Layered Topological Crystalline Insulators

Abstract

Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a threedimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the inter-layer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) (µ1, µ2) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) Mirror-symmetric TCIs are mathematically characterized by mirror Chern numbers (MCNs). The MCN is a topological invariant defined by µ 1 ≡ (µ + − µ − )/2 where µ + and µ − are Chern numbers of Bloch states with the opposite eigenvalues of a mirror operator (M z ) calculated on the mirror-invariant plane at k z = 0 in the Brillouin zone (BZ). In a three-dimensional (3D) crystal, there is a second MCN (µ 2 ) defined on the mirror-invariant plane at the boundary of the BZ k z = π (in units of 1/a, where a is the length of the primitive lattice vector along the z-axis) [26]. Moreover, considering different mirror symmetries, multiple pairs of MCNs (µ 1 , µ 2 ) can be simultaneously present in three dimensions. A complete characterization of 3D TCIs requires consideration of all the MCNs, which may allow for the possibility of new states of matter, where MCNs are locked together or undergo separate transitions. Nonetheless, previous study based only on µ 1 has not explored this situation.In this paper, by considering MCNs on all inequivalent mirror-symmetric planes in reciprocal space, we study new topological states of matter realized in a 3D layered crystal generated by stacking 2D TCI layers. We show that the layered system realizes a new class of 3D TCIs when inter-layer interaction is weak, which we will refer to as a layered TCI. The layered TCI is characterized by equal and nonzero first and second MCNs µ 1 = µ 2 = 0 with a number of metallic surface states eqaul to |µ 1 | + |µ 2 |. Increasing the inter-layer interaction, we then show that the layered TCI undergoes topological phase transitions that change the MCNs (µ 1 , µ 2 ). Based on first-principles calculations, we predict that a heterostructure consisting of alternating layers of PbSe monolayer and hexagonal BN (h-BN) sheet realizes the layered TCI indexed by (2,2), and that it undergoes distinct topological phase transitions in the sequence (µ 1 , µ 2 ): (2, 2) → (0, 2) → (0, 0) under external uniaxial tensile strain. Our findings shed light on new states of matter allowed by the presence of multiple MCNs in a 3D crystal. They may also help guide the discovery of more topological materials. Before presenting the results, we first briefly explain arXiv:1503.05966v1 [cond-mat.mtrl-sci]

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Topological, Valleytronic, and Optical Properties of Monolayer PbS

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