手征超流$^3$ He-A中的电子泡和外尔费米子
Electron bubbles and Weyl Fermions in chiral superfluid $^3$He-A
摘要：
嵌入液体$^3$ He中的电子形成介观气泡，其半径大于$^3$ He原子之间的原子间距离，$N_{bubble}\approx 200$ $^3$ He原子的空隙，产生具有大有效质量的负离子，其散射热激发。我们发展了Bogoliubov准粒子被嵌入$^3$ He-A中的负离子的散射理论，该理论结合了$^3$ He-A的对称性破缺，特别是包含手征轴$\hat{\bf l}$的平面中的时间反演和镜像对称性。离子势的多重散射，结合手征序参量的Andreev散射，导致束缚在离子上的外尔费米子的光谱，这些外尔费米子支持电子泡中循环的质量电流-超流$^3$ He-A膜中手征边缘电流的介观实现。结果是嵌入$^3$ He-A中的电子泡获得从手性基态继承的角动量${\bf L}\approx -(N_{bubble}/2)\hbar\,\hat{\bf l}$。我们扩展的散射理论计算力的移动电子泡，斯托克斯阻力和横向力，${\bf F}_{W} = \frac{e}{c}{\bf v}\times{\bf B}_{W}$，定义由一个有效的磁场，${\bf B}_{W}\propto\hat{\bf l}$，产生的散射的外尔费米子的频谱的热准粒子的移动离子。RIKEN研究小组报道了电场驱动下电子泡的反常霍尔效应是由横向力引起的。我们的结果的散射截面，阻力和横向力的运动离子进行了比较与实验，并显示提供了一个定量的理解的迁移率和异常霍尔角的温度依赖性的正常和超流$^3$ He-A中的电子泡。我们还讨论了我们的结果与早期理论工作的负离子超流$^3$他。
英文摘要：
Electrons embedded in liquid $^3$He form mesoscopic bubbles with radii large compared to the interatomic distance between $^3$He atoms, voids of $N_{bubble}\approx 200$ $^3$He atoms, generating a negative ion with a large effective mass that scatters thermal excitations. We develop scattering theory of Bogoliubov quasiparticles by negative ions embedded in $^3$He-A that incorporates the broken symmetries of $^3$He-A, particularly time-reversal and mirror symmetry in a plane containing the chiral axis $\hat{\bf l}$. Multiple scattering by the ion potential, combined with Andreev scattering by the chiral order parameter, leads to a spectrum of Weyl Fermions bound to the ion that support a mass current circulating the electron bubble - the mesoscopic realization of chiral edge currents in superfluid $^3$He-A films. A consequence is that electron bubbles embedded in $^3$He-A acquire angular momentum, ${\bf L}\approx -(N_{bubble}/2)\hbar\,\hat{\bf l}$, inherited from the chiral ground state. We extend the scattering theory to calculate the forces on a moving electron bubble, both the Stokes drag and a transverse force, ${\bf F}_{W} = \frac{e}{c}{\bf v}\times{\bf B}_{W}$, defined by an effective magnetic field, ${\bf B}_{W}\propto\hat{\bf l}$, generated by the scattering of thermal quasiparticles off the spectrum of Weyl Fermions bound to the moving ion. The transverse force is responsible for the anomalous Hall effect for electron bubbles driven by an electric field reported by the RIKEN group. Our results for the scattering cross section, drag and transverse forces on moving ions are compared with experiments, and shown to provide a quantitative understanding of the temperature dependence of the mobility and anomalous Hall angle for electron bubbles in normal and superfluid $^3$He-A. We also discuss our results in relation to earlier theoretical work on negative ions in superfluid $^3$He.
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