Abstract
We propose a method to realize a broad class of tunable fermionic Hamiltonians in graphene bilayer. For that matter, we consider graphene bilayer functionalized with sp$^3$ defects that induce zero energy resonances hosting an individual electron each. The application of an off-plane electric field opens up a gap, so that the zero energy resonance becomes an in-gap bound state whose confinement scales inversely with the gap. Controlling both the distance among the defects and the applied electric field, we can define fermionic models, even lattices, whose hoppings and Coulomb interactions can be tuned. We consider in detail the case of triangular and honeycomb artificial lattices and we show how, for a given arrangement of the sp$^3$ centers, these lattices can undergo an electrically controlled transition between the weak and strong coupling regimes.
Highlights
The amazingly rich panoply of electronic phases that occur in solid-state matter emergesfrom the interplay of kinetic energy of the electrons and the Coulomb interaction, both electron-electron and electron-ion
Physicists have been looking for strategies to create artificial lattices to confine fermions where the geometry and the energy scales can be tuned independently in order to explore emergent electronic phases escaping the dictatorship of chemistry
We show that artificial lattices which realize model Hamiltonians can be created in graphene bilayer which allows the exploration of regimes that lead to the emergence of 2D spin-liquid phases, Mott transitions, quantized anomalous Hall phases, and fractionalized Haldane spin chains and correlated superconductivity
Summary
The amazingly rich panoply of electronic phases that occur in solid-state matter emergesfrom the interplay of kinetic energy of the electrons and the Coulomb interaction, both electron-electron and electron-ion. Examples of artificial lattices include optical traps for cold atoms [1], arrays of quantum dots [2,3], and surface adatoms [4,5,6,7] None of these approaches have reached yet the point where a systematic exploration of large-scale lattices with nontrivial phases can be controlled in the quantum regime. Scanning tunneling microscope (STM) has been used to arrange hundreds of carbon monoxide molecules [4] and thousands of chlorine atoms [8] on a copper surface, defining artificial lattices for electrons in surface states This approach does not allow further electrical control of the. We propose functionalized graphene bilayer with an electrically controlled band gap as a flexible and tunable platform to define both fermion and spin model Hamiltonians with a variety of one- and two-dimensional (1D and 2D) lattices with a highly tunable energy scales and filling factors. We propose to induce an array of states by chemical functionalization, which would permit to control the location of the bounded states
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