In condensed matter physics, Hofstadter’s butterfly describes the complex energy spectrum of electrons in a 2D lattice subjected to both a magnetic field and a periodic potential. It refers to the behavior of electrons in specific types of materials under specific conditions.
Researchers at The University of Manchester’s National Graphene Institute (NGI) have revisited one of the most ancient materials on Earth, graphite, and discovered new physics that has eluded the field for decades.
Natural graphite is not as simple as one might think, despite being composed entirely of layers of carbon atoms arranged in a honeycomb pattern. The order in which these atomic layers stack on top of one another can produce different types of graphite with different stacking orders of consecutive atomic planes.
Because hexagonal stacking characterizes the majority of naturally occurring graphite, it is one of the most “ordinary” materials on the planet. The graphite crystal structure is a repeating pattern. This pattern is disrupted at the crystal’s surface, resulting in ‘surface-states,’ which are like waves that gradually fade away as you go deeper into the crystal. However, how surface states in graphite can be tuned is not well understood.
The unusual 2.5D quantum Hall effect in graphite arises as the interplay between two quantum physics textbook phenomena – Landau quantization in strong magnetic fields and quantum confinement, leading to yet another new type of quantum effect.Prof. Vladimir Fal’ko
The two leading fields in 2D materials research are Van der Waals technology and twistronics (stacking two 2D crystals at a twist angle to tune the properties of the resulting structure to a large extent due to moiré pattern formed at their interface). The NGI team, led by Prof. Artem Mishchenko, is now using a moiré pattern to tune the surface states of graphite, similar to a kaleidoscope with everchanging pictures as the lens is rotated, revealing the extraordinary new physics behind graphite.
In particular, Prof. Mishchenko expanded twistronics technique to three-dimensional graphite and found that moiré potential does not just modify the surface states of graphite, but also affects the electronic spectrum of the entire bulk of graphite crystal. Much like the well-known story of The Princess and The Pea, the princess felt the pea right through the twenty mattresses and the twenty eider-down beds. In the case of graphite, the moiré potential at an aligned interface could penetrate through more than 40 atomic graphitic layers.
This research, published in the latest issue of Nature, studied the effects of moiré patterns in bulk hexagonal graphite generated by crystallographic alignment with hexagonal boron nitride. The most fascinating result is the observation of a 2.5-dimensional mixing of the surface and bulk states in graphite, which manifests itself in a new type of fractal quantum Hall effect – a 2.5D Hofstadter’s butterfly.
Prof. Artem Mishchenko of The University of Manchester, who discovered the 2.5-dimensional quantum Hall effect in graphite previously, stated, “Graphite gave rise to the celebrated graphene, but people are normally not interested in this ‘old’ material.” And now, despite our accumulated knowledge of graphite of various stacking and alignment orders over the years, we still find graphite to be a very appealing system with so much yet to be explored.” One of the paper’s lead authors, Ciaran Mullan, added, “Our work opens up new possibilities for controlling electronic properties by twistronics not only in 2D but also in 3D materials.”
Prof. Vladimir Fal’ko, Director of the National Graphene Institute and theoretical physicist at the Department of Physics and Astronomy, added: “The unusual 2.5D quantum Hall effect in graphite arises as the interplay between two quantum physics textbook phenomena – Landau quantization in strong magnetic fields and quantum confinement, leading to yet another new type of quantum effect.”