What about U in nanoscale systems?
- David Jacob (Universidad del País Vasco UPV/EHU, Spain)
- Massimo Capone (International School for Advanced Studies (SISSA), Italy)
- Silke Biermann (Ecole Polytechnique, France)
State of the art in the ab initio computation of the electronic structure and transport properties of nanoscale junctions consists mainly of density functional theory (DFT) calculations, in combination with the Landauer-Büttiker transport theory  or non-equilibrium Green’s functions . However, by construction this mean-field like methodology cannot capture the dynamic correlations originating from strongly interacting and localized electrons, leading e.g. to Kondo and Coulomb blockade physics. In the last decade, DFT based transport calculations, combined with advanced many-body approaches, such as Dynamical Mean-Field Theory (DMFT)  paved the road for an ab initio description of strong local electronic correlations in nanoscale junctions. Schemes for treating non-local correlation effects in nanoscale junctions, such as the dynamical vertex approximation have been proposed , but have not been implemented yet in an ab initio context.
The description of actual non-equilibrium effects in nanoscale junctions with applied bias voltage requires an out of equilibrium formulation of DMFT  and correspondingly an out of equilibrium solution of the Anderson impurity model  which up until now have only been achieved on the model level. Moderate local and non-local correlation effects in actual out of equilibrium nanoscale junctions can now be described fully ab initio by a non-equilibrium GW approach . On the other hand, very recently a pure DFT-like approach, called steady-state DFT or i-DFT, has been devised for the calculation of transport properties through nanoscale junctions, capable of describing strong correlations effects such as Coulomb blockade and Kondo physics in out of equilibrium situations .
Similar to the case of nanoscale junctions, state of the art for the ab initio description of heterostructures, layered systems in general, surfaces and interfaces mainly relies on DFT calculations of periodic supercells . More recently DMFT and DFT+DMFT schemes for heterostructures, surfaces and interfaces of strongly correlated materials have appeared and have been successfully applied to these kinds of systems . Finally, the latest developments in numerical solver techniques have increased the efficiency of ab initio many-body techniques to a point to make supercells accessible that allow for the theoretical description of correlated materials with defects or vacancies .
 N. D. Lang, PRB 52, 5335 (1995)
 J. Taylor et al., PRB 63, 245407 (2001); J. J. Palacios et al., PRB 64, 115411 (2001); M. Brandbyge et al., PRB 65, 165401 (2002)
 D. Jacob et al., PRL 103, 016803 (2009); ibid., PRB 82, 195115 (2010)
 A. Valli et al., PRL 104, 246402
 P. Schmidt and H. Monien, arXiv:cond-mat/0202046, J. K. Freericks et al., Phys. Rev. Lett. 97, 266408 (2006)
 C. Gramsch et al., Phys. Rev. B 88, 235106 (2013); G. Cohen et al., Phys. Rev. Lett. 112, 146802 (2014)
 K. S. Thygesen, Phys. Rev. B 77, 115333 (2008)
 G. Stefanucci and S. Kurth, Nano Lett. 15, 8020 (2015); S. Kurth and G. Stefanucci, Phys. Rev. B 94, 241103(R) (2016) ; arXiv:1706.02753
 DFT calculations for layered systems
 J. Freericks, “Transport in multilayered nanostructures: the dynamical mean-field theory approach”, World Scientific (2006); P. Hansmann et al., PRL 103, 016401 (2009); F. Lechermann et al., PRB 90, 085125 (2014); H. Chen and A. J. Millis, J. Phys.: Condens. Matter 29, 243001 (2017)
 S. Backes et al., Phys. Rev. B 94, 241110(R) (2016); P. Delange et al., Phys. Rev. B 94, 100102(R) (2016); F. Lechermann et al., Phys. Rev. B 93, 121103(R) (2016)