scholarly journals Quantum Hall phases emerging from atom–photon interactions

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Alexander V. Poshakinskiy ◽  
Janet Zhong ◽  
Yongguan Ke ◽  
Nikita A. Olekhno ◽  
Chaohong Lee ◽  
...  
Keyword(s):  
Quantum Hall Effect ◽  
Quantum Electrodynamics ◽  
Quantum Hall ◽  
Landau Levels ◽  
Topological Order ◽  
Edge States ◽  
Quantum Structure ◽  
Many Body ◽  
Photon Interactions ◽  
Synthetic Magnetic Field

AbstractWe reveal the emergence of quantum Hall phases, topological edge states, spectral Landau levels, and Hofstadter butterfly spectra in the two-particle Hilbert space of an array of periodically spaced two-level atoms coupled to a waveguide (waveguide quantum electrodynamics). While the topological edge states of photons require fine-tuned spatial or temporal modulations of the parameters to generate synthetic magnetic fields and the quantum Hall effect, here we demonstrate that a synthetic magnetic field can be self-induced solely by atom–photon interactions. The fact that topological order can be self-induced in what is arguably the simplest possible quantum structure shows the richness of these waveguide quantum electrodynamics systems. We believe that our findings will advance several research disciplines including quantum optics, many-body physics, and nonlinear topological photonics, and that it will set an important reference point for the future experiments on qubit arrays and quantum simulators.

VERTEX OPERATORS IN THE QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (03) ◽  
pp. 509-527 ◽  
Author(s):  
MICHAEL STONE
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Group Action ◽  
Quantum Hall ◽  
Vertex Operators ◽  
Edge States ◽  
Many Body ◽  
Level I ◽  
The Many

The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.

scholarly journals Edge probes of topological order

2020 ◽  
Vol 35 (18) ◽  
pp. 2030009 ◽  
Author(s):  
Moty Heiblum ◽  
D. E. Feldman
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Experimental Techniques ◽  
Topological Order ◽  
Edge States ◽  
Integer Quantum Hall Effect ◽  
Noise Measurements ◽  
Integer Quantum ◽  
Dimensional Electron Gas

According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines the topological order in the gapped bulk. As the bulk is less accessible, the last two decades saw the emergence of several experimental techniques that invoke the study of the compressible edge. We review the properties of the edge, and describe several experimental techniques that include shot noise and thermal noise measurements, interferometry, and energy (thermal) transport at the edge. We pay special attention to the filling factor 5/2 in the first excited Landau level (in two-dimensional electron gas in GaAs), where experimental evidence of a non-Abelian topological order was found. A brief discussion is devoted to recent interferometry experiments that uncovered unexpected physics in the integer quantum Hall effect. The article also addresses the theory of edge states, for systems with Abelian and non-Abelian topological orders.

Localization and many-body interactions in the quantum Hall effect determined by polarized optical emission

1991 ◽  
Vol 44 (8) ◽  
pp. 4006-4009 ◽  
Author(s):  
B. B. Goldberg ◽  
D. Heiman ◽  
M. Dahl ◽  
A. Pinczuk ◽  
L. Pfeiffer ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Optical Emission ◽  
Many Body ◽  
Many Body Interactions

scholarly journals Topological gaps by twisting

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Matheus I. N. Rosa ◽  
Massimo Ruzzene ◽  
Emil Prodan
Keyword(s):  
Magnetic Field ◽  
Quantum Hall Effect ◽  
Twist Angle ◽  
Quantum Hall ◽  
Topological Phases ◽  
Edge States ◽  
Layered Systems ◽  
Virtual Laboratories ◽  
Higher Dimensional ◽  
Chern Numbers

AbstractTwisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twisted n-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.

scholarly journals Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sungmin Kim ◽  
Johannes Schwenk ◽  
Daniel Walkup ◽  
Yihang Zeng ◽  
Fereshte Ghahari ◽  
...  
Keyword(s):  
Atomic Force Microscopy ◽  
Chemical Potential ◽  
Quantum Hall ◽  
Broken Symmetry ◽  
Topological Order ◽  
Edge States ◽  
Force Microscopy ◽  
Atomic Force ◽  
Intimate Relation ◽  
Boundary Measurements

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.

Magnetocapacitance Investigation of Quantum Hall Effect and Edge States

1997 ◽  
Vol 11 (22) ◽  
pp. 2593-2619 ◽  
Author(s):  
Sadao Takaoka ◽  
Kenichi Oto ◽  
Kazuo Murase
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Electron System ◽  
Edge Length ◽  
Capacitance Measurement ◽  
Edge States ◽  
Bulk Conductivity ◽  
Cyclotron Radius ◽  
Bulk State

The quantum Hall effect for the GaAs/AlGaAs heterostrcture is investigated by an ac capacitance measurement between the two-dimensional electron system (2DES) and the gate on GaAs/AlGaAs. The capacitance minima at the quantum Hall plateaus are mainly determined not by the 2DES area under the gate but by the edge length of 2DES. There exists the high conductive region due to the edge states along the 2DES boundary, when the bulk conductivity σxx is small enough at low temperatures and high magnetic fields. From the temperature and frequency dependence of the capacitance minima, it is found that the measured capacitance consists of the contribution from the edge states and that of the bulk state, which is treated as a distributed circuit of a resistive plate with the conductivity σxx. The evaluated width of edge states from the capacitance is much larger than the magnetic length and the cyclotron radius expected from the one-electron picture. This wide width of edge states can be explained by the compressible-incompressible strip model, in which the screening effect is taken into account. Further the bulk conductivity of less than 10-12 S (S=1/Ω) is measured by the capacitance of the Corbino geometry sample, where the edge states are absent and the capacitance is determined by only σxx in this geometry. The localization of the bulk state is investigated by the obtained σxx.

scholarly journals Quantum parity Hall effect in Bernal-stacked trilayer graphene

2019 ◽  
Vol 116 (21) ◽  
pp. 10286-10290 ◽  
Author(s):  
Petr Stepanov ◽  
Yafis Barlas ◽  
Shi Che ◽  
Kevin Myhro ◽  
Greyson Voigt ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Exchange Interactions ◽  
Mirror Reflection ◽  
Edge States ◽  
State Variables ◽  
Coulomb Interactions ◽  
Spin Polarized ◽  
Trilayer Graphene

The quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system’s mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance σxx is first quantized to 4e2/h at a small perpendicular magnetic field B⊥, establishing the presence of four edge channels. As B⊥ increases, σxx first decreases to 2e2/h, indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong B⊥ limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.

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