scholarly journals Self-duality of the integer quantum Hall to insulator transition: Composite fermion description

2019 ◽  
Vol 100 (23) ◽  
Author(s):  
Prashant Kumar ◽  
Yong Baek Kim ◽  
S. Raghu
Keyword(s):  
Quantum Hall ◽  
Insulator Transition ◽  
Composite Fermion ◽  
Self Duality ◽  
Integer Quantum

scholarly journals Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films

2015 ◽  
Vol 113 (2) ◽  
pp. 280-285 ◽  
Author(s):  
Nicholas P. Breznay ◽  
Myles A. Steiner ◽  
Steven Allan Kivelson ◽  
Aharon Kapitulnik
Keyword(s):  
Magnetic Field ◽  
Indium Oxide ◽  
Quantum Hall ◽  
Oxide Films ◽  
Insulator Transition ◽  
Hall Resistance ◽  
Self Duality ◽  
Universal Values ◽  
The Magnetic Field ◽  
Indium Oxide Films

We combine measurements of the longitudinal (ρxx) and Hall (ρxy) resistivities of disordered 2D amorphous indium-oxide films to study the magnetic-field tuned superconductor-to-insulator transition (H-SIT) in the T→0 limit. At the critical field, Hc, the full resistivity tensor is T independent with ρxx(Hc)=h/4e2 and ρxy(Hc)=0 within experimental uncertainty in all films (i.e., these appear to be “universal” values); this is strongly suggestive that there is a particle–vortex self-duality at H=Hc. The transition separates the (presumably) superconducting state at H<Hc from a “Hall-insulator” phase in which ρxx→∞ as T→0 whereas ρxy approaches a nonzero value smaller than its “classical value” H/nec; i.e., 0<ρxy<H/nec. A still higher characteristic magnetic field, Hc*>Hc, at which the Hall resistance is T independent and roughly equal to its classical value, ρxy≈H/nec, marks an additional crossover to a high-field regime (probably to a Fermi insulator) in which ρxy>H/nec and possibly diverges as T→0. We also highlight a profound analogy between the H-SIT and quantum-Hall liquid-to-insulator transitions (QHIT).

scholarly journals Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Yi Yang ◽  
Bo Zhen ◽  
John D. Joannopoulos ◽  
Marin Soljačić
Keyword(s):  
Quantum Hall ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Spin Orbit ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

scholarly journals An all-epitaxial nitride heterostructure with concurrent quantum Hall effect and superconductivity

2021 ◽  
Vol 7 (8) ◽  
pp. eabf1388
Author(s):  
Phillip Dang ◽  
Guru Khalsa ◽  
Celesta S. Chang ◽  
D. Scott Katzer ◽  
Neeraj Nepal ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Electron Gas ◽  
Quantum Hall ◽  
High Electron Mobility Transistor ◽  
High Electron ◽  
2D Electron Gas ◽  
Integer Quantum Hall Effect ◽  
Topological Quantum ◽  
Integer Quantum

Creating seamless heterostructures that exhibit the quantum Hall effect and superconductivity is highly desirable for future electronics based on topological quantum computing. However, the two topologically robust electronic phases are typically incompatible owing to conflicting magnetic field requirements. Combined advances in the epitaxial growth of a nitride superconductor with a high critical temperature and a subsequent nitride semiconductor heterostructure of metal polarity enable the observation of clean integer quantum Hall effect in the polarization-induced two-dimensional (2D) electron gas of the high-electron mobility transistor. Through individual magnetotransport measurements of the spatially separated GaN 2D electron gas and superconducting NbN layers, we find a small window of magnetic fields and temperatures in which the epitaxial layers retain their respective quantum Hall and superconducting properties. Its analysis indicates that in epitaxial nitride superconductor/semiconductor heterostructures, this window can be significantly expanded, creating an industrially viable platform for robust quantum devices that exploit topologically protected transport.

scholarly journals Wiedemann-Franz laws and Sl(2, ℤ) duality in AdS/CMT holographic duals and one-dimensional effective actions for them

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dmitry Melnikov ◽  
Horatiu Nastase
Keyword(s):  
Quantum Hall Effect ◽  
Effective Action ◽  
Transport Coefficients ◽  
Quantum Hall ◽  
Dual Theory ◽  
One Dimensional ◽  
Integer Quantum Hall Effect ◽  
Weakly Coupled ◽  
Holographic Duals ◽  
Integer Quantum

Abstract In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of Sl(2, ℤ) on this transport, for theories with an AdS/CMT dual. We find that Sl(2, ℤ) restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is $$ \overline{L}=\overline{\kappa}/\left( T\sigma \right)={cg}_4^2\uppi /3 $$ L ¯ = κ ¯ / Tσ = cg 4 2 π / 3 , from the weakly coupled gravity dual. In a self-dual theory this value is also the value of L = κ/(Tσ) in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized SY Kq models and the AdS4 gravity dual, we calculate the transport coefficients and show how they can be matched at large q. We construct a generalization of this effective action that is invariant under Sl(2, ℤ) and can describe vortex conduction and integer quantum Hall effect.

scholarly journals Geometric entanglement in integer quantum Hall states

2021 ◽  
Vol 103 (11) ◽  
Author(s):  
Benoit Sirois ◽  
Lucie Maude Fournier ◽  
Julien Leduc ◽  
William Witczak-Krempa
Keyword(s):  
Quantum Hall ◽  
Quantum Hall States ◽  
Integer Quantum ◽  
Hall States
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