Relativistic k.p Hamiltonians for centrosymmetric topological insulators from ab initio wave functions

Abstract

We present a method to microscopically derive a small-size k$\cdot$p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true ${\mathbb{Z}}_2$ topological invariant. We consider bulk crystals and thin films of Bi${}_2$Se${}_3$, Bi${}_2$Te${}_3$, and Sb${}_2$Te${}_3$. It turns out that the effective continuous k$\cdot$p models with open boundary conditions often incorrectly predict the topological character of thin films.

6 pages, 4 figures, 1 table

References in corpus (4)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Magneto-optics of massive Dirac fermions in bulk Bi2Se3

Cited by in corpus (4)

• Quantum Transport in Topological Semimetals under Magnetic Fields
• Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers
• 2D and 3D topological phases in BiTe$X$ compounds
• Ultrahigh magnetic field spectroscopy reveals the band structure of the 3D topological insulator Bi${}_2$Se${}_3$