Experimental determination of tetramer molecular orbital states in lacunar spinel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>GaNb</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>Se</mml:mi><mml:mn>8</m

In <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>A</a:mi><a:msub><a:mi>M</a:mi><a:mn>4</a:mn></a:msub><a:msub><a:mi>X</a:mi><a:mn>8</a:mn></a:msub></a:mrow></a:math> lacunar spinel systems, the formation of structural clusters in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>T</b:mi><b:mi>d</b:mi></b:msub></b:math> symmetry has led to the systems and its properties being commonly described by a <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>M</c:mi><c:mn>4</c:mn></c:msub></c:math> molecular orbital picture and its associated spin, charge, and orbital degrees of freedom. However, the nature of the molecular orbital states in the cluster is yet to be elucidated by means of photoemission spectroscopy. Here, we show that the experimental photoemission spectra in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>GaNb</d:mi><d:mn>4</d:mn></d:msub><d:msub><d:mi>Se</d:mi><d:mn>8</d:mn></d:msub></d:mrow></d:math> are consistent with the formation of a coherent, molecular orbital state resulting from the electronic tetramerization of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>Nb</e:mi><e:mn>4</e:mn></e:msub></e:math>, providing very direct validation of the molecular orbital picture in lacunar spinel systems. We find that, while the hybridization between Nb <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>4</f:mn><f:mi>d</f:mi></f:mrow></f:math> and Se <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>4</g:mn><g:mi>p</g:mi></g:mrow></g:math> in the valence band is non-negligible, the states crossing the Fermi level are mostly nonbonding, indicating that the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>Nb</h:mi><h:mn>4</h:mn></h:msub></h:math> cluster picture is valid to describe the ground-state properties of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:msub><i:mi>GaNb</i:mi><i:mn>4</i:mn></i:msub><i:msub><i:mi>Se</i:mi><i:mn>8</i:mn></i:msub></i:mrow></i:math>. The spectral weight at the Fermi level is suppressed, indicating the presence of electronic correlations which can provide a coupling of the spin/orbital degrees of freedom with charge fluctuations.