Twisted semiconductor bilayers $\mathrm{MoTe_2}$ and $\mathrm{WSe_2}$

6 problems

• Nature of the fractional quantum spin Hall state in twisted $\mathrm{MoTe_2}$

  Contested

  At three holes per moire cell, twisted $\mathrm{MoTe_2}$ near 2.1 degrees conducts along its edges with $3/2$ times the basic conductance quantum $e^{2}/h$ while keeping time-reversal symmetry (no preferred direction of time), and no accepted theory explains it.

• Why the zero-field $1/3$ state is weaker than the $2/3$ state

  Open

  In twisted $\mathrm{MoTe_2}$ the zero-field fractional Hall state at two thirds band filling is clear in transport while the one-third state is fragile or absent, the reverse of the ordinary fractional quantum Hall effect, where one third is the strongest.

• Pairing state of superconductivity next to fractional anomalous Hall states

  Open

  Twisted $\mathrm{MoTe_2}$ superconducts at fillings next to its fractional quantum anomalous Hall states (zero-field fractional Hall states), and it is unknown whether the pairs break time-reversal symmetry and carry topological edge modes.

• Mechanism of superconductivity in twisted bilayer $\mathrm{WSe_2}$

  Open

  Twisted $\mathrm{WSe_2}$ superconducts at twist angles near 3.65 and 5 degrees, next to insulating or possibly magnetic states, and the attraction that pairs its electrons is unknown.

• Composite Fermi liquid at half filling without magnetic field

  Partially resolved

  At half filling of the lowest twisted-MoTe2 band, theory predicts a metal of composite fermions (electrons bound to vortices) like the one in a half-filled Landau level, but with no applied field.

• Non-Abelian fractional state in a zero-field moire Chern band

  Open

  Some predicted fractional states host non-Abelian anyons, quasiparticles whose exchange changes the system's state in an order-dependent way, and twisted $\mathrm{MoTe_2}$ may host one with no magnetic field.