Crystalline-symmetry-protected Majorana modes in coupled quantum dots

We propose a minimalist architecture for achieving various crystalline-symmetry-protected Majorana modes in an array of coupled quantum dots. Our framework is motivated by the recent experimental demonstrations of two-site and three-site artificial Kitaev chains in a similar setup. We find that introducing a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>π</a:mi></a:math>-phase domain wall in the Kitaev chain leads to a pair of mirror-protected Majorana zero modes located at or near the junction. Joining two <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>π</b:mi></b:math> junctions into a closed loop, we can simulate two distinct classes of two-dimensional higher-order topological superconducting phases, both carrying symmetry-protected Majorana modes around the sample corners. As an extension of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>π</c:mi></c:math> junction, we further consider a general vertex structure where <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>n</d:mi></d:math> Kitaev chains meet, i.e., a Kitaev <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>n</e:mi></e:math> vertex. We prove that such an <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>n</f:mi></f:math> vertex, if respecting a dihedral symmetry group <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>D</g:mi><g:mi>n</g:mi></g:msub></g:math>, necessarily carries <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>n</h:mi></h:math> vertex-bound Majorana modes protected by the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>D</i:mi><i:mi>n</i:mi></i:msub></i:math> symmetry. Resilience of the junction and vertex Majorana bound states against disorder and correlation effects is also discussed. Our architecture paves the way for designing, constructing, and exploring a wide variety of artificial topological crystalline phases in quantum-dot experiments.