Integer and fractional Chern insulators in twisted bilayer MoTe2 (2305.00973v3)

Abstract: Chern insulators, which are the lattice analogs of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices. To date, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field, but fractional Chern insulators have been reported only in graphene-based systems under a finite magnetic field. The emergence of semiconductor moir\'e materials, which support tunable topological flat bands, opens a new opportunity to realize fractional Chern insulators. Here, we report the observation of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor {\nu}=1 and 2/3, the system is incompressible and spontaneously breaks time reversal symmetry. We determine the Chern number to be 1 and 2/3 for the {\nu}=1 and {\nu}=2/3 gaps, respectively, from their dispersion in filling factor with applied magnetic field using the Streda formula. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for demonstration of quantized fractional Hall conductance and anyonic excitation and braiding in semiconductor moir\'e materials.

• The paper demonstrates the emergence of integer (ν = 1) and fractional (ν = 2/3) Chern insulators in twisted bilayer MoTe₂ at zero magnetic field.
• It reports precise Chern numbers and orbital magnetization measurements that confirm topological order without external magnetic fields.
• The study explores electric-field–driven phase transitions, highlighting potential applications in quantum electronics and fault-tolerant computation.

Integer and Fractional Chern Insulators in Twisted Bilayer MoTe₂

The exploration of topological phases in condensed matter physics continues to unravel complex states of matter that hold potential for advancements in quantum technology. In this paper, the authors investigate twisted bilayer transition metal dichalcogenides (TMDs), specifically MoTe₂, to demonstrate the emergence of integer and fractional Chern insulators (CIs) at zero magnetic field. Utilizing small-angle twisted bilayer MoTe₂ with an angle of 3.4 degrees, the authors employ local electronic compressibility and magneto-optical techniques to probe and reveal profound insights into the behavior of these insulators at particular filling factors.

Key Findings

The main breakthrough described in this paper is the observation of both integer CIs at a hole filling factor of ν = 1 and fractional CIs (FCIs) at ν = 2/3 in a zero magnetic field setting. The complex interlayer interactions within the twisted bilayer structure facilitate the stabilization of these states. Specifically, the ν = 1 state exhibits characteristics of a conventional CI, while the ν = 2/3 state represents an FCI, which conventionally requires a strong magnetic field to emerge.

• Chern Numbers: By utilizing the Streda formula, the authors determine Chern numbers of 1 and 2/3 for the ν = 1 and ν = 2/3 states, respectively. These measurements confirm topological order in the absence of an external magnetic field, a significant observation for FCIs, which are typically seen under intense magnetic fields.
• Orbital Magnetization: The paper also reports orbital magnetization related to the topological states, with estimates of the change in orbital magnetization (∆M/𝑛𝑀𝑀) being approximately 0.4 μB and 0.05 μB for the ν = 1 and ν = 2/3 states, respectively. These findings highlight the significant role of electron-electron interactions in determining the physical properties of these topological phases.
• Topological Phase Transitions: One of the remarkable aspects of this paper is the investigation of topological phase transitions, driven by the interlayer potential difference. The ν = 1 state undergoes a transition to a non-topological Mott insulator under an increased electric field, while the ν = 2/3 state becomes compressible and likely transits to a correlated Fermi liquid state. This connotes continuous phase transitions analogous to those predicted in recent theoretical works on TMD moiré materials.

Implications and Future Directions

The realization of CIs and FCIs at zero magnetic field in twisted bilayer TMDs such as MoTe₂ paves the way for developing new quantum electronic devices that leverage intrinsic topological properties without the reliance on external magnetic fields. This ability to host topologically nontrivial states in a controlled manner has substantial implications for fault-tolerant quantum computation, as these states could potentially support anyonic excitations necessary for topological qubits.

Furthermore, this paper opens key discussions regarding the stability and manipulation of FCIs within semiconductor moiré materials. The implementation of electric-field-tuned phase transitions presents an efficient mechanism to paper complex phase behavior and control topological order in these systems, offering pathways for future exploration in both experimental and theoretical landscapes.

Future Research: Achieving electrical contacts suitable for transport measurements and dynamic manipulation of anyonic excitations remains a critical challenge. <br>Future research could focus on:

1. Enhancing material synthesis techniques to optimize the purity and uniformity of moiré superlattices.
2. Exploring alternative TMD materials and twist angles to broaden the understanding and applicability of zero-field FCIs.
3. Developing methodologies for real-time manipulation of anyonic states for potential integration into quantum computing platforms.

In conclusion, the paper provides a valuable contribution to the understanding of topological phases and represents a significant step forward in harnessing the novel properties of twistronics within the quest for innovative quantum technologies.