Quantum mechanics

Algorithm

Engineering

Mathematical physics

Dirac (video compression format)

Square (algebra)

Economics

Neutrino

Projection (relational algebra)

Band gap

Surface (topology)

Square root

Mechanical engineering

Physics

Nonlinear system

Mathematics

Semimetal

Geometry

Combinatorics

Finance

Topology (electrical circuits)

Manifold (fluid mechanics)

Honeycomb

Order (exchange)

Weyl semimetal

Nature Communications

The mathematical foundation of quantum mechanics is built on linear algebra, while the application of nonlinear operators can lead to outstanding discoveries under some circumstances, such as the prediction of positron, a direct outcome of the Dirac equation which stems from the square-root of the Klein-Gordon equation. In this article, we propose a model of square-root higher-order Weyl semimetal (SHOWS) by inheriting features from its parent Hamiltonians. It is found that the SHOWS hosts both “Fermi-arc” surface and hinge states that respectively connect the projection of the Weyl points on the side surface and arris. We theoretically construct and experimentally observe the exotic SHOWS state in three-dimensional (3D) stacked electric circuits with honeycomb-kagome hybridizations and double-helix interlayer couplings. Our results open the door for realizing the square-root topology in 3D solid-state platforms.

Square-root higher-order Weyl semimetals