Beyond the conventional Emery model: crucial role of long-range hopping for cuprate superconductivity

Eric Jacob; M. O. Malcolms; Viktor Christiansson; Leonard M. Verhoff; Paul Worm; Liang Si; Philipp Hansmann; Thomas Schäfer; Karsten Held

arXiv · 2605.07739

Beyond the conventional Emery model: crucial role of long-range hopping for cuprate superconductivity

Eric Jacob·M. O. Malcolms·Viktor Christiansson·Leonard M. Verhoff·Paul Worm·Liang Si·Philipp Hansmann·Thomas Schäfer·Karsten Held

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Abstract

The Emery model is the quintessential model for cuprate superconductors. In his eponymous paper, Emery only considered the next-nearest-neighbor oxygen-copper hopping. Later, also the relevance of nearest- and next-nearest oxygen-oxygen hoppings has been pointed out. Using dynamical vertex approximation, we find a superconducting dome consistent with cuprates. However, long-range hoppings beyond the three conventional hopping parameters are necessary for the quantitatively correct phase diagram and for a proper d-wave order parameter.

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Eric Jacob, M. O. Malcolms, Viktor Christiansson, Leonard M. Verhoff, Paul Worm, Liang Si, Philipp Hansmann, Thomas Schäfer, Karsten Held. 2026-05-08. Beyond the conventional Emery model: crucial role of long-range hopping for cuprate superconductivity. https://arxiv.org/abs/2605.07739

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