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Updated: Jan 22, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
Published on: July 11, 2025
Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands
Jian Kang1, Oskar Vafek1,2
1National High Magnetic Field Laboratory, Tallahassee, Florida, 32304, USA.
Abstract:
We identify states favored by Coulomb interactions projected onto the Wannier basis of the four narrow bands of the "magic angle" twisted bilayer graphene. At the filling of 2 electrons/holes per moiré unit cell, such interactions favor an insulating SU(4) ferromagnet. The kinetic terms select the ground state in which the two valleys with opposite spins are equally mixed, with a vanishing magnetic moment per particle. We also find extended excited states, the gap to which decreases in the magnetic field. An insulating stripe ferromagnetic phase is favored at 1 electron/hole per unit cell.
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Titration Calculations: Strong Acid - Strong Base
A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:
(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:
Band Theory
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...
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Titration of a Strong Acid with a Strong Base
Angle of Twist: Problem Solving
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