scholarly journals Measurement of topological order based on metric-curvature correspondence

2021 ◽  
Vol 104 (19) ◽  
Author(s):  
Gero von Gersdorff ◽  
Wei Chen
Keyword(s):  
2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sungmin Kim ◽  
Johannes Schwenk ◽  
Daniel Walkup ◽  
Yihang Zeng ◽  
Fereshte Ghahari ◽  
...  

AbstractThe quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $${{\nu }}={{0}},\pm {{1}}$$ ν = 0 , ± 1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.


2017 ◽  
Vol 14 (2) ◽  
pp. 160-165 ◽  
Author(s):  
Zhihuang Luo ◽  
Jun Li ◽  
Zhaokai Li ◽  
Ling-Yan Hung ◽  
Yidun Wan ◽  
...  
Keyword(s):  

2013 ◽  
Vol 111 (9) ◽  
Author(s):  
Norbert Schuch ◽  
Didier Poilblanc ◽  
J. Ignacio Cirac ◽  
David Pérez-García

2007 ◽  
Vol 19 (14) ◽  
pp. 145212 ◽  
Author(s):  
Shunsuke Furukawa ◽  
Grégoire Misguich ◽  
Masaki Oshikawa

2006 ◽  
Vol 2 (5) ◽  
pp. 309-310 ◽  
Author(s):  
Maciej Lewenstein

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Xiao-Gang Wen

We review the progress in the last 20–30 years, during which we discovered that there are many new phases of matter that are beyond the traditional Landau symmetry breaking theory. We discuss new “topological” phenomena, such as topological degeneracy that reveals the existence of those new phases—topologically ordered phases. Just like zero viscosity defines the superfluid order, the new “topological” phenomena define the topological order at macroscopic level. More recently, we found that at the microscopical level, topological order is due to long-range quantum entanglements. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges and fractional statistics. Long-range quantum entanglements can even provide a unified origin of light and electrons; light is a fluctuation of long-range entanglements, and electrons are defects in long-range entanglements.


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