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Comptes Rendus Physique
Volume 17, n° 3-4
pages 430-446 (mars 2016)
Doi : 10.1016/j.crhy.2015.12.005
The beauty of impurities: Two revivals of Friedel's virtual bound-state concept
La beauté des impuretés : nouveaux contextes pour le concept d'état lié virtuel
 

Fig. 1




Fig. 1 : 

Occupancy of the isolated single-level atom, as a function of level position ε d , at two temperatures.


Fig. 2




Fig. 2 : 

Spectral function of the Anderson impurity model (symmetric case ε d =U /2, n d =1) showing the gradual formation of the low-energy ‘Kondo’ resonance as temperature is lowered below T K , as obtained from Numerical renormalisation-group calculations. Reproduced from Ref. [30].


Fig. 3




Fig. 3 : 

Schematic view of a quantum dot (from [35]). A two-dimensional electron gas is created at the interface between a semiconducting layer (in red) and an insulating layer (in white). A metallic backgate, as well as top gates, (in blue) allow for the control of the device.


Fig. 4




Fig. 4 : 

Coulomb blockade staircase and conductance peaks (in units of 2e2/h ), as a function of ‘gate voltage’ ε d , according to the approximate high-temperature expression (32).


Fig. 5




Fig. 5 : 

Conductance through a quantum dot in the Kondo regime: early experiments. Reproduced from Ref. [41].


Fig. 6




Fig. 6 : 

Top: Interferometric device recently used in [46] to measure the phase-shift through a quantum dot (QD). Bottom: Gate-voltage dependence of the measured phase-shift, evidencing in particular the value δ =π /2 at the center of the Coulomb blockade valley. Reproduced from Ref. [46].


Fig. 7




Fig. 7 : 

The Dynamical Mean-Field Theory (DMFT) concept. A solid is viewed as an array of atoms exchanging electrons, rather than as a gas of interacting electrons moving in a periodic potential. DMFT replaces the solid by a single atom exchanging electrons with a self-consistent medium and takes into account local many-body correlations on each site.


Fig. 8




Fig. 8 : 

Generic (schematic) phase diagram of the half-filled Hubbard model, obtained from DMFT, as a function of interaction strength and temperature normalized to the half-bandwidth D . For a lattice with frustration (e.g., with next-nearest neighbour hopping), the transition temperature into phases with long-range spin ordering is reduced. Then, a first-order transition from a metal to a paramagnetic Mott insulator becomes apparent. Adapted from Ref. [62].


Fig. 9




Fig. 9 : 

Schematic evolution of the momentum-integrated spectral function (total density of states) as the coupling is increased, for the half-filled Hubbard model in its paramagnetic phase, according to single-site DMFT. The low-energy (quasiparticle) part of the spectrum gradually narrows down, while the corresponding spectral weight is transferred to the lower and upper Hubbard bands (atomic-like excitations). Adapted from Ref. [63].

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