First-principles and model calculations show that the Dirac surface state of the topological insulator Bi 2 Te 3 survives upon moderate Mn doping of the surface layers but can lose its topological character as a function of magnetization direction. The dispersion depends considerably on the direction of the Mn magnetization: for perpendicular magnetization, a gap of 16 meV opens up at the Dirac point; for in-plane magnetization, a tiny gap can be opened or closed in dependence on the magnetization azimuth. The ground state is ferromagnetic, with a critical temperature of 12 K. The results provide a path towards a magnetic control of the topological character of the Dirac surface state and its consequences to spindependent transport properties.

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A topological insulator is realized via band inversions driven by the spin-orbit interaction. In the case of Z2 topological phases, the number of band inversions is odd and time-reversal invariance is a further unalterable ingredient. For topological crystalline insulators, the number of band inversions may be even but mirror symmetry is required. Here, we prove that the chalcogenide Bi2Te3 is a dual topological insulator: it is simultaneously in a Z2 topological phase with Z2 invariants (ν0;ν1ν2ν3) = (1;0 0 0) and in a topological crystalline phase with mirror Chern number -1. In our theoretical investigation we show in addition that the Z2 phase can be broken by magnetism while keeping the topological crystalline phase. As a consequence, the Dirac state at the (111) surface is shifted off the time-reversal invariant momentum Γ; being protected by mirror symmetry, there is no band gap opening. Our observations provide theoretical groundwork for opening the research on magnetic control of topological phases in quantum devices.

We report on a theoretical study of a d z 2 surface state at the tungsten (110) surface, addressing in detail the spin-resolved electronic structure as well as photoemission spectroscopy. In agreement with recent experiments, this surface state shows a strongly anisotropic dispersion: in the H--H direction of the surface Brillouin zone, it disperses linearly but becomes flattened along the N--N direction. The ab initio calculated spin texture agrees with the one derived from a model Hamiltonian; due to twofold surface symmetry and time-reversal symmetry, the out-of-plane spin polarization vanishes. The photoemission intensities depend sensitively on the polarization of the incident light, because of the orbital composition of the surface state. The photoelectrons become spin-polarized out-of-plane, which is attributed to breaking the timereversal symmetry by the excitation process.

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