SrTiO₃模型中超导性的自洽GW理论
Self-consistent GW theory for superconductivity in SrTiO3 models
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中文总结 AI 辅助
研究掺杂SrTiO₃超导性，求解有限温度GW方程，比较不同自洽水平，发现单次核高估配对起始温度，明确配对通道，揭示密度趋于零时配对起始尺度非零，强调初始铁电、自洽及全动量频率依赖处理的重要性。
中文摘要 AI 辅助
掺杂的SrTiO₃中的超导性在很宽的载流子密度范围内出现，包括费米能量低于极性纵向光学声子尺度的情况。在这种情况下，传统Migdal-Eliashberg理论实现所依据的假设无效。我们求解了具有完全动量和频率依赖性的有限温度GW方程，针对SrTiO₃的极性单带模型，使用从头算计算参数化的有效质量和三声子介电函数。比较不同自洽水平发现，单次（G₀W₀）核将配对起始温度高估了一到两个数量级。主导抑制来自用G取代G₀。使用自洽计算的相互作用W进一步降低并缩小了配对起始圆顶。在稀释极限下，确定配对通道为材料初始铁电屏蔽的弗罗利希声子相互作用。全方程数值解揭示，密度趋于零时配对起始尺度非零，而费米面投影或费米能量频率截断会消除它。这项工作突出了初始铁电的相关性、自洽的重要性以及在模拟类似SrTiO₃的掺杂极性半导体超导性时进行全动量和频率依赖处理的必要性。
英文摘要
Superconductivity in doped SrTiO$_3$ occurs over a wide range of carrier densities, including those for which the Fermi energy is below the polar longitudinal optical phonon scale. In this regime, the assumptions underpinning conventional implementations of Migdal-Eliashberg theory, including frequency cutoffs at the phonon scale and a Coulomb pseudopotential $μ^\ast$, are not valid. We solve the finite-temperature $GW$ equations with full momentum and frequency dependence, without cutoffs or $μ^\ast$, for polar one-band models of SrTiO$_3$, using effective masses and three-phonon dielectric functions parameterized from ab initio calculations. Comparing different self-consistency levels, namely $G_0W_0$, $GW_0$, and fully self-consistent $GW$, we find that the one-shot ($G_0W_0$) kernel overestimates the pairing-onset temperature by one to two orders of magnitude. The dominant suppression comes from replacing $G_0$ by $G$, thereby incorporating the phonon renormalization factor in the electron Green function. Using the self-consistently computed interaction $W$ further lowers and narrows the pairing-onset dome. In the dilute limit, our calculations identify the pairing channel as the Fröhlich phonon interaction screened by the incipient ferroelectricity of the material, with plasmonic and electronic screening effects negligible. The numerical solution of the full equations reveals a pairing-onset scale that remains non-zero as the density tends to zero, whereas Fermi-surface projection or Fermi-energy frequency truncation removes it. This work highlights the relevance of incipient ferroelectricity, the importance of self-consistency, and the need for a full momentum- and frequency-dependent treatment in modeling superconductivity in SrTiO$_3$-like doped polar semiconductors.
