Tunable $t-t^{\prime }-U$ Hubbard models in twisted square homobilayers

Abstract

Square lattice Hubbard models with tunable hopping ratio $t^{\prime }/t$ are highly promising for realizing a variety of quantum phases and for shedding light on key puzzles in correlated quantum materials, including higher-temperature superconductivity. We show that twisted square lattice homo-bilayers generically offer such tunability when the flat bands originate from the corner of the Brillouin zone. We reveal an emergent symmetry at low twist-angles, absent in single layers, that necessitates the vanishing of nearest neighbor hopping ($t=0$). This symmetry can be lifted by an inter-layer displacement field or by an in-plane magnetic field, introducing tunable $t$ and anisotropy, allowing access to a wide range of $t^{\prime }/t$ ratios for correlated electrons on a moiré square lattice.

5 pages + End Matter + Supplementary

References in corpus (53)

• 2D materials and van der Waals heterostructures
• Moire bands in twisted double-layer graphene
• Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds
• Fractional quantum Hall states at zero magnetic field
• Origin of Magic Angles in Twisted Bilayer Graphene
• Hubbard model physics in transition metal dichalcogenide moiré bands
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Moiré heterostructures as a condensed matter quantum simulator
• Localization and delocalization of light in photonic moire lattices
• The Hubbard Model
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Optical soliton formation controlled by angle twisting in photonic moiré lattices
• Relaxation and frequency shifts induced by quasiparticles in superconducting qubits
• Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
• Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Nickelate superconductors -- a renaissance of the one-band Hubbard model
• Space group symmetry, spin-orbit coupling and the low energy effective Hamiltonian for iron based superconductors
• High-temperature topological superconductivity in twisted double layer copper oxides
• Atomic Bose-Einstein condensate in a twisted-bilayer optical lattice
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Multiple topological transitions in twisted bilayer graphene near the first magic angle
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Ground state phase diagram of the doped Hubbard model on the 4-leg cylinder
• Superconducting gap anisotropy in monolayer FeSe thin film
• Cold atoms in twisted bilayer optical potentials
• Plaquette versus ordinary $d$-wave pairing in the $t^{\prime }$-Hubbard model on a width 4 cylinder
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Simulating twistronics without a twist
• General continuum model for twisted bilayer graphene and arbitrary smooth deformations
• Flat band in twisted bilayer Bravais lattices
• Doping a moiré Mott Insulator: A t-J model study of twisted cuprates
• Quantum disordered phase near the Mott transition in the staggered-flux Hubbard model on a square lattice
• Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice $t$-$J$ Model
• Continuum effective Hamiltonian for graphene bilayers for an arbitrary smooth lattice deformation from microscopic theories
• Capacitance of Graphene Bilayer as a Which-Layer Probe
• Magic angles and correlations in twisted nodal superconductors
• Current- and field-induced topology in twisted nodal superconductors
• Dichotomy of superconductivity between monolayer FeS and FeSe
• Quantum phase transitions of correlated electrons in two dimensions
• Local Plaquette Physics as Key Ingredient of High-Temperature Superconductivity in Cuprates
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Multiorbital singlet pairing and $d+d$ superconductivity
• Global Phase Diagram of D-wave Superconductivity in the Square-Lattice $t\text{-}J$ Model
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• Magic continuum in twisted bilayer square lattice with staggered flux
• Twisted-bilayer FeSe and the Fe-based superlattices
• Exotic pairing symmetry of interacting Dirac fermions on a $\pi$ flux lattice
• Thermodynamics of correlated electrons in a magnetic field
• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field

Cited by in corpus (2)

• Twisted Nodal Superconductors
• Engineering Hubbard models with gated two-dimensional moiré systems