Geometry of random potentials: Induction of 2D gravity in Quantum Hall plateau transitions

Abstract

In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points uniquely define a discrete surface $S$ and its dual $S^{\ast }$ made of quadrangular and $n-$gonal faces, respectively, thereby linking the geometry of the potential with the geometry of discrete surfaces. The map is parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along equipotential contours between neighbour saddle points form a network of scatterings, which define the geometric basis, in the fermionic model, for the plateau transitions. The replacement probability characterizing the network model with geometric disorder recently proposed by Gruzberg, Klümper, Nuding and Sedrakyan, is physically interpreted within the current framework as a parameter connected with the Fermi level.

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Cited by in corpus (5)

• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Instanton analysis for the spin quantum Hall symmetry class: Non-perturbative corrections to physical observables and generalized multifractal spectrum
• Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics
• Harris-Luck criterion in the plateau transition of the Integer Quantum Hall Effect