SURFACE PHYSICS SURFACE PHYSICS OF OF TOPOLOGICAL INSULATORS - PowerPoint PPT Presentation

SURFACE PHYSICS SURFACE PHYSICS OF OF TOPOLOGICAL INSULATORS TOPOLOGICAL INSULATORS MASSLESS ELECTRONS, MASSIVE IONS MASSLESS ELECTRONS, MASSIVE IONS MICHAEL EL-BATANOUNY

MASSLESS MASSLESS versus MASSIVE MASSIVE

Newton’s second law F = m a = 0 a ! E= DIPERSION RELATION

SPECIAL FEATURES SPECIAL FEATURES OF OF DISPERSION DISPERSION RELATIONS RELATIONS OF OF ELECTRONS AND ELECTRONS AND IONS IONS IN IN SOLIDS SOLIDS

MOTION OF MOTION OF ATOMS (IONS) ATOMS (IONS)

PARTICLE CHAIN PHONONS

MOTION OF ELECTRONS MOTION OF ELECTRONS

METAL INSULATOR

INSULATOR METAL

ELECTRONIC DISPERSION IN GRAPHENE

TOPOLOGICAL PROPERTIES

TOPOLOGICAL INVARIANTS GAUSS BONNET

Gauss ‐ Bonnet Theorem ∫ S k dA = 2 (1 – g ) Mod 2 π

TOPOLOGICAL INSULATORS TOPOLOGICAL INSULATORS

BOUNDARY ORDINARY TOPOLOGICAL INSULATOR INSULATOR v = 0 v = 1

DIRAC CONE

Dirac Cone ( Bi 2 Se 3 )

ELECTRON-ION ELECTRON-ION INTERACTION INTERACTION

SURFACE PHONON SURFACE PHONON DISPERSIONS DISPERSIONS IN THE IN THE PRESENCE OF PRESENCE OF DIRAC FERMIONS DIRAC FERMIONS

DI RAC CONE

Rayleigh branch for hom ogeneous surface

SURFACE RAYLEIGH WAVES Seismic Waves