Berlin 2024 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Poster: Statistical Physics

DY 31.24: Poster

Wednesday, March 20, 2024, 15:00–18:00, Poster C

Amorphous topological insulator: towards quantum Hall criticality — •Johannes Dieplinger¹, Soumya Bera², and Naba P Nayak² — ¹Institute of Theoretical Physics, University of Regensburg, D-93040 Germany — ²Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India

We numerically investigate the critical properties of a topological transition in a two-dimensional lattice with randomly distributed points. The trivial to topological Anderson insulator transition belongs to the unitary class A of the ten-fold symmetry classification of non-interacting fermions. The model intrinsically breaks the time-reversal symmetry without the need for an external mag- netic field, often referred to as the Chern insulator. This transition is induced by varying the density of lattice points or adjusting the mass parameter. Using the two-terminal conductance and multi- fractality of the wavefunction, we found that the amorphous topological insulator exhibits the same universality as the integer quantum Hall transition. The localization length exponent is between ν = 2.55 - 2.61 regardless of the approach to the critical point, thus pointing towards the universal nature of the transition across the topological phase boundary in the non-crystalline model. The irrelevant exponent, y for both observables, is y = 0.3(1), slightly smaller than values obtained using transfer matrix analysis in the Chalker-Coddigton network. Additionally, the analysis of the entire distribution function of the inverse participation ratio reveals a potentially non-parabolic multi- fractal spectrum at the critical point of the quantum anomalous Hall transition.

Keywords: Quantum Hall effect; amorphous matter; critical exponents; multifractality