Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles

Abstract

This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor components of the wavefunction exhibit an increasing number of zeros, resembling the changes in the quantum Hall wavefunction as the Landau level index is increased. The wavefunction zeros are characterized by a chirality, with zeros of the same chirality clustering near the center of the moiré unit cell, while opposite chirality zeros are pushed to the boundaries of the unit cell. The enhanced phase winding at higher magic angles suggests an increased circulating current. Physical implications for scanning tunneling spectroscopy, orbital magnetization and interaction effects are discussed.

Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene

“…Interestingly, the eigenstates of E τ n n,+ (k) are exactly degenerate over the whole mBZ, as are the eigenstates of E τ n n,− (k). This is due to the combination of the 2-fold rotation about the axis normal to the plane, spinless time reversal and the chiral particle-hole symmetries [41,55,60,62]…”

Exact Landau Level Description of Geometry and Interaction in a Flatband

“…The leading Umklapp processes scatter electron by b 1,2,3 shown in Fig. 1 with the same real amplitude w1 due to the C 3 and the exact intra-valley inversion symmetry [43]. In Fig.…”

“…( 49) is motivated by the relation between σ(z) and θ 1 (z) as shown in Eq. (43). One can always choose a 1 to be real to achieve a simpler expression:…”

Hartree-Fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides

“…Even for zero displacement field, D = 0, the moiré single particle eigenstates at a general wavevector k are non-degenerate [11,12]. However, for small twist angle (many atoms in the moiré unit cell) and weak interlayer hybridization we may restrict our attention to monolayer states very near the single layer K 0 / K 0 points, so that the single layer valence band may be approximated as a parabola…”