Scientists at Princeton University use innovative technology to observe electrons in graphene crystals. Graphene has carbon atoms of a monoatomic layer. They found that the strong interaction between electrons in a high magnetic field prompted them to form an unusual crystal structure. These crystals show the spatial periodicity corresponding to the quantum superposition state electrons. This discovery reveals the complex quantum phase that electrons can form due to interaction, which is the basis of a wide range of phenomena in many materials.

Contemporary technology controls how electrons interact by applying a strong magnetic field and recently stacking multiple layers of graphene together. The discovery of graphene led to the Nobel Prize in Physics in 20 10, which opened up a new field for exploring electronic physics, especially for studying the collective behavior of electrons.

Now, Princeton researchers have found that the strong interaction between electrons in graphene drives them to form a complex pattern of crystal structure superposition determined by quantum effect, and electrons exist at multiple atomic sites at the same time. This experiment, published in the recent journal Science, also shows that this new quantum crystal has undergone strange deformation with the electron wave function.

Previous studies have shown that graphene exhibits novel electrical properties, but no study has ever been able to observe the nature of quantum States so deeply with such a high spatial resolution.

In order to achieve this unparalleled resolution level, researchers use a scanning tunneling microscope based on the "quantum tunneling" effect, operating in a very high vacuum to keep the surface of the sample clean, and make high-resolution measurements at a very low temperature without interference from heat flow.

When an electron reaches the lowest energy state dominated by its quantum properties, it can also be observed by a microscope. In the presence of magnetic field, microscope can be used to determine the spatial structure of quantized energy level. The quantization of energy is a discrete energy value without any intermediate value, which is a characteristic of quantum physics theory. Contrary to classical physics, classical physics allows continuous energy values.

The researchers focused on the lowest quantized energy level in graphene and drew the wave function diagram of the lowest quantized energy level in the presence of magnetic field with a microscope. When graphene was turned into a neutral state by a nearby switch, researchers found complex electron wave patterns.

In metals, the wave function of electrons is distributed in the whole crystal, while in ordinary insulators, electrons are frozen and have no special preference for the crystal structure of atoms. In a very low field, the scanning tunneling microscope image shows that the electron wave function of graphene chooses one sub-lattice position instead of another. More importantly, by increasing the magnetic field, a significant bond mode is observed, which corresponds to the existence of electron wave function in quantum superposition, which means that an electron occupies two unequal positions at the same time.

In cooperation with the University of California, Berkeley, the research team developed a method to extract the mathematical characteristics of electron quantum wave function from scanning tunneling microscope data, that is, to describe the so-called phase angle of its quantum superposition. The analysis reveals the significant winding of one of these phase angles around the defect and the related change of the other phase angle.