Stacking of charge-density waves in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2</mml:mn><mml:mi mathvariant="normal">H</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi>NbSe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> bila

We employ electronic-structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mn>2</a:mn><a:mi mathvariant="normal">H</a:mi><a:mtext>−</a:mtext><a:msub><a:mi>NbSe</a:mi><a:mn>2</a:mn></a:msub></a:math>. We demonstrate that the vertical stacking can give rise to a variety of patterns that may lower the symmetry of the charge-density waves exhibited separately by the two composing <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mn>1</c:mn><c:mi mathvariant="normal">H</c:mi><c:mtext>−</c:mtext><c:msub><c:mi>NbSe</c:mi><c:mn>2</c:mn></c:msub></c:math> monolayers. The general tendency to a spontaneous symmetry breaking observed in the ground state and the first excited states is shown to originate from a non-negligible interlayer coupling. Simulated images for scanning tunneling microscopy as well as geometric structure factors show signatures of the different stacking orders. This may not only be useful to reinterpret past experiments on surfaces and thin films, but it may also be exploited to devise ad hoc experiments for the investigation of the stacking order in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mn>2</e:mn><e:mi mathvariant="normal">H</e:mi><e:mtext>−</e:mtext><e:msub><e:mi>NbSe</e:mi><e:mn>2</e:mn></e:msub></e:math>. We anticipate that our analysis not only applies to the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mn>2</g:mn><g:mi mathvariant="normal">H</g:mi><g:mtext>−</g:mtext><g:msub><g:mi>NbSe</g:mi><g:mn>2</g:mn></g:msub></g:math>, but is also relevant for thin films and bulk, whose smallest centrosymmetric component is indeed the bilayer. Finally, our results illustrate clearly that the vertical stacking is not only important for 1T structures, as exemplified by the metal-to-insulator transition observed in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mn>1</i:mn><i:mi mathvariant="normal">T</i:mi><i:mtext>−</i:mtext><i:msub><i:mi>TaS</i:mi><i:mn>2</i:mn></i:msub></i:math>, but seems to be a general feature of metallic layered transition metal dichalcogenides as well. Published by the American Physical Society 2024