Doping a moiré Mott insulator: A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mi>J</mml:mi></mml:math> model study of twisted cuprates

Abstract

We theoretically explore twisted cuprate multilayers, a moir\'e material family where the individual layers are themselves strongly correlated. We study the twisted t-J model, using a slave-boson mean field treatment that is compatible with Mott physics at small doping. Furthermore, we incorporate the interlayer tunneling form-factor dictated by the symmetry of the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital. Including both these features leads to a phase diagram distinct from earlier weak-coupling treatments that predicted large gap spontaneous topological superconductors. Instead, we find that spontaneous time reversal (T) breaking occurs around twist angle of $\ensuremath{\theta}={45}^{\ensuremath{\circ}}$, but only in a narrow window. Moreover, a nearly gapless superconductor is obtained, whose spectroscopic features parallels that in monolayer cuprates, despite the broken time reversal and reflection symmetries. At smaller $\ensuremath{\theta}$ however, driving an interlayer current can lead to a gapped topological phase. The energy-phase relation of the interlayer Josephson junction displays notable double-Cooper-pair tunneling which dominates around ${45}^{\ensuremath{\circ}}$. The $\ensuremath{\theta}$ dependence of the Josephson critical current and the Shapiro steps are consistent with recent experiments. Utilizing the moir\'e structure as a probe of correlation physics, e.g., the pair density wave state, is discussed.

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