Twisted Graphene Achieves Tunable Quantum Anomalous Hall Effect with Chern Number 5

Scientists are increasingly focused on manipulating topological states of matter for next-generation electronics, and a new study details a significant advance in controlling the quantum anomalous Hall (QAH) effect. Zhangyuan Chen, Naitian Liu, and Jiannan Hua, all from the Key Laboratory for Quantum Materials of Zhejiang Province at Westlake University, alongside colleagues including Xiang, Zhou, and Ding, report the creation of a series of tunable QAH insulators within the twisted rhombohedral graphene family. Their research demonstrates that the crucial Chern number , and therefore the topological properties , can be actively tuned by altering layer configuration, applying electrostatic doping, and utilising displacement fields, opening up exciting possibilities for dynamically controlling high-Chern-number topological materials and potentially revolutionising device design.

Tuning Chern Number in Twisted Graphene Layers

Scientists have demonstrated a breakthrough in controlling the quantum anomalous Hall (QAH) effect within twisted rhombohedral graphene family materials.This research establishes a highly versatile platform for designing and dynamically controlling high-Chern-number topological matter, paving the way for advanced topological electronics. The team achieved precise tuning of the Chern number, a key characteristic of QAH insulators, through manipulation of layer configuration, in-situ electrostatic doping, and the application of displacement fields. Specifically, researchers observed QAH states with a Chern number equal to the number of rhombohedral layers in twisted monolayer-rhombohedral N-layer graphene, denoted as (1+N) L, at a moiré filling of ν=1, where N represented 3, 4, or 5 layers.
Experiments confirmed these findings through the observation of quantized Hall resistance and validation using the Streda formula, solidifying the theoretical predictions. Furthermore, in twisted monolayer-trilayer graphene, the study unveiled states exhibiting |C|=3 at ν=3, with the sign of the Chern number being reversibly switched via electrostatic doping or displacement field application. This level of control represents a significant advancement in manipulating topological properties. The research doesn’t stop there; in twisted Bernal bilayer-rhombohedral tetralayer graphene (2+4) L, scientists demonstrated a displacement-field-driven topological phase transition between two distinct QAH states possessing Chern numbers of C=3 and C=4 at ν=1.

These devices were fabricated using a van der Waals assembly technique, carefully stacking graphene layers with a controlled twist angle and fully encapsulating them with hexagonal boron nitride and dual-graphite gates. This configuration allows for independent tuning of carrier density and displacement field, crucial for observing the desired topological states. The formation of a moiré superlattice was confirmed through resistivity peaks at full band filling and Brown-Zak oscillations, providing precise characterization of the twist angle. Self-consistent Hartree-Fock calculations based on a continuum model further validated the experimental observations, confirming the presence of isolated topological flat bands with valley Chern numbers matching the layer number. The ability to engineer and dynamically control high-Chern-number topological states opens exciting possibilities for low-power-consumption electronics, multi-channel quantum transport, and the exploration of exotic fractional topological phases. This work represents a substantial step towards realizing functional topological electronics and accessing previously unattainable quantum phenomena, establishing twisted rhombohedral graphene as a premier material for future research in this rapidly evolving field.

Twisted Graphene Multilayers with h-BN Encapsulation exhibit correlated

Scientists engineered a highly controlled platform for investigating the quantum anomalous Hall (QAH) effect using twisted rhombohedral multilayer graphene. The study pioneered a cut-and-stack process to create rhombohedral multilayers with a precisely tuned twist angle of 3θ, ensuring controlled moiré superlattice formation. Researchers then fully encapsulated these stacks with top and bottom hexagonal boron nitride (h-BN) dielectrics, incorporating dual-graphite gates for independent electrostatic manipulation of the n and D parameters. Intentional misalignment of the graphene with the h-BN was crucial to prevent unwanted moiré structures, and Raman mapping confirmed the presence of rhombohedral stacking domains within the final structures.

The team employed self-consistent Hartree-Fock calculations, based on a continuum model, to predict the band structures of twisted 1+N layer graphene, revealing an isolated topological flat band with a nonzero valley Chern number C matching the layer number N, where N equals 3, 4, or 5. This theoretical prediction was then experimentally verified through meticulous device fabrication and characterization. Experiments utilized the dual-gate structure to tune the Fermi level to odd integer moiré fillings, accessing topologically nontrivial states with a Chern number equal to N. Magnetic hysteresis loops were measured on devices with layer configurations of (1+3) L, (1+4) L, and (1+5) L, revealing quantized Hall resistivities of h/3e, h/4e, and h/5e, respectively, directly confirming the layer-dependent Chern number.

Detailed νD maps of the longitudinal resistivity (ρ௫௫) were acquired at a magnetic field of 0 Tesla for all devices, demonstrating the emergence of QAH states when electrons were polarized away from the moiré interface by applying a negative displacement field (D). Fine νD maps, measured under a small magnetic field of 0.1 T (90 mT), revealed clear minima in ρ௫௫ and maxima in ρ௫௬ within specific D ranges: 0.540 ൏D൏0.420V nm⁻¹ for the (1+3) L device and 0.700 ൏D൏0.470V nm⁻¹ for the (1+4) L device. The team further verified the presence of QAH states by measuring ρ௫௫ and ρ௫௬ as functions of both ν and D at fixed parameters, observing well-defined plateaus in ρ௫௬ alongside vanishing ρ௫௫. To independently confirm the Chern number, scientists harnessed the Streda formula, analyzing Landau fan diagrams derived from magnetic field-dependent transport measurements.

The slopes of these diagrams yielded values of C=3 for the (1+3) L device and C=4 for the (1+4) L device, providing further validation of the topological states. The robustness of these QAH effects was demonstrated by maintaining decent quantization up to 3 K, with Curie temperatures reaching approximately 8 K. Furthermore, the study identified an unconventional Chern insulator with C=2 at ν=3/2, suggesting interaction-induced doubling of the moiré unit cell and the potential role of topological charge order.

Tunable Chern Numbers in Twisted Graphene Layers offer

Scientists have achieved a breakthrough in the creation of quantum anomalous Hall (QAH) insulators, demonstrating tunable Chern numbers through innovative layer engineering of twisted rhombohedral graphene. The research details a series of QAH insulators where the Chern number, a key characteristic defining topological electronic properties, can be precisely controlled via layer configuration, electrostatic doping, and displacement field application. Experiments revealed QAH states with a Chern number of C=N in twisted monolayer-rhombohedral N-layer graphene, denoted as (1+N) L, at a moiré filling of ν=1, where N represents the layer number of rhombohedral graphene and takes values of 3, 4, and 5. These findings were experimentally validated through measurements of quantized Hall resistance and confirmation using the Streda formula.

The team measured states with |C|=3 in twisted monolayer-trilayer graphene at ν=3, successfully switching the sign of the Chern number using both electrostatic doping and displacement field manipulation. Furthermore, a displacement-field-driven topological phase transition was demonstrated in twisted Bernal bilayer-rhombohedral tetralayer graphene (2+4) L, transitioning between distinct QAH states with C=3 and C=4 at ν=1. Measurements confirm that this work establishes twisted rhombohedral graphene as a versatile platform for designing and dynamically controlling high-Chern-number topological materials. Specifically, the researchers fabricated devices using a van der Waals assembly technique, carefully stacking monolayer or bilayer graphene onto rhombohedral multilayer graphene with a controlled twist angle of approximately 3θ.

The stacks were fully encapsulated with hexagonal boron nitride and equipped with dual-graphite gates, enabling independent control of carrier density and displacement field. Raman mapping confirmed the presence of rhombohedral stacking domains within the assembled structures. The formation of a moiré superlattice was evidenced by resistivity peaks observed at full band filling (ν=4), allowing for precise determination and verification of the twist angle via Brown-Zak oscillations.Self-consistent Hartree-Fock calculations, based on a continuum model, revealed that the first conduction band in the twisted 1 N L graphene is an isolated topological flat band carrying a valley Chern number directly proportional to the layer number N. An optimized interlayer potential, achieved through displacement field tuning, further enhances the topological properties. These calculations predict that strong Coulomb interactions within the flat band lift spin and valley degeneracy, resulting in a spin- and valley-polarized orbital Chern band at odd integer moiré fillings, paving the way for advanced quantum transport investigations.

Tunable Chern Numbers in Twisted Graphene reveal novel

Scientists have demonstrated tunable quantum anomalous Hall (QAH) insulators in twisted rhombohedral graphene structures.These QAH insulators exhibit a Chern number that can be controlled through layer configuration, electrostatic doping, and displacement field manipulation. Specifically, researchers observed QAH states with a Chern number equal to the number of rhombohedral layers at a particular moiré filling, notably N=3, 4, and 5. Furthermore, the team observed states with a Chern number of ±3 in twisted monolayer-trilayer structures, successfully switching the sign using electrostatic doping or displacement fields.

A displacement-field-driven topological phase transition between distinct QAH states with Chern numbers of 3 and 4 was also demonstrated in twisted Bernal bilayer-rhombohedral tetralayer graphene. This work establishes twisted rhombohedral graphene as a versatile platform for designing and dynamically controlling high-Chern-number topological materials, opening avenues for both fundamental research and potential quantum device engineering. The authors acknowledge that residual disorder or imperfect contact may contribute to the non-quantization of certain measurements, representing a limitation of the current devices. Future research could focus on extending this design principle to create even higher Chern number bands using thicker graphene stacks and exploring the potential for chiral Majorana edge modes through proximity-induced superconductivity, potentially leading to novel topological electronics.