Adiabatic approximation and Aharonov-Casher bands in twisted homobilayer transition metal dichalcogenides

Journal Article · Thu Jul 11 00:00:00 EDT 2024 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.110.035130· OSTI ID:2396923

Shi, Jingtian ^[1]; Morales-Durán, Nicolás ^[2]; Khalaf, Eslam ^[3]; MacDonald, A. H. ^[2]

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1. University of Texas at Austin, TX (United States); The University of Texas at Austin
2. University of Texas at Austin, TX (United States)
3. Harvard University, Cambridge, MA (United States)

Topological flat moiré bands with nearly ideal quantum geometry have been identified in homobilayer transition metal dichalcogenide moiré superlattices, and are thought to be crucial for understanding the fractional Chern insulating states recently observed therein. Previous study proposed viewing the system using an adiabatic approximation that replaces the position dependence of the layer spinor with a nonuniform periodic effective magnetic field. When the local zero-point kinetic energy of this magnetic field cancels identically against that of an effective Zeeman energy, a Bloch-band version of Aharonov-Casher zero-energy modes, which we refer to as Aharonov-Casher band, emerges leading to ideal quantum geometry. Here, we critically examine the validity of the adiabatic approximation and identify the parameter regimes under which Aharonov-Casher bands emerge. We show that the adiabatic approximation is accurate for a wide range of parameters including those realized in experiments. Furthermore, we show that while the cancellation leading to the emergence of Aharonov-Casher bands is generally not possible beyond the leading Fourier harmonic, the leading harmonic is the dominant term in the Fourier expansions of the zero-point kinetic energy and Zeeman energy. Finally, the leading harmonic expansion accurately captures the trend of the bandwidth and quantum geometry, although it may fail to quantitatively reproduce more detailed information about the bands such as the Berry curvature distribution.

• Research Organization: Harvard University, Cambridge, MA (United States); University of Texas at Austin, TX (United States)
• Sponsoring Organization: DE-SC0019481; USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0019481
• OSTI ID: 2396923
• Alternate ID(s): OSTI ID: 2473753
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 110; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
Adiabatic approximation
Aharonov-Casher band
Fractional Chern insulator
Twisted homobilayer transitional metal dichalcogenides