Quantum Hall Effects Meet Superconductivity
Schematic representation of a Cooper pair in the Brillouin zone of a honeycomb lattice
Superconducting phase diagram for Landau levels created by synthetic gauge fields preserving time reversal symmetry
Prof. Bruno Uchoa proposed the existence of an exotic condensate of electron pairs which can live deep inside the quantum Hall regime. This novel quantum state of matter may be present in a class of materials with synthetic gauge fields. Those crystals can form the so called Landau levels, a fingerprint of the quantum Hall effect, in the complete absence of a magnetic flux at every lattice site. Known examples include strained honeycomb crystals and deformed optical lattices. In a recent article published in Physical Review Letters, Bruno suggested that this novel state offers promising perspectives for studying the coexistence of quantum Hall effects and superconductivity, even in the quantum limit.
A cornerstone of quantum physics and transport is exemplified in the quantum Hall effect, where electrons moving is a 2D plane subjected to a perpendicular magnetic field form cyclotronic orbits having a discrete spectrum of energy levels, known as Landau levels. In bulk, the cyclotronic motion of the electrons leads to insulating behavior, while at the edges, skipping orbits create metallic edge states with quantized conductivity. Another cornerstone is the phenomenon of superconductivity, where electrons form Cooper pairs, which can carry charge without dissipating any current. Those two quantum states do not typically coexist with each other, because of a known property of superconductors to completely expel magnetic fluxes in their bulk, the Meissner effect.
This new quantum state of matter proposed in Bruno's work could be an example of a class of phase transitions driven by quantum fluctuations. Here, zero temperature phase transitions separate compressible superconducting states, at partial filling of the Landau Levels, from incompressible non-superconducting states, at integer filling. Those states were predicted to show exotic transport and spectroscopic signatures, such as anomalous quantized conductivities in normal-superconducting junctions and Andreev edge states. The high degeneracy of the Landau levels also motivates serious proposals for the detection of high temperature superconductivity in similar systems.
Read more: B. Uchoa, Y. Barlas, Phys. Rev. Lett. 111, 046604 (2013)