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In solid state physics, edge modes are excitations (of electrons or quasi-particles) seen at the boundary or at a corner of a crystalline materials, where the dynamics may be different from that in the crystal’s bulk.
A notable example are edge modes of topological insulators: As their name suggests, these topological phases of matter are in fact insulating in their bulk, but on their boundary they behave like conductors/metals, due to “edge modes” which may carry electric current.
For the time being see any of the main references at topological insulator and at fractional quantum Hall systems.
See also:
On edge modes in fractional quantum Hall systems:
Original articles:
Xiao-Gang Wen: Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states, Phys. Rev. B 41 (1990) 12838 [doi:10.1103/PhysRevB.41.12838]
Xiao-Gang Wen: Theory of Edge States in Fractional Quantum Hall Effects, International Journal of Modern Physics B 06 10 (1992) 1711-1762 [doi:10.1142/S0217979292000840]
Xiao-Gang Wen: Topological order in rigid states and edge excitations in fractional quantum Hall states, Advances in Physics 44 5 (1995) 405-437 [arXiv:cond-mat/9506066, doi;10.1080/00018739500101566]
On edge mode tunneling:
Claudio Chamon, Xiao-Gang Wen: Resonant tunneling in the fractional quantum Hall regime, Phys. Rev. Lett. 70 (1993) 2605 [doi:10.1103/PhysRevLett.70.2605]
Claudio Chamon, D. E. Freed, S. A. Kivelson, S. L. Sondhi, Xiao-Gang Wen: Two point-contact interferometer for quantum Hall systems, Phys. Rev. B 55 (1997) 2331 [doi:10.1103/PhysRevB.55.2331]
G. Dolcetto, S. Barbarino, D. Ferraro, N. Magnoli, M. Sassetti: Tunneling between helical edge states through extended contacts, Phys. Rev. B 85 (2012) 195138 [arXiv:1203.4486, doi:10.1103/PhysRevB.85.195138]
Review:
A. M. Chang: Chiral Luttinger liquids at the fractional quantum Hall edge, Rev. Mod. Phys. 75 (2003) 1449 [doi:10.1103/RevModPhys.75.1449]
David Tong: Edge Modes, chapter 6 of: The Quantum Hall Effect, lecture notes (2016) [arXiv:1606.06687, course webpage, pdf, pdf]
On edges modes in topological insulators:
On edge modes via Chern-Simons theory (cf. also AdS3-CFT2 and CS-WZW correspondence):
See also:
Last revised on May 13, 2025 at 06:07:50. See the history of this page for a list of all contributions to it.