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The phenomenology and radical changes seen in materials properties traversing a quantum phase transition has captivated condensed matter research. Strong electronic correlations lead to novel ground states, including magnetic order, nematicity and unconventional superconductivity. To provide a microscopic model for these requires detailed knowledge of the electronic structure in the vicinity of the Fermi energy, promising a complete understanding of the physics of the quantum critical point. The strontium ruthenates provide an ideal material system to explore this physics using spectroscopic techniques, providing high-quality atomically flat surfaces. Spectroscopic confirmation of the energy and field-dependence of the electronic structure would allow verification of this scenario, as well as assessing the role of quantum fluctuations. Here, we demonstrate such a measurement using scanning tunneling microscopy at temperatures below 100mK.¹

Our results show that even in zero field the surface electronic structure of Sr₃Ru₂O₇ is strongly C₂ symmetric and that an out-of-plane magnetic-field drives both a Lifshitz transition and induces a charge-stripe order, suggesting that as in Sr₂RuO₄,² the surface exhibits subtle differences in its properties compared to the bulk. Our results provide a microscopic picture of the field-induced changes of the electronic structure across the Lifshitz transition from quasi-particle interference imaging.