Robustness and Universality of Surface States in Dirac Materials

Abstract

Ballistically propagating topologically protected states harbor exotic transport phenomena of wide interest. Here we describe a nontopological mechanism that produces such states at the surfaces of generic Dirac materials, giving rise to propagating surface modes with energies near the bulk band crossing. The robustness of surface states originates from the unique properties of Dirac-Bloch wavefunctions which exhibit strong coupling to generic boundaries. Surface states, described by Jackiw-Rebbi-type bound states, feature a number of interesting properties. Mode dispersion is gate tunable, exhibiting a wide variety of different regimes, including nondispersing flat bands and linear crossings within the bulk bandgap. The ballistic wavelike character of these states resembles the properties of topologically protected states; however, it requires neither topological restrictions nor additional crystal symmetries. The Dirac surface states are weakly sensitive to surface disorder and can dominate edge transport at the energies near the Dirac point.

arXiv comment16 pages, 4 figures

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• Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors
• Guiding Dirac fermions in graphene with a carbon nanotube
• Topological photonics on superconducting quantum circuits with parametric couplings
• Fermi arcs and surface criticality in dirty Dirac materials
• Edge states in a two-dimensional non-symmorphic semimetal
• Spontaneously-Induced Dirac Boundary State and Digitization in a Nonlinear Resonator Chain
• Surface quantum critical phenomena in disordered Dirac semimetals
• Bound states and controllable currents on Topological Insulator surfaces with extended magnetic defects
• Anomalous Hall Effect in Bismuth
• Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators
• Boundary criticality for the Gross-Neveu-Yukawa models
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Macroscopic-ranged proximity effect in graphite