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Tphysicsletters/vol-10/no-1296/CInteger and fractional Chern insulators in twisted bilayer MoTe2

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Integer and fractional Chern insulators in twisted bilayer MoTe2

Yihang Zeng1

Theoretical Physics Letters

2023 ° 02(05) ° 10-1296

https://www.wikipt.org/tphysicsletters

DOI: 10.1490/698700.590tpl

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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 1-4 . To date, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field 3, 5-11, but fractional Chern insulators have been reported only in graphene-based systems under a finite magnetic field 12, 13. The emergence of semiconductor moiré materials 14, 15, which support tunable topological flat bands 16, 17, opens a new opportunity to realize fractional Chern insulators 18-20. 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 𝝂 = 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 𝝂 = 𝟏 and 𝝂 = 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 21 in semiconductor moiré materials.

Introduction

Fractional Chern insulators (FCIs), which can in principle host the fractional quantum Hall effect and non-Abelian excitations at zero magnetic field, are highly sought-after phases of matter in condensed matter physics 22-28. The experimental realization of FCIs may also revolutionize other fields, such as topological quantum computation 21. But FCIs have proven notoriously challenging to realize experimentally because they require not only a topological flat band but also particular quantum band geometry 17-19, 29-33 . Band-structure engineering by forming moiré superlattices has emerged as a powerful approach to realize topological flat bands 11, 14, 15, 29, 34. A recent experiment has shown that FCIs can be stabilized in magic-angle twisted bilayer graphene at about 5 T, where the magnetic field is mainly responsible for redistributing the Berry curvature of the original topological bands 13. With widely tunable electronic properties, moiré materials based on transition metal dichalcogenide (TMD) semiconductors have been predicted to support topological flat bands with appropriate band geometry to favor FCIs at zero magnetic field 18-20. Of particular interest are small-angle twisted TMD homobilayers of the AA-stacking type (Fig. 1a). They support a honeycomb moiré lattice with two sublattices residing in two different layers 16, 17. The topmost moiré valence bands are composed of the spin-valley locked states from the K or K’ valley of the monolayers. Theoretical studies have shown that the complex interlayer hopping between the sublattice sites can induce topological moiré valence bands with non-zero spin/valley-resolved Chern numbers (𝐶) 16, 17 , and for certain twist angles, the topmost moiré band (with |𝐶| = 1) is nearly flat and exhibits a flat Berry curvature distribution 16-19. This opens the possibility of stabilizing FCIs at fractional fillings. Here we report the observation of an integer Chern insulator (CI) at 𝜈 = 1 and FCI at 𝜈 = 2/3 under zero magnetic field in 3.4-degree twisted bilayer MoTe2 (tMoTe2). The filling factor 𝜈 measures the hole doping density (n) in units of the moiré unit cell density (𝑛𝑀), and 𝜈 = 1 corresponds to quarter-band filling. These states display hallmarks of a CI. Specifically, they are incompressible, spontaneously break time reversal symmetry (TRS), linearly disperse in doping density with applied magnetic field, and carry an orbital magnetization that jumps across the charge gap. Furthermore, as the interlayer potential difference increases, our experiment at 1.6 K indicates a continuous topological phase transition from the integer CI to a topologically trivial Mott insulator, whereas the FCI becomes compressible.

Conclusion

We demonstrate an integer and a fractional CI at zero magnetic field in small-angle tMoTe2 by the local measurements of the electronic compressibility and TRS breaking. We also observe evidence for a continuous topological phase transition for both CI states that is induced by the interlayer potential difference. Our findings leave open many questions, such as the nature of the FCI and possible existence of FCIs in tMoTe2 and related materials that have no analogs in the fractional quantum Hall system. A pressing experimental task is to develop electrical contacts to these materials for transport measurements and for manipulation of the anyonic excitation for topological quantum applications. During the preparation of this manuscript, we learned about the work that reports signatures of FCIs in tMoTe2 using optical spectroscopy techniques 48 , as well as another work that reports integer CIs in tWSe2 using local compressibility measurements 49.

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Abstract

Introduction

Conclusion

References