Boundary Witten effect in multiaxion insulators

We explore novel topological responses and axionlike phenomena in three-dimensional insulating systems with spacetime-dependent mass terms encoding domain walls. Via a dimensional-reduction approach, we derive an axion-electromagnetic coupling term involving three axion fields. This term yields a topological current in the bulk and, under specific conditions of the axions, real-space topological defects such as magneticlike monopoles and hopfions. Moreover, once one of the axions acquires a constant value, a nontrivial boundary theory realizes a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>(</a:mo> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> <a:mo>)</a:mo> </a:mrow> </a:math> -dimensional analog of the Witten effect, which shows that pointlike vortices on the gapped boundary of the system acquire half-integer electric charge. Our findings reveal rich topological structures emerging from multiaxion theories, suggesting new avenues in the study of topological phases and defects.