Metallic phase of the quantum Hall effect in four-dimensional space.

@article{Edge2012MetallicPO,
  title={Metallic phase of the quantum Hall effect in four-dimensional space.},
  author={Jonathan M. Edge and Jakub Tworzydło and C. W. J. Beenakker},
  journal={Physical review letters},
  year={2012},
  volume={109 13},
  pages={
          135701
        }
}
We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space. Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the disorder strength. The critical exponent ν≈1.2 of the diverging localization length at the quantum Hall insulator-to-metal transition differs from the semiclassical value ν=1 of 4D Anderson transitions in the presence of time-reversal symmetry. Our numerical analysis is based on a mapping of the 4D Hamiltonian onto a… 
12 Citations

Figures and Tables from this paper

Four-Dimensional Quantum Hall Effect with Ultracold Atoms.
TLDR
This work identifies the linear and nonlinear quantized current responses of the 4D model, relating these to the topology of the Bloch bands, and proposes experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number.
Topological insulators with SU(2) Landau levels.
We construct continuum models of 3D and 4D topological insulators by coupling spin-1/2 fermions to an SU(2) background gauge field, which is equivalent to a spatially dependent spin-orbit coupling.
Four-dimensional topological lattices through connectivity
Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming experimentally accessible in ultracold atoms and photonics. In this paper, we propose a new type of 4D topological system that,
Efficient algorithm to compute the second Chern number in four dimensional systems
Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete
Topological quantum matter in synthetic dimensions
In the field of quantum simulation of condensed matter phenomena by artificially engineering the Hamiltonian of an atomic, molecular or optical system, the concept of synthetic dimensions has
Quantum simulation of non-trivial topology
We propose several designs to simulate quantum many-body systems in manifolds with a non-trivial topology. The key idea is to create a synthetic lattice combining real-space and internal degrees of
Topological photonics in synthetic dimensions
Topological photonics is a new and rapidly growing field that deals with topological phases and topological insulators for light. Recently, the scope of these systems was expanded dramatically by
Advances in synthetic gauge fields for light through dynamic modulation
  • D. Hey, E. Li
  • Physics, Medicine
    Royal Society Open Science
  • 2018
Photons are weak particles that do not directly couple to magnetic fields. However, it is possible to generate a photonic gauge field by breaking reciprocity such that the phase of light depends on
Topological quantum matter with cold atoms
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have
Measuring Chern numbers in Hofstadter strips
Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the
...
1
2
...

References

SHOWING 1-10 OF 59 REFERENCES
Physics Today.
TLDR
Using a combination of x-ray diffraction and electron diffraction, the scientists produced a three-dimensional map of the hybridized "orbital hole" bonding copper with neighboring oxygen atoms in cuprite (Cu2O).
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Nature
  • R. Rosenfeld
  • Medicine
    Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
  • 2009
TLDR
I am writing with a simple plea to balance the voluminous articles about treatment in your journal with a modicum of information about nature and caring effects to rekindle the perception of physicians as healers, not only treaters, who relish the gifts of nature, and foster the humanistic aspect of medicine that has thrived for millennia.
Phys
  • Rev. Lett. 100, 076404
  • 2008
Phys
  • Rev. B 78, 195424
  • 2008
Metallic phase of the quantum Hall effect in four-dimensional space
  • 2013
Phys
  • Rev. Lett. 108, 133001
  • 2012
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 2012
Phys
  • Rev. B 84, 115133
  • 2011
Phys. Rev. B
  • Phys. Rev. B
  • 2011
...
1
2
3
4
5
...