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

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.

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INHOMOGENEITY OF ELECTRON LIQUID AND EFFECTS OF INTERLAYER COUPLING IN GaAs/AlGaAs SUPERLATTICES IN THE REGIME OF THE QUANTUM HALL EFFECT

International Journal of Modern Physics B ◽

10.1142/s0217979207042914 ◽

2007 ◽

Vol 21 (08n09) ◽

pp. 1409-1413

Author(s):

Y. A. PUSEP ◽

F. E. G. GUIMARÃES ◽

H. ARAKAKI ◽

C. A. DE SOUZA ◽

A. J. CHIQUITO

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Filling Factor ◽

Quantum Hall ◽

Interlayer Coupling ◽

Integer Quantum Hall Effect ◽

Weakly Coupled ◽

Integer Quantum ◽

Increasing Temperature ◽

Partial Population

Formation of the electron state with the integer filling factor was studied by magneto-capacitance and magneto-photoluminescence measurements in weakly coupled GaAs/AlGaAs multilayers where quasi-two dimensional electrons revealed the integer Quantum Hall Effect. The disorder modulated compressibility of the quantized Hall phase with the filling factor ν=2 was determined. The incompressible fraction of this phase was shown to rapidly disappear with the increasing temperature. The quantized Hall phase of the weakly coupled multilayers was shown to emit the asymmetrical photoluminescence lines. We demonstrated that the observed asymmetry is caused by a partial population of the extended electron states formed in the quantized Hall conductor phase due to the disorder induced interlayer tunneling.

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SUPERCONDUCTING FEATURES IN THE INTEGER QUANTUM HALL EFFECT

Modern Physics Letters B ◽

10.1142/s0217984991002173 ◽

1991 ◽

Vol 05 (27) ◽

pp. 1809-1816

Author(s):

ROBERTO IENGO ◽

KURT LECHNER

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Effective Action ◽

Quantum Hall ◽

Total Momentum ◽

Translation Invariance ◽

Integer Quantum Hall Effect ◽

Integer Quantum

We construct an effective Action describing the Quantum Hall effect such as to allow for translation invariance and for eigenstates of both energy and total momentum, carrying Hall currents. We show that for integer filling k it entails for the Hall currents the features of a superconductor with carriers’ charge e*=ke, e being the electron’s charge, which could be tested by looking for a.c. Josephson like effects.

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

Science Advances ◽

10.1126/sciadv.abf1388 ◽

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.

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