization and relaxation of nuclear spins in a quantum dot with one resident electron is developed for arbitrary mechanisms of electron spin polarization. The dependence of the electron-nuclear spin dynamics on the correlation time $τ_c$ of electron spin precession, with frequency $Ω$, in the nuclear hyperfine field is analyzed. It is demonstrated that the highest nuclear polarization is achieved for a correlation time close to the period of electron spin precession in the nuclear field. For these and larger correlation times, the indirect hyperfine field, which acts on nuclear spins, also reaches a maximum. This maximum is of the order of the dipole-dipole magnetic field that nuclei create on each other. This value is non-zero even if the average electron polarization vanishes. It is shown that the transition from short correlation time to $Ωτ_c>1$ does not affect the general structure of the equation for nuclear spin temperature and nuclear polarization in the Knight field, but changes the values of parameters, which now become functions of $Ωτ_c$. For correlation times larger than the precession time of nuclei in the electron hyperfine field, it is found that three thermodynamic potentials ($χ$, $\bmξ$, $ς$) characterize the polarized electron-nuclear spin system. The values of these potentials are calculated assuming a sharp transition from short to long correlation times, and the relaxation mechanisms of these potentials are discussed. The relaxation of the nuclear spin potential is simulated numerically showing that high nuclear polarization decreases relaxation rate.
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