Table 2 Gaps, main order parameters, electric polarization, and valley polarization of the Hartree–Fock ground states at different integer filling factors.

From: Alternating twisted multilayer graphene: generic partition rules, double flat bands, and orbital magnetoelectric effect

Filling factor

gap(eV)

Main order parameter

Polarization

Valley polarization

−7

0.0119

szτ0σ0

−0.0103

0.398

−6

0.0208

szτ0σ0

−0.0009

0.048

−5

0.0132

szτ0σ0, s0τzσ0

−0.0110

0.624

−4

/

szτ0σ0

0.0197

−1.179

−3

0.0148

szτ0,zσ0

−0.0112

−0.406

−2

/

s0τzσ0

0.0732

−1.364

−1

0.0073

s0τzσ0

0.0585

−3.046

0

/

s0τxσy

0.1004

0.014

1

/

s0τzσ0

0.0708

−2.705

2

0.0095

szτ0σ0

0.0834

−0.030

3

0.0063

s0,zτ0,zσ0

0.0713

1.000

4

0.0131

s0τ0σ0

0.0834

0.000

5

/

s0,zτ0,zσ0

0.0771

−0.988

6

/

s0τzσ0

0.0741

−1.963

7

/

s0,zτ0,zσ0

0.0264

−0.967

  1. The unit of polarization is e Å per moiré supercell. The unit of valley polarization is charge per unit cell.