[Paper Review] Dataset for 'Mapping twist-tuned multi-band topology in bilayer WSe$_2$'

Benjamin A. Foutty, Carlos R. Kometter+6 more|arXiv (Cornell University)|Apr 19, 2023

Topological Materials and Phenomena12 references24 citations

TL;DR

Local electronic compressibility measurements reveal multiple topological bands and tunable Chern insulators in twisted bilayer WSe2 near a magic angle, including displacement-field driven topological transitions.

ABSTRACT

Datasets and code for the manuscript 'Mapping twist-tuned multi-band topology in bilayer WSe2.' See 'README.txt' for further details.

Motivation & Objective

• Map topological bands and correlated ground states in twisted bilayer WSe2 at small twist angles.
• Identify Chern insulators near a magic angle around 1.23° at zero magnetic field.
• Explore displacement-field induced topological phase transitions at nu = -1.
• Examine how ground states depend on local moiré wavelength by varying twist angle.
• Establish the topological phase diagram of a generalized Kane-Mele-Hubbard model in tWSe2.

Proposed method

• Use scanning single electron transistor (SET) microscopy to measure inverse compressibility dμ/dn and chemical potential μ(n).
• Vary twist angle locally from 1.1° to 1.6° to map moiré wavelength effects.
• Apply a locally controlled displacement field D_eff via the SET tip to tune topology and induce phase transitions.
• Compare measurements with Hartree-Fock continuum-model predictions for Kane-Mele-Hubbard–like physics.
• Study magnetic-field dependent spectra up to B ≈ 11 T to observe Hofstadter-like features.

Figure 1: Multiple topological bands and ground states in tWSe 2 . a , Schematic showing the moiré pattern in twisted WSe 2 (tWSe 2 ), in which MX and XM stacking sites (bottom illustrations) form a honeycomb lattice. b , Cartoon of lowest energy moiré bands and their occupations at the first four i

Experimental results

Research questions

• RQ1 Do twisted WSe2 bilayers host multiple topological bands with nonzero Chern numbers at small twist angles?
• RQ2 How does moiré wavelength affect correlated ground states and gaps at integer fillings?
• RQ3 Can displacement-field tuning drive topological phase transitions at integer fillings such as ν = -1?
• RQ4 What is the magnetic-field dependence of the gaps and Hofstadter states in these systems?

Key findings

• Multiple topological bands with Chern number C = +1 gaps observed at ν = -1 and ν = -3 that persist to zero magnetic field.
• Gaps at ν = -1 and ν = -3 have total Chern number C = +1, while ν = -2 and ν = -4 have C = 0, indicating distinct topological ground states.
• At a local twist angle around 1.23°, a series of quantum anomalous Hall (QAH) insulators is observed at zero field.
• Displacement-field tuning via the SET tip induces a topological phase transition at ν = -1 between a QAH state and a topologically trivial layer-polarized state.
• Twist-angle dependence shows topological gaps appear only in a narrow range (≈1.2°–1.25°), with broader angles yielding weaker or no zero-field topological states.
• Hartree-Fock continuum-model calculations support a landscape with spin-valley polarized Chern insulators and transitions to trivial states under varying D and θ.

Figure 2: Magnetic field dependence at $\theta=1.23^{\circ}$ . a Magnetic field dependence of d $\mu$ /d $n$ up to $B=11$ T. b , Thermodynamic gaps $\Delta_{(C,s)}$ for states with intercept $s$ and slope $C$ as identified by the Diophantine equation, as a function of $B$ , for the pair of competing