在可调蜂窝晶格中用费米气体产生、移动和合并狄拉克点
Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
摘要：
狄拉克点是凝聚态物理中许多迷人现象的核心，从石墨烯中的无质量电子到拓扑绝缘体中导电边缘态的出现[1，2]。在狄拉克点，两个能带线性相交，粒子表现为相对论狄拉克费米子。在固体中，材料的刚性结构决定了粒子的质量和速度，以及它们之间的相互作用。一种不同的高度灵活的方法是使用被困在干涉激光束的周期性势中的费米子原子来创建模型系统，这种方法迄今为止只被应用于探索简单的晶格结构[3，4]。在这里，我们报告的狄拉克点的创建与可调性能的可调蜂窝光晶格。利用动量分辨带间跃迁，我们观察到一个最小的带隙内的布里渊区的狄拉克点的位置。我们利用我们的晶格势的独特的可调谐性，调整的狄拉克费米子的有效质量，打破反转对称性。此外，改变晶格各向异性允许我们移动布里渊区内的狄拉克点的位置。当增加各向异性超过临界极限时，两个狄拉克点合并并相互湮灭-这种情况最近引起了相当大的理论兴趣[5-9]，但在固体中观察似乎极具挑战性[10]。我们映射出这种拓扑转变的晶格参数空间，并找到良好的协议与从头计算。我们的研究结果不仅为能带结构的拓扑结构起着关键作用的材料建模铺平了道路，而且还为探索复杂晶格几何结构与相互作用的相互作用所产生的多体相提供了途径[11，12]。
英文摘要：
Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators [1, 2]. At a Dirac point, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in the periodic potential of interfering laser beams, a method which so far has only been applied to explore simple lattice structures [3, 4]. Here we report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other - a situation which has recently attracted considerable theoretical interest [5-9], but seems extremely challenging to observe in solids [10]. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials where the topology of the band structure plays a crucial role, but also provide an avenue to explore many-body phases resulting from the interplay of complex lattice geometries with interactions [11, 12].
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