Session L28: Topological Crystalline Insulators

Searching for ideal topological crystalline insulators and topological superconductors in the Pb-Sn-In-Te system

\newline The discovery of 3D topological insulator materials and topological superconductor open up a new research field in the condensed matter physics. In order to search for the ideal topological insulator, topological crystalline insulator and topological superconductor, we have grown a large number of the single crystals of Pb-system ( Pb-Sn-In-Te) topological crystalline insulator and their topological superconductor . We have measured the physical properties on these single crystals by various techniques. We have studied the effect of crystal growth condition, impurity and composition on the bulk electrical conductivity of these single crystals. We try to find out which composition and crystal growth condition is the best for the ideal topological insulator, topological crystalline insulator and topological superconductor. We have got the bulk topological superconductor with T$_{\mathrm{c}}=$5K.   

Interplay of Dirac Fermions and Structural Deformations in Topological Crystalline Insulators

Topological crystalline insulators (TCIs) are a new class of topological materials which harbor massless Dirac surface states (SS). Theory postulates that these SS are protected by crystalline symmetries, and that SS electrons can acquire a mass if these symmetries are broken. Moreover, this unique crystalline protection has led to a series of intriguing predictions of strain-generated phenomena, such as the appearance of pseudo-magnetic fields and topological phase transitions. In this talk, I will present our scanning tunneling microscopy (STM) investigations of two TCI systems: single crystals of Pb$_{\mathrm{1-x}}$Sn$_{\mathrm{x}}$Se and strained thin films of SnTe. Simultaneous imaging of the atomic and electronic structures in TCI single crystals reveals that a fraction of the Dirac electrons acquire mass due to a surface distortion that breaks a crystalline mirror symmetry. Furthermore, we discover that even in the absence of any symmetry breaking, local strain in TCI heteroepitaxial thin films can induce spatially dependent changes in the SS dispersion associated with the momentum-space shift of the Dirac nodes. Our experiments provide the first direct visualization of the effects of strain on the SS band structure in topological materials and suggest a novel pathway for manipulation of Dirac electrons via structural deformations.   

Modulation of the surface states of SnTe films by doping impurities

Electronic structures of SnTe films doped by impurities are investigated using density functional calculations. There are surface states crossing the Fermi level in bulk SnTe, which is a topological crystalline insulator. For thin SnTe films, however, an energy gap is opened due to quantum tunneling. The gap can be reduced and even eliminated by doping impurities at the surfaces of the films, all the while keeping the mirror symmetry associated with bulk SnTe intact. Impurities with magnetic moments, on the other hand, can destroy the mirror symmetry.   

Nanomaterials of the topological crystalline insulators, Pb$_{1-x}$Sn$_x$Te and Pb$_{1-x}$Sn$_x$Se.

The study of topological insulators and their derivatives, in both 1D and 2D forms, has been the subject of great interest which has grown vastly in recent years. Topological insulators (TIs) and Topological Crystalline insulators (TCIs) exhibit exotic surface properties which are thought to be difficult to detect due to the surface signal being overwhelmed by that arising from the bulk of the material. As a result, by increasing the surface area to volume ratio, the signal from the surface states could be easier to investigate. We present results of the growth and characterisation of nanomaterials for the TCIs, Pb$_{1-x}$Sn$_x$Te and Pb$_{1-x}$Sn$_x$Se. Bulk crystals were used as starting materials for the growth, from which various morphologies of these TCIs were obtained. Nanowires of Pb$_{1-x}$Sn$_x$Te have been produced with a Sn composition of $\sim$ $x = 0.25$, at which a transition from trivial to non-trivial insulator has been reported for bulk materials. The results obtained on the growth of nanomaterials of Pb$_{1-x}$Sn$_x$Se are also described, all of which were characterised using various x-ray diffraction and electron microscopy techniques.   

Anomalous electronic states in Pb$_{1-x}$Sn$_x$Te induced by hydrostatic pressure

Dirac/Weyl semimetals have attracted strong interest. In Dirac semimetals Cd$_3$As$_2$, Na$_3$Bi, the Dirac nodes split into Weyl states in a magnetic field, which leads to novel phenomena, such as ultrahigh mobility (10$^7$ cm$^2$ V$^{-1}$ s$^{-1}$) in Cd$_3$As$_2$ [1], and the chiral anomaly in Na$_3$Bi [2]. The chiral anomaly appears as a negative longitudinal magnetoresistance. A new path to realize Weyl states is via the closing of the bulk gap in a system with broken inversion symmetry. As the gap is tuned, a Weyl semimetalic state is predicted to appear between two insulating phases [3]. We performed the hydrostatic pressure measurement for Pb$_{1-x}$Sn$_x$Te and observed that the gap of the system closes under pressure and the system shows insulator to metal phase transition. Interestingly, in the metalic phase, we observed giant negative magnetoresistance as well as anomalous hall effect which onsets only in the quantum limit. We discuss the implication of these phenomena and their relation with the Berry curvature. [1] Liang, T. et al., Nature Materials, $\mathbf{14}$, 280 (2015). [2] Xiong, J. et al., Science, $\mathbf{350}$, 413 (2015). [3] Murakami, S et al., Phys. Rev. B $\mathbf{78}$, 165313 (2008); New J. Phys. $\mathbf{9}$, 356 (2007).   

Topological crystalline semimetals in non-symmorphic lattices without time-reversal symmetry

Numerous efforts have been devoted to reveal exotic semimetallic phases with topologically non-trivial bulk and surface states in materials with strong spin-orbit coupling. Recent theoretical works on orthorhombic perovskite iridates SrIrO3 have indicated that non-symmorphic symmetry is crucial to protect a nodal line Fermi surface (FS) in addition to space-time inversion symmetry [C. Fang {\it et.al}, PRB {\bf 92}, 081201(R) (2015), Y. Chen {\it et.al}, Nat. Commu. {\bf 6}, (2015)]. In this work, we investigate possible topological semimetals in the absence of time-reversal symmetry. In principle, an anti-unitary operator, defined as a product of time-reversal and glide operators, can protect a four-fold or two-fold degenerate nodal FS.  Indeed this happens in SrIrO3 with the magnetic field along a particular direction.  A trivial gapped insulator can also occur due to a lack of such anti-unitary operation. This study shows that non-symmorphic crystals with multiple fractional lattice translations exhibit rich topological properties.   

SU(3) Quantum Hall Ferromagnetism in SnTe

The (111) surface of SnTe hosts one isotropic G-centered and three degenerate anisotropic M- centered Dirac surface states. We predict that a nematic phase with spontaneously broken C3 symmetry will occur in the presence of an external magnetic field when the N$=$0 M Landau levels are 1/3 or 2/3 filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state, and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the three-fold M Landau level degeneracy, yielding a ground state energy with 2$\pi $/3 periodicity as a function of Zeeman-field orientation angle.   

Interplay of imperfections and surface states in topological crystalline insulators

The conducting states, recently discovered at the surface of a special class of insulators – topological insulators - are distinguished for their insensitivity to local and non-magnetic surface defects. Their behavior in the presence of magnetic impurities and macroscopic imperfections of the surface is puzzling and hard to analyze quantitatively. Here, we present a systematic study of the imperfections (magnetic impurities and deviations from perfect surface cleavage) in topological crystalline insulators of the tin telluride family by using realistic first-principles-derived tight-binding models. The theoretical framework proposed is quite general and easily permits the extensions to other TI families and impurity types. The influence of the strong local correlations of the impurity atoms on the topological states stability is also discussed within the frame of the Dynamical Mean Field Theory.   

Space group constraints on weak indices in topological crystalline insulators

In this work we derive constraints on weak indices of topological insulators and superconductors coming from space group symmetry. Weak indices are topological invariants of lower dimensional slices of the Brillouin zone, notable examples are the Chern numbers in class A and weak $\mathbbm{Z}_2$ indices in class AII in 3D. The components of the weak indices form a momentum space vector that transforms in a simple fashion under space group symmetries, using results of momentum space crystallography we find the allowed values for each Bravais lattice. Nonsymmorphic symmetries, such as screw axes and glide planes pose additional constraints. Accounting for both of these we find that most space groups experience some restriction, to the extent that some cannot support nontrivial weak topological insulators and superconductors at all. This result puts a strong constraint on candidates in the experimental and numerical search for topological materials based on the lattice structure alone.   

Quantized electric quadrupole moment in Topological Crystalline Insulators

We define the quadrupole moment as a bulk topological quantity in 2-dimensional insulators. When protected by spatial symmetries, a non-trivial quadrupole with full open boundaries exhibits robust, quantized and corner-localized half-charges. Alternatively, the non-trivial quadrupole state manifests as an edge-localized non-trivial polarization (i.e. edge-localized 1-dimensional topological insulators) in systems with open boundaries along one direction but closed along the other. We characterize this phase and explore new phenomena, as well as generalizations of this moment to higher dimensions.   

Temperature dependence of angle-resolved photoemission of the crystalline topological insulator Pb$_{1-x}$Sn$_x$Se(111)

The system Pb$_{1-x}$Sn$_x$Se is a topological insulator protected by mirror symmetry. Angle-resolved photoemission investigations have so far been concentrating on (100) surfaces of bulk single crystals. Here, we systematically study (111) epitaxial films under variation of the Sn concentration (10%, 20% and 28%) and temperature (300–30 K). We report the behavior of Dirac cones at $\overline{\Gamma}$ and $\overline{M}$ points of the surface Brillouin zone across the temperature-induced topological phase transition.