Multiorbital character of the density wave in trilayer nickelate superconductors

Ruddlesden–Popper nickelates exhibit high-temperature superconductivity closely intertwined with charge and spin density waves. However, fundamental questions persist regarding the interplay between the associated density wave (DW) fluctuations and superconductivity, as well as the orbital character and symmetry underlying the DW instabilities. Here, we utilize polarized Raman scattering to investigate the phononic and electronic Raman responses of the trilayer nickelate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>La</a:mi> <a:mn>4</a:mn> </a:msub> <a:msub> <a:mi>Ni</a:mi> <a:mn>3</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>10</a:mn> </a:msub> </a:mrow> </a:math> across its concomitant charge and spin density wave transitions. In addition to distinct phonon anomalies occurring below the transition temperature, we observe a depletion of continuum spectral weight up to 114 meV and a pronounced peak centered at this energy. By combining momentum-selective information from polarized electronic Raman scattering with Raman-response model calculations based on a multiorbital Raman vertex in a reconstructed two-orbital DW state involving both <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>Ni</c:mi> <c:mtext>−</c:mtext> <c:mn>3</c:mn> <c:msub> <c:mi>d</c:mi> <c:mrow> <c:msup> <c:mi>x</c:mi> <c:mn>2</c:mn> </c:msup> <c:mo>−</c:mo> <c:msup> <c:mi>y</c:mi> <c:mn>2</c:mn> </c:msup> </c:mrow> </c:msub> </c:mrow> </c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>Ni</d:mi> <d:mtext>−</d:mtext> <d:mn>3</d:mn> <d:msub> <d:mi>d</d:mi> <d:msup> <d:mi>z</d:mi> <d:mn>2</d:mn> </d:msup> </d:msub> </d:mrow> </d:math> orbitals, we identify 114 meV as the energy scale <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mn>2</e:mn> <e:msub> <e:mi mathvariant="normal">Δ</e:mi> <e:mi>DW</e:mi> </e:msub> </e:mrow> </e:math> of the DW gap, characterized by incoherent opening and non-mean-field behavior. Furthermore, the model calculations reveal that the corresponding <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mn>2</g:mn> <g:msub> <g:mi mathvariant="normal">Δ</g:mi> <g:mi>DW</g:mi> </g:msub> </g:mrow> </g:math> peak has a multiorbital origin, requiring both orbital contributions and their mixing beyond single-orbital projections, thus shedding light on the nature of the DW instabilities in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:msub> <i:mi>La</i:mi> <i:mn>4</i:mn> </i:msub> <i:msub> <i:mi>Ni</i:mi> <i:mn>3</i:mn> </i:msub> <i:msub> <i:mi mathvariant="normal">O</i:mi> <i:mn>10</i:mn> </i:msub> </i:mrow> </i:math> .