Heavy-fermion quantum criticality, hidden order and Kondo insulators

5 problems

• Kondo breakdown versus spin-density-wave criticality in heavy-fermion metals

  Contested

  At a heavy-fermion quantum critical point either magnetism appears while the f electrons stay bound to conduction electrons, or the binding itself (Kondo screening) breaks down; which happens decides the theory.

• Do Kondo insulators host charge-neutral fermions with a Fermi surface

  Contested

  Some insulators built from heavy-fermion elements, such as YbB12 and SmB6, show metal-like signatures, heat conduction by mobile carriers and quantum oscillations, while not conducting electricity; this would require particles that carry heat but no charge.

• Is SmB6 a topological Kondo insulator

  Partially resolved

  SmB6 conducts on its surface while its interior insulates at low temperature; theory predicts these surface states are topological, meaning protected by symmetry and band structure, but this is not settled.

• What is the order parameter of hidden order in URu2Si2

  Contested

  Below 17.5 K, URu2Si2 enters an ordered phase that releases a large amount of entropy, yet nearly forty years of experiments have not identified what orders.

• Does the Fermi volume of YbRh2Si2 jump at its critical field

  Contested

  Hall-effect data suggest that the number of electrons in the Fermi sea of YbRh2Si2 changes abruptly at a critical magnetic field when cooled to zero temperature.