超导理论的强局部变分法,以及相干相互作用和作用-反作用原理

ChaoFan Yu, Xuyang Chen, ZhiHua Luo
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The\ntheory predicts that the coupling strength $Vg(0)$ reduces to\n$\\tilde{V}g(0)=e^{-\\left(1-\\alpha_{1}\\right)^{2} k^{2} / 4 \\lambda^{2}} Vg(0)$,\nand the Cooper pair reduces similarly. For weak coupling, $\\alpha_1=1$, and\nwhen $Vg(0)=0.1$, $\\Delta_{\\mathrm{A \\cdot C}}=108 \\Delta_{\\text{BCS}}$, but\n$\\Delta_{\\mathrm{A \\cdot C}}$ decreases to $28 \\Delta_{\\text{BCS}}$ at\n$Vg(0)=0.2$. For strong coupling, $\\alpha_1=0$, if $Vg(0)=1.4$, $\\tilde{V}\ng(0)$ reduces to 0.2, and the smaller Cooper pair $\\widetilde{C_{k \\uparrow}\nC_{-k \\downarrow}}$ reduces to $0.14 C_{k \\uparrow} C_{-k \\downarrow}$.\nAdditionally, $\\Delta_{\\mathrm{A \\cdot C}} = 0.5676~\\text{eV} \\gg \\hbar\n\\omega_{\\text{D}}$, and the local stacking force is\n$\\widetilde{V}_{\\text{st}}=0.264 ~\\text{eV}$. 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引用次数: 0

摘要

对于双模电子配对,我们提出了一种由强局域波动驱动的局域堆积力配对机制,其中两个直线配对轨道上的绑库珀配对$C_{-k\downarrow}C_{k\arrow}e^{ik\cdot r}$取代了巡回配对。基于相干相互作用和作用-反作用原理,构建了强局域变分理论,能量极值方程和能隙方程形成了自洽对,涉及局域变分参数$\lambda$、能隙$\Delta$和能量截止值$\hbar \omega_0$。当$hbar \omega_0(j)$接近其截止值时,$\lambda$和$\Delta$收敛到固定值。理论预测,耦合强度 $Vg(0)$ 降为:$tilde{V}g(0)=e^{-\left(1-\alpha_{1}\right)^{2} k^{2} / 4 \lambda^{2}。/ 4 \lambda^{2}}Vg(0)$,库珀对也同样如此。对于弱耦合,$\alpha_1=1$,当$Vg(0)=0.1$时,$\Delta_{\mathrm{A \cdot C}}=108\Delta_{text{BCS}}$,但当$Vg(0)=0.2$时,$\Delta_{mathrm{A \cdot C}}$下降到$28\Delta_{text{BCS}}$。对于强耦合,$\alpha_1=0$,如果$Vg(0)=1.4$,$\tilde{V}g(0)$会减小到0.2,较小的库珀对$\widetilde{C_{k \uparrow}C_{-k \downarrow}}$ 会减小到$0.14 C_{k \uparrow}.此外,$\Delta_{\mathrm{A \cdot C}}=0.5676~\text{eV}。\gg \hbar\omega_{\text{D}}$ ,局部堆积力为$widetilde{V}_{\text{st}}=0.264 ~\text{eV}$ 。当 $k^2/\lambda^2 =$ const 时,局部强度增加,导致堆积力显著增长。因此,$\hbar \omega_0$ 和 $\Delta$ 产生了唯一的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Strong local variational approach for superconductivity theory, and the principles of coherent interaction and action-counteraction
For the two-mode electron pairing, we propose a local stacking force pairing mechanism driven by strong local fluctuations, with two straight pairing orbits where the tying Cooper pairing $C_{-k\downarrow}C_{k\uparrow}e^{ik\cdot r}$ replaces the itinerant pairing. Based on coherent interaction and action-counteraction principles, the strong local variational theory is constructed, with the energy extremum and gap equations forming self-consistent pairs, involving the local variational parameter $\lambda$, energy gap $\Delta$, and the energy cut-off $\hbar \omega_0$. As $\hbar \omega_0(j)$ approaches its cut-off, $\lambda$ and $\Delta$ converge to fixed values. The theory predicts that the coupling strength $Vg(0)$ reduces to $\tilde{V}g(0)=e^{-\left(1-\alpha_{1}\right)^{2} k^{2} / 4 \lambda^{2}} Vg(0)$, and the Cooper pair reduces similarly. For weak coupling, $\alpha_1=1$, and when $Vg(0)=0.1$, $\Delta_{\mathrm{A \cdot C}}=108 \Delta_{\text{BCS}}$, but $\Delta_{\mathrm{A \cdot C}}$ decreases to $28 \Delta_{\text{BCS}}$ at $Vg(0)=0.2$. For strong coupling, $\alpha_1=0$, if $Vg(0)=1.4$, $\tilde{V} g(0)$ reduces to 0.2, and the smaller Cooper pair $\widetilde{C_{k \uparrow} C_{-k \downarrow}}$ reduces to $0.14 C_{k \uparrow} C_{-k \downarrow}$. Additionally, $\Delta_{\mathrm{A \cdot C}} = 0.5676~\text{eV} \gg \hbar \omega_{\text{D}}$, and the local stacking force is $\widetilde{V}_{\text{st}}=0.264 ~\text{eV}$. With $k^2/\lambda^2 =$ const, the local strength increases, causing the stacking force to grow significantly. Thus, $\hbar \omega_0$ and $\Delta$ yield a unique solution.
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