Liu, Cheng-ChengZhou, Jin-JianYao, YuguiZhang, Fan2017-04-262017-04-262016-02-092016-02-090031-9007http://hdl.handle.net/10735.1/5378Includes supplementary material.While strong topological insulators (STIs) were experimentally realized soon after they were theoretically predicted, a weak topological insulator (WTI) has yet to be unambiguously confirmed. A major obstacle is the lack of distinct natural cleavage surfaces to test the surface selective hallmark of a WTI. With a new scheme, we discover that β-Bi₄Χ₄ (Χ = Br, I), dynamically stable or synthesized before, can be a prototype WTI with two natural cleavage surfaces, where two anisotropic Dirac cones stabilize and annihilate, respectively. We further find four surface-state Lifshitz transitions under charge doping and two bulk topological phase transitions under uniaxial strain. Near the WTI-STI transition, there emerges a novel Weyl semimetal phase, in which the Fermi arcs generically appear at both cleavage surfaces whereas the Fermi circle only appears at one selected surface.en©2016 American Physical Society. All rights reservedPhase transformations (Statistical physics)lWeak interactions (Nuclear physics)Strong interactions (Nuclear physicsBi4br4Liu, Cheng-Cheng, Jin-Jian Zhou, Yugui Yao, and Fan Zhang. 2016. "Weak Topological Insulators and Composite Weyl Semimetals: β-Bi₄Χ₄ (Χ = Br, I)" Physical Review Letters 116(6), doi:10.1103/PhysRevLett.116.0668011166