Nonperturbative theory of effective Hamiltonians for deformations in two-dimensional materials: Moiré systems and dislocations

Rost, F.; Gupta, R.; Fleischmann, M.; Weckbecker, D.; Olivares, J.; Vogl, Michael; Sharma, S.; Pankratov, Oleg; Shallcross, S.

doi:10.1103/physrevb.100.035101

Cited by 27 publications

(15 citation statements)

References 28 publications

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“…It is apparent that any experiment that yields additional information about the pairing mechanism in a superconducting BLG is highly desirable. In this Rapid Communication, we adopt an effective Hamiltonian model where the interaction between the two pristine graphene layers is described by a coupling matrix [59,63,64]. When one of the pristine graphene layers is subjected to an in-plane displacement or commensurate twist, all corresponding modifications are encoded into the coupling matrix.…”

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confidence: 99%

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Josephson effect in graphene bilayers with adjustable relative displacement

Alidoust

Jauho

Akola

2020

Phys. Rev. Research

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The Josephson current is investigated in a superconducting graphene bilayer where pristine graphene sheets can make in-plane or out-of-plane displacements with respect to each other. The superconductivity can be of an intrinsic nature, or due to a proximity effect. The results demonstrate that the supercurrent responds qualitatively differently to relative displacement if the superconductivity is due to either intralayer or interlayer spin-singlet electron-electron pairing, thus providing a tool to distinguish between the two mechanisms. Specifically, both the AA and AB stacking orders are studied with antiferromagnetic spin alignment. For the AA stacking order with intralayer and on-site pairing no current reversal is found. In contrast, the supercurrent may switch its direction as a function of the in-plane displacement and out-of-plane interlayer coupling for the cases of AA ordering with interlayer pairing and AB ordering with either intralayer or interlayer pairing. In addition to sign reversal, the Josephson signal displays many characteristic fingerprints which derive directly from the pairing mechanism. Thus, measurements of the Josephson current as a function of the graphene bilayer displacement open up the means to achieve deeper insights into the superconducting pairing mechanism.

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confidence: 99%

“…This transformation evolves the AA, AB, and AC initial orderings into AB, AC, and AA orderings, respectively, when changing from 0 to unity (see Refs. [53,59,63,64]). The resulting modifications of the respective band structures are presented in the Supplemental Material [66].…”

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confidence: 99%

Josephson effect in graphene bilayers with adjustable relative displacement

Alidoust

Jauho

Akola

2020

Phys. Rev. Research

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“…Following the approach used in Refs. [63,71,[82][83][84][85] the Hamiltonian describing TBLG is given by…”

Section: A Modelmentioning

confidence: 99%

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

Benlakhouy,

Jellal,

Bahlouli

et al. 2021

Preprint

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We study the magnetic field induced Hofstadter butterfly in twisted bilayer graphene (TBG) in various kinds of situations. First, we study the equilibrium case and identify the interlayer hopping processes that are most crucial for the appearance of a Hofstadter butterfly. Surprisingly, the hopping processes that are important for the appearance of the Hofstadter butterfly can be categorized as AA stacking type -that is interlayer hoppings between equivalent sublattices. This is in contrast to AB/BA-type hoppings that are important for the appearance of flat bands in magic angle TBG and were discussed in [1]. We also find that if AB-type interlayer-hopping processes are turned off the resulting model is chiral but differs from the model discussed in [1]. Therefore, TBG has two separate chiral limits -one of them is important to understand the formation of flat bands and the other for the Hofstadter butterfly. Taking this as motivation we discuss how the role of AA-type hoppings in combination with lattice relaxation effects can make individual Landau levels slightly harder to resolve in an experimental setting than one would expect from a non-relaxed lattice setting. Finally, we consider the impact of different forms of light on the fractal structure of the butterfly. Particularly, we study the impact of circularly polarized light and longitudinal light originating from a waveguide. As the system is exposed to circularly polarized light we find butterflies with increasingly pronounced asymmetry with respect to energy E = 0. This is due to the introduction of a gap term that breaks the chiral symmetries for both of the two chiral limits mentioned above. Lastly, we study the effect of longitudinal light that can be produced at the exit of a waveguide. Here, we find that no additional terms that break chiral symmetry are introduced. Therefore, it is found to lead to no increase in asymmetry of the energy spectrum. In fact, we identify specific experimentally accessible driving regimes in which the TBG achieves any of the two chiral limits.

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“…The starting point of our discussion is the effective Hamiltonian that describes twisted bilayer graphene [1,25,38,[107][108][109]…”

Section: System Description a Static Hamiltonianmentioning

confidence: 99%

Effective Floquet Hamiltonians for periodically-driven twisted bilayer graphene

Vogl,

Rodriguez-Vega,

Fiete

2020

Preprint

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We derive effective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polarized light in two different regimes beyond the weak-drive, high frequency regime. First, we consider a driving protocol relevant for experiments with frequencies smaller than the bandwidth and weak amplitudes and derive an effective Hamiltonian, which through a symmetry analysis, provides analytical insight into the rich effects of the drive. We find that circularly polarized light at low frequencies can selectively decrease the strength of AA-type interlayer hopping while leaving the AB-type unaffected. Then, we consider the intermediate frequency, and intermediate-strength drive regime. We provide a compact and accurate effective Hamiltonian which we compare with the van Vleck expansion and demonstrate that it provides a significantly improved representation of the exact quasienergies. Finally, we discuss the effect of the drive on the symmetries, Fermi velocity and the gap of the Floquet flat bands.

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Nonperturbative theory of effective Hamiltonians for deformations in two-dimensional materials: Moiré systems and dislocations

Cited by 27 publications

References 28 publications

Josephson effect in graphene bilayers with adjustable relative displacement

Josephson effect in graphene bilayers with adjustable relative displacement

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

Effective Floquet Hamiltonians for periodically-driven twisted bilayer graphene

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