Colliding quasiparticles to reconstruct their effective Hamiltonians

非技术摘要：我们的国家竞争力依赖于我们使信息技术更快、更节能、更紧凑、更实惠的能力。这种创新需要发现和实施新的方法来表征并优化材料对电和光的响应。为了充分理解电荷是如何在现代电子学和光学中普遍存在的极其强大和快速变化的电场中运动的，人们需要知道被称为布洛赫波函数的量，它在90多年前被数学推导出来，但一直没有得到实验证实。PI和他的团队最近开发了一种强大的方法，可以从结晶固体上的实验数据重建布洛赫波函数。该项目支持在几种具有当前科学和技术重要性的半导体中重建布洛赫波函数。该项目支持的研究生研究人员在实验凝聚态物理方面接受广泛而深入的训练，并反过来指导本科生研究人员，通过给他们简单电路的实践经验来激励K-12学生，并在毕业后定位为对国家竞争力至关重要的技术领域的领导者。技术文摘：对于现代凝聚态物理中的许多问题，既要知道准粒子有效哈密顿量的能量特征值，又要知道它的布洛赫波函数，由此可以计算出贝瑞曲率。通过对布里渊区的Berry曲率积分，可以对材料进行拓扑分类。角分辨光谱学使人们能够测量许多材料的能带结构。然而，在准动量空间的每个点上定义的布洛赫波函数和贝里曲率是极难测量的。这个项目利用了一个独特的机会来重建半导体中准粒子的有效哈密顿量，这是由高阶边带生成（HSG）现象实现的。HSG可以被认为是一个三步的过程，其中(1)弱探测激光产生电子-空穴对，(2)强太赫兹频率激光绝热加速电子和空穴，先远离，然后彼此靠近，(3)电子和空穴碰撞并重新组合，发射带走与碰撞相关动能的边带。电子和空穴被加速时所经过的带的贝里曲率就印在它的极化上。在这个项目中，控制GaAs（包括应变的影响）、GeS（层状半导体）和其他半导体中准粒子动力学的有效哈密顿量的参数将通过比较计算和测量的矩阵来重建，这些矩阵将边带的极化与激发它们的探测激光的极化联系起来。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical abstract: Our national competitiveness relies on our ability to make information technology faster, more energy efficient, more compact, and more affordable. Such innovation requires the discovery and implementation of new methods to characterize and then optimize the responses of materials to electricity and light. To fully understand how electrical charges move in the extremely strong and rapidly-varying electric fields that pervade modern electronics and optics, one needs to know quantities called Bloch wavefunctions, which were derived mathematically more than 90 years ago but have resisted experimental determination. The PI and his team have recently developed a robust method to reconstruct Bloch wavefunctions from experimental data which was demonstrated on a crystalline solid. The project supports reconstruction of Bloch wavefunctions in a several semiconductors that are of current scientific and technological importance. The graduate student researchers supported by this project receive broad and deep training in experimental condensed matter physics, and in turn mentor undergraduate researchers, inspire K-12 students by giving them hands-on experience with simple electrical circuits and, upon graduation are positioned for leadership in technical fields crucial to national competitiveness. Technical abstract: For many problems in modern condensed matter physics, it is important to know both the energy eigenvalues of a quasiparticle effective Hamiltonian, as well as its Bloch wavefunctions, from which the Berry curvature can be calculated. By integrating the Berry curvature over the Brillouin zone, materials can be classified topologically. Angle-Resolved Photoemission Spectroscopy enables one to measure the band structure of many materials. However, the Bloch wavefunctions and Berry curvature, which are defined at each point in quasi-momentum space, are extremely difficult to measure. This project exploits a unique opportunity to reconstruct the effective Hamiltonian of quasiparticles in semiconductors that is enabled by the phenomenon of high-order sideband generation (HSG). HSG can be thought of as a three-step process in which (1) a weak probe laser creates electron-hole pairs, (2) a strong terahertz-frequency laser adiabatically accelerates the electrons and holes first away from and then back towards each other, and (3) the electrons and holes collide and recombine, emitting sidebands that carry off the kinetic energy associated with the collision, and on whose polarization is imprinted the Berry curvature of the bands through which the electrons and holes have been accelerated. In this project, the parameters of the effective Hamiltonian that governs quasiparticle dynamics in GaAs (including the effects of strain), GeS (a layered semiconductor), and other semiconductors will be reconstructed by comparing the calculated and measured matrices that relate the polarization of sidebands to the polarization of the probe laser that excited them.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.