Superfluid phases of $^3$He in nano-scale channels
Superfluid phases of $^3$He in nano-scale channels
复制标题
纳米级通道中 $^3$He 的超流相
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Sauls
中科院分区：
文献类型：
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作者：
J. Wiman;J. Sauls
将超流氦$^3 $限制在与p波库珀对的径向尺寸相当的长度尺度上，可以通过稳定在大块氦$^3 $中没有观察到的对称性破缺相来极大地改变相图。我们认为超流$^3$He限制在长圆柱形通道半径$100\mbox{ nm}$，并报告新的理论预测的平衡超流相强约束下。结果是基于强耦合的金斯堡-朗道理论与精确的数值最小化的自由能泛函，以确定平衡相和它们的稳定区域的制定。本文介绍了标准GL强耦合理论的一个扩展，它精确地解释了高压下的相图，包括定义体A相稳定区域的三临界点和$T_{AB}（p）$线。我们还介绍了可调的边界条件，使我们能够探索边界散射范围从最大到最小的pairbreaking，并报告结果的相图作为压力，温度和边界条件的函数。发现了四个稳定相：一个极性相稳定在附近的$T_c$，一个强烈的各向异性，圆柱形模拟体B相稳定在足够低的温度下，和两个手性A-样阶段具有明显不同的轨道对称性，其中之一自发地打破旋转对称轴的圆柱形通道。这些相的相对稳定性敏感地依赖于压力和边界散射的破偶程度。这些阶段所表现出的对称性破缺引起了不同的签名在横向NMR共振光谱。我们提出的理论结果的横向NMR频率偏移作为温度的函数，r.f.脉冲倾斜角和静态NMR场取向。
Confinement of superfluid $^3$He on length scales comparable to the radial size of the p-wave Cooper pairs can greatly alter the phase diagram by stabilizing broken symmetry phases not observed in bulk $^3$He. We consider superfluid $^3$He confined within long cylindrical channels of radius $100\mbox{ nm}$, and report new theoretical predictions for the equilibrium superfluid phases under strong confinement. The results are based on the strong-coupling formulation of Ginzburg-Landau theory with precise numerical minimization of the free energy functional to identify the equilibrium phases and their regions of stability. We introduce an extension of the standard GL strong-coupling theory that accurately accounts for the phase diagram at high pressures, including the tri-crital point and $T_{AB}(p)$ line defining the region of stability for the bulk A-phase. We also introduce tuneable boundary conditions that allow us to explore boundary scattering ranging from maximal to minimal pairbreaking, and report results for the phase diagram as a function of pressure, temperature, and boundary conditions. Four stable phases are found: a polar phase stable in the vicinity of $T_c$, a strongly anisotropic, cylindrical analog of the bulk B phase stable at sufficiently low temperatures, and two chiral A-like phases with distinctly different orbital symmetry, one of which spontaneously breaks rotation symmetry about the axis of the cylindrical channel. The relative stability of these phases depends sensitively on pressure and the degree of pairbreaking by boundary scattering. The broken symmetries exhibited by these phases give rise to distinct signatures in transverse NMR resonance spectroscopy. We present theoretical results for the transverse NMR frequency shifts as functions of temperature, the r.f. pulse tipping angle and the static NMR field orientation.