Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2610.16930

Microscopic Modeling of Interlayer Tunneling in Twisted Bilayer Cuprates

Siddhant Panda, Andreas Kreisel, Laura Fanfarillo, P. J. Hirschfeld

Published Oct 12, 2026• 0 citations
arXivHTMLPDF

Abstract

The field of twistronics, recently extended to twisted bilayer cuprate systems, has generated considerable interest due to the prediction of $d+id'$ states close to a $45^\circ$ twist, as suggested by multiple experimental probes. Theoretical studies of these systems using a variety of models and many-body theoretical techniques have revealed multiple competing order parameters. The large variability in experimental results and theoretical predictions demands an accurate microscopic model for these systems, in particular a more realistic description of the interlayer tunneling. In this study, we fit the in-plane hopping and compute the interlayer tunneling amplitudes by calculating the orbital overlap between $d_{x^2-y^2}$ wave functions at each site of the twisted square-lattice model. We observe sign-changing tunneling amplitudes, a strong twist-angle dependence of the direct tunneling term, and long-range tunneling amplitudes that often dominate over direct tunneling. We investigate the band structure, Fermi surfaces, and spectral functions in comparison with those obtained from the phenomenological model and find a substantial redistribution of spectral weight that modifies the competition between different superconducting ground states. We determine the phase diagram as a function of twist angle, filling, and direct tunneling strength, which is controlled by the $c$-axis distance between the monolayers, and observe a reduction in the region of time-reversal-symmetry-breaking (TRSB) $d+id'$ states compared with the phenomenological model. Finally, we investigate the Josephson critical current across the phase diagram and find strongly suppressed critical currents close to a $45^\circ$ twist, consistent with experimental observations.

DOI
10.48550/arxiv.2610.16930

Related papers

Doping dependence of chiral superconductivity in near 45∘ twisted bilayer cuprates

Mathieu Bélanger, David Sénéchal

We study a one-band Hubbard model for a twisted cuprate bilayer with a twist angle of $43.{6}^{\ensuremath{\circ}}$ and a moir\'e cell containing 58 sites. We use the variational cluster approximation (VCA), which treats short-range correlations exactly and leads, in single layers, to a dome of $d$-wave superconductivity away from half filling from strong on-site repulsion alone. We find a time-reversal-symmetry (TRS) breaking phase in a small doping interval in the overdoped region when interlayer tunneling is strong enough. Contrary to expectations, being closer to the ${45}^{\ensuremath{\circ}}$ twist angle does not expand this TRS region compared to a previous study [Lu and S\'en\'echal, Phys. Rev. B 105, 245127 (2022)] on a ${53}^{\ensuremath{\circ}}$ twist angle. This is attributed to the fact that the two superconducting states in competition have almost identical nodal structures.

arXiv:2306.05485•Physical review. B./Physical review. B•Jan 5, 2024•8 citations

Quench of chiral superconductivity by quantum phase fluctuations in twisted cuprate bilayers

Y Shi, Mengxian Zhao, Fei Yang +2 more

Following theoretical proposals of chiral $d+id'$ superconductivity in twisted cuprate bilayers, experimental signatures of time-reversal symmetry breaking (TRSB) remain highly controversial. Here we demonstrate that quantum phase fluctuations fundamentally reshape the phase diagram of this proposed chiral state. Unlike regular superconducting orders, the chiral $d+id'$ state requires long-range coherence of an interlayer phase degree of freedom and is therefore intrinsically vulnerable to phase fluctuations. Incorporating these fluctuations nearly eliminates the chiral phase over most parts of the phase diagram, restricting it to a narrow twist-angle window and ultra-low temperatures. Phase fluctuations also strongly weaken Josephson phase locking near a twist angle of $45^\circ$. More broadly, our work establishes quantum phase fluctuations as a fundamental constraint on the emergence of TRSB phases in low-dimensional layered quantum materials.

arXiv:2607.00630•Jul 1, 2026•0 citations

Doping phase diagram of a Hubbard model for twisted bilayer cuprates

Xiancong Lu, David Sénéchal

We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle $\ensuremath{\theta}=53.{13}^{\ensuremath{\circ}}$ and as a function of doping, using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, we observe a sudden change of the relative sign of the $d$-wave order parameters of two layers between the underdoped and overdoped regimes. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the relative phase of the two layers changes continuously from 0 to $\ensuremath{\pi}$. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method, probably owing to the very small energy difference between the different states involved.

arXiv:2112.00487•Physical review. B./Physical review. B•Jun 21, 2022•24 citations

Collective phase modes in twisted ddd-wave superconducting bilayers

Y Shi, Mengxian Zhao, Fei Yang +2 more

Twisted cuprate bilayers have been predicted to host high-temperature chiral $d+id'$ superconductivity, originating from higher-order Josephson coupling processes. In such two-dimensional superconducting systems, long-wavelength fluctuations in the phase of the superconducting order parameter constitute gapless collective modes and therefore remain significant even at zero temperature. Here, we perform a theoretical analysis of the low-energy phase fluctuations in twisted $d$-wave superconducting bilayers within a self-consistent harmonic approximation, systematically retaining Josephson coupling to all orders. We demonstrate that higher-order Josephson coupling processes lead to nontrivial modifications of the phase dynamics. The momentum-resolved summand of the relative-phase stiffness is nonzero even in the normal state because interlayer tunneling explicitly breaks the intralayer U(1) symmetry, but its momentum integral vanishes for the continuum dispersion. The relative-phase stiffness is smaller in the $d+id'$ phase than in the $d$-wave phase, while the overall-phase stiffness has the opposite behavior. Furthermore, phase fluctuations strongly soften the Josephson plasma frequency near a twist angle of $45^\circ$ and also substantially reduce the Josephson critical current.

arXiv:2607.00662•Jul 1, 2026•0 citations

Interlayer bias effect on time-reversal symmetry breaking in twisted bilayer cuprates

Mathieu Bélanger, David Sénéchal

We study a one-band Hubbard model of twisted bilayer cuprates with a twist angle of $53.{13}^{\ensuremath{\circ}}$. By introducing an interlayer bias, we simulate heterobilayers of different dopings. Using the variational cluster approximation, we probe the effect of this bias on the time-reversal symmetry-breaking (TRSB) phase. Doping differences between layers affect the region where TRSB occurs; we construct a phase diagram mapping out the TRSB phase in the ${n}_{1}\ensuremath{-}{n}_{2}$ plane, with ${n}_{\ensuremath{\ell}}$ being the electron density on layer $\ensuremath{\ell}$. We also map the spontaneous supercurrent on the same plane.

arXiv:2311.02207•Physical review. B./Physical review. B•Feb 6, 2024•4 citations

Fermionic Monte Carlo Study of a Realistic Model of Twisted Bilayer Graphene

Johannes Stephan Hofmann, Eslam Khalaf, Ashvin Vishwanath +2 more

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.

arXiv:2105.12112•Physical Review X•Mar 30, 2022•73 citations
The field of twistronics, recently extended to twisted bilayer cuprate systems, has generated considerable interest due to the prediction of d+id′d+id'd+id′ states close to a 45∘45^\circ45∘ twist, as suggested by multiple experimental probes. Theoretical studies of these systems using a variety of models and many-body theoretical techniques have revealed multiple competing order parameters. The large variability in experimental results and theoretical predictions demands an accurate microscopic model for these systems, in particular a more realistic description of the interlayer tunneling. In this study, we fit the in-plane hopping and compute the interlayer tunneling amplitudes by calculating the orbital overlap between dx2−y2d_{x^2-y^2}dx2−y2​ wave functions at each site of the twisted square-lattice model. We observe sign-changing tunneling amplitudes, a strong twist-angle dependence of the direct tunneling term, and long-range tunneling amplitudes that often dominate over direct tunneling. We investigate the band structure, Fermi surfaces, and spectral functions in comparison with those obtained from the phenomenological model and find a substantial redistribution of spectral weight that modifies the competition between different superconducting ground states. We determine the phase diagram as a function of twist angle, filling, and direct tunneling strength, which is controlled by the ccc-axis distance between the monolayers, and observe a reduction in the region of time-reversal-symmetry-breaking (TRSB) d+id′d+id'd+id′ states compared with the phenomenological model. Finally, we investigate the Josephson critical current across the phase diagram and find strongly suppressed critical currents close to a 45∘45^\circ45∘ twist, consistent with experimental observations.
We study a one-band Hubbard model for a twisted cuprate bilayer with a twist angle of $43.{6}^{\ensuremath{\circ}}$ and a moir\'e cell containing 58 sites. We use the variational cluster approximation (VCA), which treats short-range correlations exactly and leads, in single layers, to a dome of ddd-wave superconductivity away from half filling from strong on-site repulsion alone. We find a time-reversal-symmetry (TRS) breaking phase in a small doping interval in the overdoped region when interlayer tunneling is strong enough. Contrary to expectations, being closer to the ${45}^{\ensuremath{\circ}}$ twist angle does not expand this TRS region compared to a previous study [Lu and S\'en\'echal, Phys. Rev. B 105, 245127 (2022)] on a ${53}^{\ensuremath{\circ}}$ twist angle. This is attributed to the fact that the two superconducting states in competition have almost identical nodal structures.
Following theoretical proposals of chiral d+id′d+id'd+id′ superconductivity in twisted cuprate bilayers, experimental signatures of time-reversal symmetry breaking (TRSB) remain highly controversial. Here we demonstrate that quantum phase fluctuations fundamentally reshape the phase diagram of this proposed chiral state. Unlike regular superconducting orders, the chiral d+id′d+id'd+id′ state requires long-range coherence of an interlayer phase degree of freedom and is therefore intrinsically vulnerable to phase fluctuations. Incorporating these fluctuations nearly eliminates the chiral phase over most parts of the phase diagram, restricting it to a narrow twist-angle window and ultra-low temperatures. Phase fluctuations also strongly weaken Josephson phase locking near a twist angle of 45∘45^\circ45∘. More broadly, our work establishes quantum phase fluctuations as a fundamental constraint on the emergence of TRSB phases in low-dimensional layered quantum materials.
We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle $\ensuremath{\theta}=53.{13}^{\ensuremath{\circ}}$ and as a function of doping, using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, we observe a sudden change of the relative sign of the ddd-wave order parameters of two layers between the underdoped and overdoped regimes. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the relative phase of the two layers changes continuously from 0 to $\ensuremath{\pi}$. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method, probably owing to the very small energy difference between the different states involved.
Twisted cuprate bilayers have been predicted to host high-temperature chiral d+id′d+id'd+id′ superconductivity, originating from higher-order Josephson coupling processes. In such two-dimensional superconducting systems, long-wavelength fluctuations in the phase of the superconducting order parameter constitute gapless collective modes and therefore remain significant even at zero temperature. Here, we perform a theoretical analysis of the low-energy phase fluctuations in twisted ddd-wave superconducting bilayers within a self-consistent harmonic approximation, systematically retaining Josephson coupling to all orders. We demonstrate that higher-order Josephson coupling processes lead to nontrivial modifications of the phase dynamics. The momentum-resolved summand of the relative-phase stiffness is nonzero even in the normal state because interlayer tunneling explicitly breaks the intralayer U(1) symmetry, but its momentum integral vanishes for the continuum dispersion. The relative-phase stiffness is smaller in the d+id′d+id'd+id′ phase than in the ddd-wave phase, while the overall-phase stiffness has the opposite behavior. Furthermore, phase fluctuations strongly soften the Josephson plasma frequency near a twist angle of 45∘45^\circ45∘ and also substantially reduce the Josephson critical current.
We study a one-band Hubbard model of twisted bilayer cuprates with a twist angle of $53.{13}^{\ensuremath{\circ}}$. By introducing an interlayer bias, we simulate heterobilayers of different dopings. Using the variational cluster approximation, we probe the effect of this bias on the time-reversal symmetry-breaking (TRSB) phase. Doping differences between layers affect the region where TRSB occurs; we construct a phase diagram mapping out the TRSB phase in the ${n}_{1}\ensuremath{-}{n}_{2}$ plane, with ${n}_{\ensuremath{\ell}}$ being the electron density on layer $\ensuremath{\ell}$. We also map the spontaneous supercurrent on the same plane.
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.