Time-reversal symmetry breaking versus chiral symmetry breaking in twisted bilayer graphene

Abstract

By applying a self-consistent Hartree-Fock approximation, we show that the mechanism of dynamical symmetry breaking can account for the insulating phase that develops about the charge neutrality point of twisted bilayer graphene around the magic angle. (i) If the Coulomb interaction is screened by metallic gates, the opening of a gap between the lowest-energy valence and conduction bands proceeds through the breakdown of chiral symmetry at strong coupling. Increasing the dielectric screening, however, we find a critical coupling at which chiral symmetry breaking is suppressed, triggering a very strong signal for time-reversal symmetry breaking with Haldane mass. (ii) If the long-range tail of the Coulomb interaction is not screened, we see the appearance of yet a different dominant pattern at strong coupling, which is characterized by breaking the time-reversal invariance but with opposite flux in the two sublattices of each carbon layer, with the consequent valley symmetry breaking. In this case a gap is also opened in the Dirac cones, but superposed to the splitting of the degeneracy of the low-energy bands at the K points of the moiré Brillouin zone.

Importance of long-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene

“…These results are in agreement with another atomistic calculation which found that only retaining Hubbard interactions can only yield insulating states at charge neutrality [57,58], and also continuum model Hartree-Fock calculations that break C 2 symmetry [55]. To overcome the limitations of the current approach, future research should investigate longer-ranged exchange interactions [51][52][53][54][55][56] and the influence of ordering tendencies with q = 0 which could give rise to alternative symmetry-breaking mechanisms such as valley [9] and rotational [24] symmetry.…”

“…While these calculations have yielded many useful insights, they do not capture atomic-scale interactions (such as on-site interactions within carbon p z orbitals) and often only include a few bands near the Fermi level with the effect of all other bands being described by an effective dielectric constant. Few groups have attempted to capture the interplay of long-ranged and short-ranged interactions using atomistic calculations: González and Stauber [56] studied the properties of tBLG in different dielectric environments using atomistic Hartree-Fock theory, and Sboychakov et al [57,58] developed an atomistic Hubbard model with electron-electron interactions beyond the atomistic Hubbard interactions. These studies investigated the properties of tBLG at a single twist angle, and therefore, did not study in detail the doping and twist-angle dependence of the interplay of long-ranged and short-ranged interactions.…”

Short Versus Long Range Exchange Interactions in Twisted Bilayer Graphene

“…[ 66,67 ] Moreover, these atomistic approaches can also include long‐ranged interactions, such as self‐consistent Hartree interactions. [ 68–73 ]…”

“…[66,67] Moreover, these atomistic approaches can also include long-ranged interactions, such as self-consistent Hartree interactions. [68][69][70][71][72][73] A significant limiting factor of self-consistent atomistic approaches for broken symmetry phases is their computational cost. [71,74,75] Some examples of such calculations exist in the literature, [71][72][73]76] but modeling of the full phase diagram -as function of twist angle and doping level, amongst other experimental variables -has not yet been achieved.…”

“…[68][69][70][71][72][73] A significant limiting factor of self-consistent atomistic approaches for broken symmetry phases is their computational cost. [71,74,75] Some examples of such calculations exist in the literature, [71][72][73]76] but modeling of the full phase diagram -as function of twist angle and doping level, amongst other experimental variables -has not yet been achieved. For example, González and Stauber [72,73] used a Green's functions based method to study the effect of long-ranged interactions and the interplay between long and short-ranged interactions, but only at 1.16°and either at charge neutrality or −2 electrons per moiré unit cell.…”