Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111 USA.
Phys Rev Lett. 2015 Aug 14;115(7):076601. doi: 10.1103/PhysRevLett.115.076601. Epub 2015 Aug 11.
We study the quantum phase diagram of a three dimensional noninteracting Dirac semimetal in the presence of either quenched axial or scalar potential disorder, by calculating the average and the typical density of states as well as the inverse participation ratio using numerically exact methods. We show that as a function of the disorder strength a half-filled (i.e., undoped) Dirac semimetal displays three distinct ground states, namely an incompressible semimetal, a compressible diffusive metal, and a localized Anderson insulator, in stark contrast to a conventional dirty metal that only supports the latter two phases. We establish the existence of two distinct quantum critical points, which respectively govern the semimetal-metal and the metal-insulator quantum phase transitions and also reveal their underlying multifractal nature. Away from half-filling the (doped) system behaves as a diffusive metal that can undergo Anderson localization only, which is shown by determining the mobility edge and the phase diagram in terms of energy and disorder.
我们通过数值精确方法计算平均态和典型态密度以及倒易参与比，研究了在存在淬火轴向或标量势无序的情况下，三维非相互作用狄拉克半金属的量子相图。我们表明，作为无序强度的函数，半满（即未掺杂）狄拉克半金属显示出三种不同的基态，即不可压缩的半金属、可压缩的扩散金属和局域安德森绝缘体，这与仅支持后两种相的常规脏金属形成鲜明对比。我们确定了两个不同的量子临界点的存在，它们分别控制着半金属-金属和金属-绝缘体的量子相变，并揭示了它们的多重分形性质。在远离半满的情况下（掺杂）系统表现为扩散金属，只能经历安德森局域化，这可以通过确定移动边缘和相图来证明，相图是关于能量和无序的。
