Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator

In the paper

“while the band continua in the composition range of δ = 0 . 0 to δ = 0 . 4 are degenerate, the Dirac-like bands at δ = 0 . 6 and beyond are spin polarized (see Figs. 2, 3, and 4).”

In the paper

“we report the observation of a topological phase transition in a tunable spin-orbit system BiTl(S 1 -δ Se δ ) 2”

• Also stated in: § Abstract · p. 3 · boosted

  “We demonstrate the existence of a topological phase transition in TlBi(S 1 -δ Se δ ) 2”

In the paper

“Both bands demarcating the gap show three dimensional dispersion where binding energies vary with momentum perpendicular to the surface, k z , [as probed via varying incident photon energy ( 25 )] and roughly correspond to the expected position for the valence and conduction bands.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [25] 25. Materials and methods are available as supporting material on Science Online.

In the paper

“the δ = 0 . 0 compound features a direct band gap in its bulk, whereas the δ = 1 . 0 indicates a slightly indirect gap.”

In the paper

“As the selenium concentration is increased, the low-lying bands separated by a gap of energy 0.15eV at δ = 0 . 0 are observed to approach each other and the gap decreases to less than 0.05eV at δ = 0 . 4.”

In the paper

“Above the Dirac node, a quasi-particle moving in + k (+ˆ x ) direction is locked with +ˆ y spin-polarization state, whereas below the node, the + k moving quasi-particle state is locked with -ˆ y spin.”

In the paper

“Interestingly, for the hexagonal case, a six-fold symmetric quasi-particle scattering profile is seen, indicating the possibility for a fluctuating spin-density-wave type magnetic instability which connects the parallel pieces of the observed spin-polarized FS (Fig. 3, C and D).”

In the paper

“In particular, a ν 0 = 1 = θ/π topology requires the terminated surface to have a Fermi surface (FS) that supports a nonzero Berry's phase (an odd as opposed to an even multiple of π = θ =axion angle), which is not realizable in an ordinary spin-orbit or trivial ( ν 0 = 0 = θ ) insulator.”

In the paper

“It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice via odd number of band inversions, driving the system through a topological quantum phase transition.”

• Also stated in: § Abstract · p. 3 · hedged

  “It is believed that a trivial insulator can be twisted into a ν 0 = 1 = θ/π topological state by signaling the appearance of unusual spin vortex-like [or Skyrmionlike ( 1 )] arrangements via increasing spin-orbit interaction or by modulating the lattice parameters, thereby driving the system through a topological quantum phase transition ( 1, 2 ).”

What the sources say

• Not checked yetcites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source
• Not checked yetcites [2] 2. L. Fu, C. L. Kane, E. J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98 , 106803 (2007). source

In the paper

“Topological insulators (TIs) in three dimensions are nonmagnetic insulators with novel surface states (SSs) that are a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the materials ( 1-5 ).”

What the sources say

• Not checked yetcites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source
• Not checked yetcites [2] 2. L. Fu, C. L. Kane, E. J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98 , 106803 (2007). source
• Not checked yetcites [3] 3. J. E. Moore, Topological insulators: the next generation. Nature Physics 5 , 378 (2009).http://www.nature.com/nphys/journal/v5/n6/full/nphys1294.html source
• Not checked yetcites [4] 4. X.-L. Qi, T. L. Hughes, S.-C. Zhang, Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78 , 195424 (2008). source
• Not checked yetcites [5] 5. M. Z. Hasan, H. Lin, A. Bansil, Warping the cone on a topological insulator. Physics 2 , 108 (2009) and http://www.nature.com/nphys/journal/v5/n6/full/nphys1294.html source

In the paper

“Strong TIs are distinguished from ordinary insulators by a finite topological quantum number or an invariant ( ν 0 ) or equivalently an axion angle parameter ( θ ).”

In the paper

“Spins tangentially arranged on such a circular FS lead to a Berry's phase of π , which is also a measure of the topological invariant and the axion angle ( ν 0 = 1 = θ/π ) of the system ( 1, 4, 6 ).”

What the sources say

• Not checked yetcites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source
• Not checked yetcites [4] 4. X.-L. Qi, T. L. Hughes, S.-C. Zhang, Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78 , 195424 (2008). source
• Not checked yetcites [6] 6. D. Hsieh et al ., A tunable topological insulator in the spin helical Dirac transport regime. Nature 460 , 1101 (2009); and D. Hsieh et al ., A topological Dirac insulator in a quantum spin Hall phase. Nature 452 , 970 (2008). Work completed and submitted in 2007, also see, http://online.itp.ucsb.edu/online/motterials07/hasan/ (2007) source

In the paper

“The value of ν 0 or θ depends on the parity eigenvalues of the wavefunctions in time reversal symmetric materials ( 1, 2 )”

What the sources say

• Not checked yetcites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source
• Not checked yetcites [2] 2. L. Fu, C. L. Kane, E. J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98 , 106803 (2007). source

In the paper

“this could also be a consequence of an intrinsically broader topological transition.”

In the paper

“however, that the surface remains gapped at δ = 0 . 4 suggests that the material is still on the trivial side.”

In the paper

“Such terms correspond to analogs of cubic and higher order Dresselhaus effects arising from the symmetry of the crystal potential.”

In the paper

“can be determined from spin texture details of the spin-orbit surface states that form when the bulk is terminated as demonstrated by Hsieh et al . ( 6, 7 ).”

What the sources say

• Not checked yetcites [6] 6. D. Hsieh et al ., A tunable topological insulator in the spin helical Dirac transport regime. Nature 460 , 1101 (2009); and D. Hsieh et al ., A topological Dirac insulator in a quantum spin Hall phase. Nature 452 , 970 (2008). Work completed and submitted in 2007, also see, http://online.itp.ucsb.edu/online/motterials07/hasan/ (2007) source
• Not checked yetcites [7] 7. D. Hsieh et al ., Observation of unconventional quantum spin textures in topological insulators. Science 323 , 919 (2009). source

In the paper

“Based on a mean field Zener theory, it has recently been shown that a helical magnetic order (HMO) is expected if the surface state topology is in the 3D vectorial spin texture (Fig. 4D) regime, the system can then achieve unusually high critical temperature, even up to T HMO ∼ 100 K ( 30 ).”

What the sources say

• Not checked yetcites [30] 30. J. H. Jiang, S. Wu, Spin susceptibility and helical magnetic order at the edge of topological insulators due to Fermi surface nesting. http://arxiv.org/abs/1012.1299v2 (2010).

In the paper

“A more extreme example is the TI, ntype bulk doped Bi 2 Te 3 , which features a highly warped concave-in snowflake-shaped FS because of its large k F and a small band gap ( 25 ).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [25] 25. Materials and methods are available as supporting material on Science Online.