Theory of quasiparticle interference in mirror symmetric 2D systems and its application to surface states of topological crystalline insulators

Abstract

We study symmetry protected features in the quasiparticle interference (QPI) pattern of 2D systems with mirror symmetries and time-reversal symmetry, around a single static point impurity. We show that, in the Fourier transformed local density of states (FT-LDOS), $ρ(\bq,ω)$, while the position of high intensity peaks generically depends on the geometric features of the iso-energy contour at energy $\omega$, the \emph{absence} of certain peaks is guaranteed by the opposite mirror eigenvalues of the two Bloch states that are (i) on the mirror symmetric lines in the Brillouin zone (BZ) and (ii) separated by scattering vector $\bq$. We apply the general result to the QPI on the $<001>$-surface of topological crystalline insulator Pb${}_{1-x}$Sn${}_x$Te and predict all vanishing peaks in $ρ(\bq,ω)$. The model-independent analysis is supported by numerical calculations using an effective four-band model derived from symmetry analysis.

Six-page text plus 2.5-page appendices, three figures and one table. Accepted version

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• Visualizing heavy fermions emerging in a quantum critical Kondo lattice
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Cited by in corpus (25)

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• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
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• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Surface States of Topological Crystalline Insulators in IV-VI Semiconductors
• Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
• Topological non-symmorphic crystalline insulators
• Symmetry breaking and Landau quantization in topological crystalline insulators
• Stiefel-Whitney classes and topological phases in band theory
• Universal signatures of Fermi arcs in quasiparticle interference on the surface of Weyl semimetals
• Classification of topological crystalline insulators based on representation theory
• Valleytronics on the Surface of Topological Crystalline Insulator: Elliptic Dichroism and Valley-Selective Optical Pumping
• Quasiparticle scattering from topological crystalline insulator SnTe (001) surface states
• Intra- and Interband Electron Scattering in the Complex Hybrid Topological Insulator Bismuth Bilayer on Bi${}_2$Se${}_3$
• Distinct topological crystalline phases in models for the strongly correlated topological insulator SmB6
• Inducing Lifshitz transition by extrinsic doping of surface bands in topological crystalline insulator Pb${}_{1-x}$Sn${}_x$Se
• Field Theory of Nematicity in the Spontaneous Quantum Anomalous Hall effect
• Thermoelectric effects in topological crystalline insulators
• Odd-Parity Quasiparticle Interference in the Superconductive Surface State of UTe2
• Ab-initio Theory of Fourier-transformed Quasiparticle Interference Maps and Application to the Topological Insulator Bi${}_2$Te${}_3$
• Topological crystalline protection in a photonic system
• Surface reconstruction in a tight-binding model for the topological Kondo insulator SmB6
• Quasiparticle interference and spectral function of the UTe${}_2$ superconductive surface band
• Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator
• Intermediate band analysis in Green's functions calculations of quasiparticle interference