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Saddle point singularity and topological phase diagram in a tunable topological crystalline insulator (TCI)

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 Added by M Zahid Hasan
 Publication date 2014
  fields Physics
and research's language is English




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A topological crystalline insulator (TCI) is a new phase of topological matter, which is predicted to exhibit distinct topological quantum phenomena, since space group symmetries replace the role of time-reversal symmetry in the much-studied Z$_2$ topological insulators. Utilizing high-resolution angle-resolved photoemission spectroscopy (ARPES), we reveal the momentum space nature of interconnectivity of the Fermi surface pockets leading to a saddle point singularity within the topological surface state alone in the TCI Pb$_{0.7}$Sn$_{0.3}$Se. Moreover, we show that the measured momentum-integrated density of states exhibits pronounced peaks at the saddle point energies, demonstrating the van Hove singularities (VHSs) in the topological surface states, whose surface chemical potential, as we show, can be tuned via surface chemical gating, providing access to the topological correlated physics on the surface. Our experimental data reveal a delicate relationship among lattice constant, band gap and spin-orbit coupling strength associated with the topological phase transition in Pb$_{1-x}$Sn$_{x}$Se. Furthermore, we explore the robustness of the TCI phase with VHS in Pb$_{1-x}$Sn$_{x}$Se, which shows a variety of distinct topological phase transitions driven by either thermal instability or broken crystalline symmetry, and thus revealing a rich topological phase diagram connectivity in Pb$_{1-x}$Sn$_{x}$Se for the first time.



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We report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI) Pb1-xSnxSe as a function of various material parameters including composition x, temperature T and crystal structure. Our spectroscopic data demonstrate the electronic groundstate condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states response to circularly polarized light. Our results show that each material parameter can tune the system between trivial and topological phase in a distinct way unlike as seen in Bi2Se3 and related compounds, leading to a rich and unique topological phase diagram. Our systematic studies of the TCI Pb1-xSnxSe are valuable materials guide to realize new topological phenomena.
A Z2 topological insulator protected by time-reversal symmetry is realized via spin-orbit interaction driven band inversion. For example, the topological phase in the Bi-Sb system is due to an odd number of band
Saddle-point van Hove singularities in the topological surface states are interesting because they can provide a new pathway for accessing exotic correlated phenomena in topological materials. Here, based on first-principles calculations combined with a $mathbf {k cdot p}$ model Hamiltonian analysis, we show that the layered platinum mineral jacutingaite (Pt$_2$HgSe$_3$) harbours saddle-like topological surface states with associated van Hove singularities. Pt$_2$HgSe$_3$ is shown to host two distinct types of nodal lines without spin-orbit coupling (SOC) which are protected by combined inversion ($I$) and time-reversal ($T$) symmetries. Switching on the SOC gaps out the nodal lines and drives the system into a topological insulator state with nonzero weak topological invariant $Z_2=(0;001)$ and mirror Chern number $n_M=2$. Surface states on the naturally cleaved (001) surface are found to be nontrivial with a unique saddle-like energy dispersion with type II van Hove singularities. We also discuss how modulating the crystal structure can drive Pt$_2$HgSe$_3$ into a Dirac semimetal state with a pair of Dirac points. Our results indicate that Pt$_2$HgSe$_3$ is an ideal candidate material for exploring the properties of topological insulators with saddle-like surface states.
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The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. 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
We present a novel 3D topological insulator, termed the Takagi topological insulator (TTI), which is protected by the sublattice symmetry and spacetime inversion symmetry. The symmetries enable the Takagi factorization in the Hamiltonian space. Due to the intrinsic O(N) gauge symmetry in the Takagi factorization, a Z2 topological invariant is formulated. We examine the physical consequences of the topological invariant through a Dirac model, which exhibits exotic bulk boundary correspondence. The most stable phases are a number of novel third-order topological insulators featured with odd inversion pairs of corners hosting zero-modes. Furthermore, the nontrivial bulk invariant corresponds to a rich cross-boundary-order phase diagram with a hierarchical cellular structure. Each cell with its own dimensionality corresponds to a certain configuration of boundary states, which could be of mixed orders.
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