Quantum Oscillations in Graphene

Oscillations of physical properties of materials with magnetic field are a well-known and important phenomenon in physics. Despite having a variety of experimental manifestations, there are only a few basic types of oscillations: those of either quantum or semiclassical origin. Quantum oscillations are determined by the Landau quantization of the energy levels of metals in high magnetic fields and are usually observed at very low temperatures and in very clean single crystalline metallic materials.

The study of these oscillations gives us important information about particle and atom properties. For example, it allows to map out the Fermi surface. It also allows to extract information about the masses and the mean free path of the quasiparticles and the degree of electronic correlations in various strongly correlated electronic systems.

Quantum oscillations can be seen in cyclotron motion of charge carriers in metals and semiconductors. This motion leads to Landau quantization and magneto-oscillatory behavior in their properties. Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. When subject to both a magnetic field and a periodic electrostatic potential, two-dimensional systems of electrons exhibit a self-similar recursive energy spectrum. Known as Hofstadter’s butterfly, this complex spectrum results from an interplay between the characteristic lengths associated with the two quantizing fields and is one of the first quantum fractals discovered in physics.

Partial periodic table with a picture of each Fermi surface.

Usually, to observe these quantum oscillations, it is required to used cryogenic temperatures. However, a research team led by R. Krishna Kumar from the University of Manchester showed that graphene superlattices support a different type of quantum oscillation that does not rely on Landau quantization. They observed that these oscillations are extremely robust and persist well above room temperature in magnetic fields of only a few tesla. They attributed this phenomenon to repetitive changes in the electronic structure of superlattices such that charge carriers experience effectively no magnetic field at simple fractions of the quantum flux. They used this to explore the physics of Hofstadter butterfly systems at high temperatures.

“Oscillatory quantum effects always present milestones in our understanding of material properties. They are exceedingly rare. It is more than 30 years since a new type of quantum oscillation was reported. […] Our oscillations stand out by their extreme robustness, happening under ambient conditions in easily accessible magnetic fields.” – Andre Geim, University of Manchester

They obtained interesting results on Hofstadter’s butterfly, a fractal pattern that describes the behavior of electrons in a magnetic field. In the original theoretical work on which Hofstadter’s butterfly is based electrons modeled to create the fractal pattern were treated as Bloch electrons (electrons that do not interact with one another and move within a periodic electric potential within a lattice). The new results shown in graphene illustrates how these complex fractal patterns can be viewed as Langmuir quantization which is the quantization of cyclotron orbits (taking what is normally thought of as a circular orbit and instead viewing it as linear).

“Our work helps to demystify the Hofstadter butterfly. The complex fractal structure of the Hofstadter butterfly spectrum can be understood as simple Landau quantization in the sequence of new metals created by a magnetic field.” – Professor Vladimir Falko, Director of the National Graphene Institute

Quantum oscillations have always been considered as very brittle, easily destroyed at higher temperatures. But now it is proven that they can be observed at room temperature, or even higher. This is a very promising news for possible new applications of these and other systems which are based on Van der Waals stacking of two-dimensional materials.

Continue reading at: https://phys.org/news/2017-09-quantum-phenomena-graphene-superlattices.html