Session X35: Topological Insulators: Theory III

Search for New Topological Insulators

Topological insulators (TIs) host a novel quantum phase of electrons which is characterized by topologically protected surface states originating from the effects of spin-orbit and time-reversal symmetries. While several families of TIs have already been found, the intense world-wide search for new classes of TIs continues unabated. This interest is driven by the need for materials with greater structural flexibility and tunability to enable viable applications in spintronics and quantum computing. We have used first-principles band theory computations in combination with angle-resolved photoemission experiments to successfully predict many new classes of topologically interesting materials, including Bi2Se3 series, the ternary half-Heusler compounds, thallium-based chalcogenides, and the Li2AgSb and Ge$_n$Bi$_{2m}$Te$_{3m+n}$ families. [1-5] Work supported by the Office of Basic Energy Sciences, US DOE.\\[4pt] [1] H. Lin, R. S. Markiewicz, L. A. Wray, L. Fu, M. Z. Hasan, and A. Bansil, Physical Review Letters \textbf{105}, 036404 (2010). \\[0pt] [2] H. Lin, L. A. Wray, Y. Xia. S. Y. Xu, S. Jia, R. J. Cava, A. Bansil, and M. Z. Hasan, Nature Materials \textbf{9}, 546 (2010). \\[0pt] [3] W. Al-Sawai {\it et al.}, Physical Review B \textbf{82}, 125208 (2010). \\[0pt] [4] L. A. Wray {\it et al.}, Nature Physics (2010, in press).\\[0pt] [5] S.-Y. Xu {\it et al.}, arXiv:1007.5111 (2010).   

Spin-texture of three-dimensional topological insulators: Bi$_2$Te$_3$, Bi$_2$Se$_3$ and Sb$_2$Te$_3$

We have investigated the nature of surface states in the Bi$_2$Te$_3$, Bi$_2$Se$_3$ and Sb$_2$Te$_3$ family of 3D topological insulators using first-principles calculation as well as $k\cdot p$ scheme [1]. Recent spin-resolved photoemission experiments suggest that electrons on the surface of a topological insulator behave as massless relativistic particles with an intrinsic angular momentum (spin) which is locked to their translational momentum [2,3]. We have computed the in-plane spin-textures of all three aforementioned compounds to demonstrate the `spin-helical' nature of the 2D fermions. In addition, the spin must acquire a finite out-of-the-plane component to preserve the bulk topological invariant [1]. We study this quantity in particular since there are possibilities of observing new quantum effects. Work supported by the US DOE.\\[4pt] [1] L. Fu, Phys. Rev. Lett. {\bf 103}, 266801, (2009). \\[0pt] [2] D. Hsieh {\it et al.}, Science {\bf 323}, 919 (2009). \\[0pt] [3] D. Hsieh {\it et al.}, Nature {\bf 460}, 1101 (2009).   

First principles analysis of quantum transport in Bi2Se3 3D topological insulators

By carrying out density functional theory (DFT) within the Keldysh nonequilibrium Green's function formalism (NEGF), we have investigated quantum transport properties of the Bi2Se3 topological insulator from atomistic first principles without any phenomenological parameters. Using the scattering states, our results vividly reveal the surface Dirac fermions and helical edge spin states in the momentum space. We have also determined the real-space distribution of the helical edge spin states which provide the penetration depth of the surface topological conducting channels into the bulk Bi2Se3 crystal. Our first principles calculations take into account the full non-collinear spin structure and spin-orbit interaction, the details of these technical advances within the NEGF-DFT quantum transport formalism will also be briefly discussed.   

Electrically controllable surface magnetism on the surface of topological insulator

We study theoretically the RKKY interaction between magnetic impurities on the surface of a three dimensional topological insulator, mediated by the massless and massive helical Dirac electrons. Exact analytical expression of RKKY interaction shows that the spin- spin interaction consists of the Heisenberg-like, Ising-like and Dzyaloshinskii-Moriya (DM)-like terms caused by the helicity of the topological surface states. It provides us a new way to realize various spin models, e.g., DM model, XXZ model and XZ model, and control surface magnetism by tuning the Fermi energy, and/or the distance between the two local spins. The gap opened by doped magnetic ions can lead to a short-range Bloembergen- Rowland interaction via the virtual interband interaction when the Fermi energy is located in the gap. The competition among the Heisenberg, Ising and DM terms leads to rich spin configurations and anomalous Hall effect on different lattices.   

Ordering of magnetic impurities and tunable electronic properties of topological insulators

We study collective behavior of magnetic adatoms randomly distributed on the surface of a topological insulator. As a consequence of the spin-momentum locking on the surface, the RKKY- type interactions of two adatom spins depend on the direction of the vector connecting them, thus interactions of an ensemble of adatoms are frustrated. We show that at low temperatures the frustrated RKKY interactions give rise to two phases: an ordered ferromagnetic phase with spins pointing perpendicular to the surface, and a disordered spin-glass-like phase. The two phases are separated by a quantum phase transition driven by the magnetic exchange anisotropy. Ferromagnetic ordering occurs via a finite-temperature phase transition. The ordered phase breaks time-reversal symmetry spontaneously, driving the surface states into a gapped state, which exhibits an anomalous quantum Hall effect and provides a realization of the parity anomaly. We find that the magnetic ordering is suppressed by potential scattering. Our work indicates that controlled deposition of magnetic impurities provides a way to modify the electronic properties of topological insulators.   

Possible Strong Topological Insulator Phase in Li$_{2}$IrO$_{3}$

Recently Na$_{2}$IrO$_{3}$, a layered 5$d$ transition metal oxide compound, was suggested to be a possible topological insulator (TI) based on the $j_{eff}=1/2$ states induced by the strong spin-orbit coupling of Ir 5$d$ states, but its realization has not been clarified yet. In search of the TI phase in transition metal oxides, we propose Li$_{2}$IrO$_{3}$ to be a candidate for the three-dimensional strong TI. By carrying out Wannier function analysis based on first-principles calculations, we constructed a low energy effective Hamiltonian, which leads to a three-dimensional extension of the Kane-Mele model with third-nearest-neighbor hopping within the Ir honeycomb layer and a significant inter-layer coupling. The nature of spin-orbit coupled states near the Fermi level depends on the change of the trigonal crystal field driven by the lattice deformations. A competition between the third next-nearest-neighbor hopping parameter and the trigonal crystal field is found to play a key role in determining the topological character of Li$_{2}$IrO$_{3}$.   

Half-Heusler Topological Insulators: A First-Principle Study with the Tran-Blaha Modified Becke-Johnson Density Functional

We systematically investigate the topological band structures of half-Heusler compounds using first-principles calculations. The modified Becke-Johnson exchange potential together with local density approximation for the correlation potential (MBJLDA) has been used here to obtain accurate band inversion strength and band order. Our results show that a large number of half-Heusler compounds are candidates for three-dimensional topological insulators. The difference between band structures obtained using the local density approximation (LDA) and MBJLDA potential is also discussed.   

Toplogical electronic structure in half-Heusler topological insulators

We investigate the details of electronic band structure of a series of 28 ternary half-Heusler compounds MM$^\prime$X of MgAgAs-type where M = (Lu, La, Sc, Y) and M$^{\prime}$X=(PtBi, AuPb, PdBi, PtSb, AuSn, NiBi, PdSb). Our results show that the $Z_2$ topological order is due to a single band inversion at the $\Gamma$-point. Half-Heusler compounds can be either topologically nontrivial semimetals, nontrivial metals, or trivial insulators. Our analysis reveals a straightforward relationship between the band inversion strength (extent of deviation from the critical point), the atomic charge of constituents, and the lattice parameter. Our findings suggest a general method for identifying $Z_2$ topological insulators in nonmagnetic ternary compounds.   

Topological insulating behavior in conducting property of crystalline Ge-Sb-Te

Phase-change random access memory (PRAM) is one of the most promising materials for data storage application. Especially, Ge-Sb-Te$_{ }$(GST) is considered as the best candidates for next generation nonvolatile memories because of the rapid and reversible cycles between the crystalline and amorphous structures. GeTe and Sb$_{2}$Te$_{3 }$are the main components of GSTs, and have finite band gaps in the bulk phase. Sb$_{2}$Te$_{3}$ is topological insulator that has gapless edge states while maintaining bulk energy gap. These surface states are robust to external perturbations because they are protected by time-reversal symmetry. We report a discovery, through first-principles calculations, that crystalline GST phase-change materials exhibit the topological insulating property. Our calculations show that the materials become topological insulator or develop conducting surface-like interface states depending on the layer stacking sequence. It is shown that the conducting interface states originate from topological insulating Sb$_{2}$Te$_{3}$ layers in GSTs and can be crucial to the electronic property of the compounds. These interface states are found to be quite resilient to atomic disorders but sensitive to the uniaxial strains. We presented the mechanisms that destroy the topological insulating order in GSTs and investigated the role of Ge migration that is believed to be responsible for the amorphorization of GSTs.   

Ab initio study of topological order induced by symmetry breaking in PbTe

Topological insulator (TI) is a new class of materials that have an energy gap in bulk phase but contain linear and chiral band dispersions on their surface. The topological insulating order can be initiated by parity inversion in time-reversal symmetric momenta. We studied the topological insulating properties of PbTe under uniaxial strain using first-principles methods. PbTe is a narrow-gap semiconductor with trivial topological insulating order. While it is known to have band inversion under pressure at a time-reversal symmetric k-point, the degeneracy at the k-point prevents the overall parity inversion which is needed to induce the TI order. In this presentation, we show that uniaxial strain can break the symmetry and thus induce topologically nontrivial order in PbTe.   

Electronic structure of the side surface of Bi$_{2}$Se$_{3}$

We investigate the electronic band structure of a side surface geometry, other than the conventional [111] surface, of the topological insulator Bi$_{2}$Se$_{3}$ using the first-principles pseudopotential calculations. As Bi$_{2}$Se$_{3}$ is known to be a strong topological insulator, it is expected that an arbitrary surface would have the topological surface state characterized by Dirac-cone-like band dispersion and spin-momentum coupling. Here we indeed obtain surface states with linear band dispersion around the Gamma point, but with a strong anisotropy with different group velocities along different k-directions. Low energy effective hamiltonian is proposed, and physical implications of the anisotropic Dirac fermions are also discussed.   

Spatial characters of metallic surface states of topological insulators

We study the electronic structure of metallic surface states in Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$, and Sb$_{2}$Te$_{3}$ using an ab-initio pseudopotential density-functional method. We implemented the spin-orbit interaction into the SIESTA in a form of additional fully non-local projectors. For surface states on (001) surface, we used a supercell containing 10 quintuple layers. We obtained bulk and surface electronic structures of topological insulators Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$, and Sb$_{2}$Te$_{3}$, which are close to previous theoretical results and consistent with Dirac-cone band dispersions measured by angle-resolved photoemission spectroscopy. Then, we analyzed the wavefunctions of the metallic surface states near the Fermi level to find out spatial distributions of the surface-state wavefunctions, which turn out to be localized in the surface region with a typical spread of about 2 quintuple layers, and the shapes of the wavefunctions around Bi (or Sb) atoms close to the surface. This work was supported by the NRF of Korea (Grant No. 2009-0081204) and KISTI Supercomputing Center (Project No. KSC-2008-S02-0004).   

Chern-Simons orbital magnetoelectric coupling in generic insulators

The isotropic Chern-Simons coupling $\theta$ is a component of the orbital contribution to the magnetoelectric coupling.\footnote{A. Malashevich {\it et al.}, New J. Phys. {\bf 12}, 053032 (2010); A.~M. Essin {\it et al.}, Phys. Rev. B {\bf 81}, 205104 (2010). } In a generic insulator it can have any value, while it must be exactly $\pi$ in a strong Z$_2$ topological insulator. The results of our first-principles density-functional calculations for the ordinary magnetoelectrics Cr$_2$O$_3$, BiFeO$_3$ and GdAlO$_3$ confirm that the Chern-Simons contribution is quite small in these materials.\footnote{S. Coh {\it et al.}, arXiv:1010.6071.} We discuss various strategies for finding insulators for which $\theta$ is large but not equal to $\pi$. For example, we show that if the spatial inversion and time-reversal symmetries of the Z$_2$ topological insulator Bi$_2$Se$_3$ are broken by hand, large induced changes appear in the Chern-Simons magnetoelectric coupling. We also perform an analysis based on space-group representation theory to determine the simplest possible magnetic structures which allow for a non-zero and possibly large value of $\theta$.   

Theoretical prediction of new topological insulators in filled skutterudites

We have reported a unique class of topological insulators, filled skutterudite (FS) compounds, using ab initio calculations. We find that several FSs are not only two-dimensional topological insulators as quantum wells like HgTe, but also three-dimensional topological Kondo insulators. Different from previously reported topological insulators, they have unique band inversion feature in band structures. Their advantages are discussed to realize superconductivity proximity and other topological phenomena.   

Three-Dimensional Topological Insulators in I-III-VI$_2$ and II-IV-V$_2$ Chalcopyrite Semiconductors

Using first-principles calculations, we investigate the band topology of the ternary chalcopyrite family. Our method is based on the adiabatic continuity of the Hamiltonian combined with direct calculation of the Z2 topological invariants in inversion-symmetry breaking systems. We show that a large number of these compounds are candidates for three-dimensional topological insulators. Moreover, The topological order can be tuned and controlled by lattice strain. The excellent physical properties of these compounds make them an appealing platform for novel quantum phenomena.   

Edge states and the bulk-boundary correspondence in Dirac Hamiltonians

We present an analytic prescription for computing the edge dispersion $E(k)$ of a tight-binding Dirac Hamiltonian terminated at an abrupt crystalline edge. Specifically, we consider translationally invariant Dirac Hamiltonians with nearest-layer interaction. The result is a geometric formula that relates the existence of surface states as well as their energy dispersion to properties of the bulk Hamiltonian. We give examples of how the formula can be used to find the edge state dispersion in various topologically ordered systems. We further prove the bulk-boundary correspondence between the Chern number and the chiral edge modes for quantum Hall systems within the class of Hamiltonians studied here. Our results can be extended to the case of continuum theories which are quadratic in momentum, as well as other symmetry classes.