Quantum Hall effect in 3-D topological materials

The rugged landscapes in these illustrations depict the electric potential on the surface of 2D materials that exhibit the quantum Hall effect. The level of ruggedness corresponds to impurities in the system, and the water level represents the “Fermi energy,” or filling level of electrons. In the quantum Hall effect (left), the percolation threshold (middle) is a fine-tuned energy state that marks the transition to topological order. New research by physicists at Rice University, the University of California Berkeley and the Karlsruhe Institute of Technology has found “stacks” of this special 2D state that protect patterns of quantum entanglement (right) throughout the surface energy spectrum of 3D topological materials. Credit: M. Foster/Rice University

Researchers have found surprising evidence that the quantum Hall effect exists in topological superconductors that could be used to build fault-tolerant quantum computers. The quantum Hall effect was first measured in two-dimensional materials. 

The study presented strong numerical evidence for a surprising link between 2-D and 3-D phases of topological matter. The quantum Hall effect was discovered in 2-D materials, and laboratories worldwide are in a race to make 3-D topological superconductors for quantum computing.

The team found a  particular class of 3-D topological superconductors that should exhibit ‘energy stacks’ of 2-D electronic states at their surfaces. Each of these stacked states is a robust ‘reincarnation’ of a single, very special state that occurs in the 2-D quantum Hall effect.

They discovered a link between the critical 2-D quantum Hall state and the 3-D systems. Like the 1D edge state that persists above the transition energy in 2-D quantum Hall materials, the calculations revealed a persistent 2-D boundary state in the 3-D systems. And not just any 2-D state; it is exactly the same 2-D percolation state that gives rise to 1D quantum Hall edge states. (Phys.org)

The study has been published in Physical Review X.

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