Reconstruction of Bloch wavefunctions of holes in a semiconductor

A central goal of condensed-matter physics is to understand how the diverse electronic and optical properties of crystalline materials emerge from the wavelike motion of electrons through periodically arranged atoms. However, more than 90 years after Bloch derived the functional forms of electronic waves in crystals(1) (now known as Bloch wavefunctions), rapid scattering processes have so far prevented their direct experimental reconstruction. In high-order sideband generation(2-9), electrons and holes generated in semiconductors by a near-infrared laser are accelerated to a high kinetic energy by a strong terahertz field, and recollide to emit near-infrared sidebands before they are scattered. Here we reconstruct the Bloch wavefunctions of two types of hole in gallium arsenide at wavelengths much longer than the spacing between atoms by experimentally measuring sideband polarizations and introducing an elegant theory that ties those polarizations to quantum interference between different recollision pathways. These Bloch wavefunctions are compactly visualized on the surface of a sphere. High-order sideband generation can, in principle, be observed from any direct-gap semiconductor or insulator. We thus expect that the method introduced here can be used to reconstruct low-energy Bloch wavefunctions in many of these materials, enabling important insights into the origin and engineering of the electronic and optical properties of condensed matter.Bloch wavefunctions of two types of hole in gallium arsenide are reconstructed by measuring the polarization of light emitted by collisions of electrons and holes accelerated by a terahertz laser.

凝聚态物理学的一个核心目标是理解晶体材料多样的电学和光学性质是如何从电子在周期性排列的原子中所做的波状运动中产生的。然而，在布洛赫推导出晶体中电子波的函数形式（现在被称为布洛赫波函数）90多年后，快速散射过程迄今为止一直阻碍着对它们进行直接的实验重构。在高次边带产生过程中，近红外激光在半导体中产生的电子和空穴被强太赫兹场加速到高动能，并在散射之前重新碰撞发射近红外边带。在此，我们通过实验测量边带偏振，并引入一种精妙的理论将这些偏振与不同的重新碰撞路径之间的量子干涉联系起来，从而重构了砷化镓中两种空穴在比原子间距长得多的波长下的布洛赫波函数。这些布洛赫波函数在一个球面上被简洁地可视化呈现。原则上，从任何直接带隙半导体或绝缘体中都可以观察到高次边带产生。因此我们期望这里介绍的方法能够用于重构许多这类材料中的低能布洛赫波函数，从而对凝聚态物质的电学和光学性质的起源及调控提供重要的见解。通过测量由太赫兹激光加速的电子和空穴碰撞所发射的光的偏振，重构了砷化镓中两种空穴的布洛赫波函数。