标题： 薄镉晶体电导率的 Sondheimer 振荡量化 显示英文标题

标题： Quantization of Sondheimer oscillations of conductivity in thin cadmium crystals

摘要： 数十年前，桑德海默发现，承载弹道电子的金属晶体的电导率随磁场振荡。 这些以磁场为周期且周期与样品厚度成正比的振荡，在半经典框架下得到了理解。 在这里，我们研究了厚度在12.6到475$\mu$米之间的镉单晶中的纵向和横向电导率。当磁场足够大或样品足够厚时，振荡幅度会像以前报道的那样呈 $B^{-4}$衰减。 相比之下，前十个振荡遵循 $B^{-2.5}e^{-B/B_0}$的磁场依赖性，其振幅由电导量子、样品厚度、磁长度以及费米面几何形状决定。 我们证明它们超出了半经典图景，因为指数前因子表明存在不同量子态之间的量子隧穿。 我们描绘了这些量子振荡的画面，其中镉中半狄拉克带的线性色散起着关键作用。 这些振荡是由最低朗道管与费米面上由限制效应诱导的平坦环面相交产生的。 半经典磁电导的正负修正可以通过相干螺旋态之间的破坏性和建设性干涉交替出现。 桑德海默振荡的量子极限成为阿哈罗诺夫-玻姆通量量子化的另一种表现形式。 显示英文摘要

摘要： Decades ago, Sondheimer discovered that the electric conductivity of metallic crystals hosting ballistic electrons oscillates with magnetic field. These oscillations, periodic in magnetic field and the period proportional to the sample thickness, have been understood in a semi-classical framework. Here, we present a study of longitudinal and transverse conductivity in cadmium single crystals with thickness varying between 12.6 to 475 $\mu$m. When the magnetic field is sufficiently large or the sample sufficiently thick, the amplitude of oscillation falls off as $B^{-4}$ as previously reported. In contrast, the ten first oscillations follow a $B^{-2.5}e^{-B/B_0}$ field dependence and their amplitude is set by the quantum of conductance, the sample thickness, the magnetic length and the Fermi surface geometry. We demonstrate that they are beyond the semi-classical picture, as the exponential prefactor indicates quantum tunneling between distinct quantum states. We draw a picture of these quantum oscillations, in which the linear dispersion of the semi-Dirac band in the cadmium plays a crucial role. The oscillations arise by the intersection between the lowest Landau tube and flat toroids on the Fermi surface induced by confinement. Positive and negative corrections to semi-classical magneto-conductance can occur by alternation between destructive and constructive interference in phase-coherent helical states. The quantum limit of Sondheimer oscillations emerges as another manifestation of Aharanov-Bohm flux quantization.