Selection rules for quasiparticle interference with internal nonsymmorphic symmetries

Abstract

We study how nonsymmorphic symmetries that commute with lattice translations are reflected in the quasiparticle interference (QPI) maps measured by scanning tunneling microscopy (STM). QPI maps, which result from scattering of Bloch states off impurities, record the interference of incoming and scattered waves as a function of energy and tip's position. Although both the impurity and the tip generically break spatial symmetries, we find that the QPI maps provide universal information on these symmetries. The symmetries impose constraints on the relation between various momentum components of the Bloch functions. These relations result in selection rules on certain momentum transfers in QPI maps. We find that universal information is encoded in the absence of QPI signal, or in the relative intensity of its replications. We show examples for one-dimensional chains and an effective model of the layered compound $\mathrm{ZrSiS}$. We discuss the implications of our theory in the analysis of observed QPI of the Weyl semimetal $\mathrm{TaAs}$. Our theory is particularly relevant for materials in rod and layer space groups, or when a correlated order parameter, such as antiferromagnetism, enlarges the unit cell.

5 pages, 3 figures; Published version with supplementary material

References in corpus (9)

• Topological quantum chemistry
• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• Dirac materials
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topological classification of crystalline insulators through band structure combinatorics
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• Surface floating 2D bands in layered nonsymmorphic semimetals: ZrSiS and related compounds
• Imaging electronic states on topological semimetals using scanning tunneling microscopy
• Selection rules for quasiparticle interference with internal nonsymmorphic symmetries

Cited by in corpus (8)

• Quasiparticle Interference Studies of Quantum Materials
• Symmetry-selective quasiparticle scattering and electric field tunability of the ZrSiS surface electronic structure
• Selection rules for quasiparticle interference with internal nonsymmorphic symmetries
• Quasiparticle interference observation of the topologically non-trivial drumhead surface state in ZrSiTe
• Quasiparticle interference in altermagnets
• Local and global patterns in quasiparticle interference: a reduced response function approach
• Hyperbolic fringe signal for twin impurity quasiparticle interference
• Projective Quasiparticle Interference of a Single Scatterer to Analyze the Electronic Band Structure of ZrSiS