scholarly journals Interplay of topology and interactions in quantum Hall topological insulators: U(1) symmetry, tunable Luttinger liquid, and interaction-induced phase transitions

2016 ◽  
Vol 94 (3) ◽  
Author(s):  
Maxim Kharitonov ◽  
Stefan Juergens ◽  
Björn Trauzettel
Keyword(s):  
Phase Transitions ◽  
Topological Insulators ◽  
Quantum Hall ◽  
Luttinger Liquid

scholarly journals Charge density waves and their transitions in anisotropic quantum Hall systems

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Yuchi He ◽  
Kang Yang ◽  
Mark Oliver Goerbig ◽  
Roger S. K. Mong
Keyword(s):  
Phase Transitions ◽  
Charge Density ◽  
Density Wave ◽  
Quantum Hall ◽  
Charge Density Waves ◽  
Stripe Phase ◽  
Electron Bubble ◽  
First Order ◽  
Bubble Phase ◽  
First Order Phase

AbstractIn recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the N = 2 Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the 2-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the 2-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.

Shape and phase transitions in quantum-Hall skyrmions

1997 ◽  
Vol 1 (1-4) ◽  
pp. 54-58 ◽  
Author(s):  
Madan Rao ◽  
Surajit Sengupta ◽  
R. Shankar
Keyword(s):  
Phase Transitions ◽  
Quantum Hall

scholarly journals Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge

2004 ◽  
Vol 70 (23) ◽  
Author(s):  
A. Boyarsky ◽  
Vadim V. Cheianov ◽  
O. Ruchayskiy
Keyword(s):  
Quantum Hall ◽  
Luttinger Liquid ◽  
Liquid Theory

scholarly journals Chiral Anomaly, Topological Field Theory, and Novel States of Matter

2018 ◽  
Vol 30 (06) ◽  
pp. 1840007 ◽  
Author(s):  
Jürg Fröhlich
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Time Reversal ◽  
Topological Insulators ◽  
Large Scale ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Open Problems ◽  
Spin Currents ◽  
Spin Orbit Interactions

Starting with a description of the motivation underlying the analysis presented in this paper and a brief survey of the chiral anomaly, I proceed to review some basic elements of the theory of the quantum Hall effect in 2D incompressible electron gases in an external magnetic field, (“Hall insulators”). I discuss the origin and role of anomalous chiral edge currents and of anomaly inflow in 2D insulators with explicitly or spontaneously broken time reversal, i.e. in Hall insulators and “Chern insulators”. The topological Chern–Simons action yielding the large-scale response equations for the 2D bulk of such states of matter is displayed. A classification of Hall insulators featuring quasi-particles with abelian braid statistics is sketched. Subsequently, the chiral edge spin currents encountered in some time-reversal invariant 2D topological insulators with spin-orbit interactions and the bulk response equations of such materials are described. A short digression into the theory of 3D topological insulators, including “axionic insulators”, follows next. To conclude, some open problems are described and a problem in cosmology related to axionic insulators is mentioned. As far as the quantum Hall effect and the spin currents in time-reversal invariant 2D topological insulators are concerned, this review is based on extensive work my collaborators and I carried out in the early 1990’s. Dedicated to the memory of Ludvig Dmitrievich Faddeev — a great scientist who will be remembered

scholarly journals Quantum Hall Network Models as Floquet Topological Insulators

2020 ◽  
Vol 125 (8) ◽  
Author(s):  
Andrew C. Potter ◽  
J. T. Chalker ◽  
Victor Gurarie
Keyword(s):  
Topological Insulators ◽  
Quantum Hall ◽  
Network Models
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