Universality of modular symmetries in two-dimensional magnetotransport

Abstract

The quantum Hall effect has bagged several Nobel prizes and is a cornerstone of modern metrology, but after four decades it continues to strain our understanding of quantum physics. This comprehensive review of scaling experiments provides substantial support for the conjecture that the morass of Hall data conceals a new type of symmetry, known as modular symmetry [C. A. L\utken and G. G. Ross, Phys. Rev. B 45, 11837 (1992)]. These infinite discrete symmetries are central to many recent developments in mathematics and string theory, but have not previously been seen in nature.