The observation of Chern mosaic and Berry bending magnetism in magic angle graphs

The observation of Chern mosaic and Berry bending magnetism in magic angle graphs

a, Schematic layout showing the backgate voltage V_bg^dc+V_bg^ac applied to the MATBG sample and the corresponding local magnetic field change B_z^ac (x,y) imaged with the scan SOT. The Chern mosaic is shown schematically in the MATBG. b, m_z (x,y,ν_↑) measured at B_a=50 mT and ν= 0.966. The red (blue) colors indicate a paramagnetic-like (diamagnetic-like) local differential magnetization. c, Chern mosaic map derived from the expansion of m_z (x,y,ν_↑) showing the C=1 (KB polarization, blue), C=-1 (KA, red), and C=0 or intermediate semimetallic regions shows ( green). Photo credit: Grover et al.

Researchers from the Weizmann Institute of Science, the Barcelona Institute of Science and Technology, and the National Institute for Material Science in Tsukuba, Japan, have recently investigated a Chern mosaic topology and Berry curvature magnetism in magic-angle graphene. Her work, published in natural physicsprovides new insights into the topological disorder that can occur in physical systems of condensed matter.

“Magic angle twisted two-layer graphene (MATBG) has attracted tremendous interest in recent years due to its experimentally accessible ribbons and created a playground of highly correlated physics,” Matan Bocarsly, one of the researchers who conducted the study, told “Such a correlated phase , which is observed in transport measurements, is the quantum anomalous Hall effect, where topological edge currents are present even in the absence of an applied current magnetic field.”

The quantum anomalous Hall effect is a charge transport-related phenomenon in which the Hall resistance of a material is quantized to what is known as the von Klitzing constant. It is similar to the so-called integer quantum Hall effect, which Bocarsly and his colleague had studied extensively in their previous work, particularly in graphene and MATBG.

Building on what they had learned so far, the researchers set out to further investigate the quantum anomalous Hall effect using the measurement tools they found most effective. To do this, they used a scan superconducting quantum interference device (SQUID) made on the tip of a sharp pipette. This device is an extremely sensitive local magnetometer (ie a sensor that measures magnetic fields) capable of capturing images at the 100 nm scale.

“By varying the carrier density of our sample, we measured the response of the local magnetic field,” Bocarsly explained. “At low applied fields, this magnetic response correlates closely with the internal orbital magnetization of the Bloch wavefunctions induced by the Berry curvature. So essentially we have a local probe that measures local Berry curvature.”

The direct measurement of the orbital magnetism induced by the local Berry curvature in MATBG is an extremely challenging task that had never been achieved before. This is because the signal is extremely weak and therefore eludes most existing magnetic measurement tools.

Bocarsly and his colleagues were the first to directly measure this elusive signal. During their experiments, they also observed a Chern mosaic topology in their sample, thus identifying a new topological fault in MATBG.

“The Chern number, or the topology of an electronic system, is commonly thought of as a global topological invariant,” Bocarsly said. “We observed that the C number is not fixed on a device scale (of the order of microns), but alternates between +1 and -1. This leads to a new type of disorder, topological disorder, in condensed matter systems that must be taken into account for device design and the like theoretical analysis.”

The recent study by this research team contributes significantly to the understanding of MATBG, both in terms of its magnetism and topology. In the future, it could inform the development of more precise theoretical models of this material, and possibly also facilitate its implementation in various quantum computing devices.

“Our low-field local orbital magnetization probe can also be used to study other fundamental properties, such as B. breaking local time-reversal symmetry,” Bocarsly added. “There are still many open questions about MATBG integer fill states and the symmetries they obey, which could be an interesting direction for future investigations.”

Direct evidence of a topological phase transition through a sign change in the Berry curved dipole

More information:
Sameer Grover et al., Chern Mosaic and Berry Bending Magnetism in Magic Angle Graphs, natural physics (2022). DOI: 10.1038/s41567-022-01635-7

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