*2.2. Kondo E*ff*ects in Silicon Nanostructures*

The three-terminal nano-device [4,5,8–12,16,17], illustrated in Figure 2 is a good example of the most simplified geometry that can be used to observe the quantum effects in silicon, when operating at sufficiently low temperatures.

As shown in Figure 2, in this type of device, two terminals are used for the source and the drain leads, which therefore dictate the direction of transport according to the polarity of the bias voltage applied on the VSource-Drain. The third terminal is typically used to apply a voltage to the VGate and in turn, to control the transition of the device between the ON state and the OFF state at room temperature [1,29,30] and the position of the quantum level that is present in this system at low temperatures when Coulomb effects are observable [4,29,30]. For geometries, like the one shown below in Figure 2, the VGate can in principle also control the transparency of the tunneling barriers <sup>Γ</sup>in,i and <sup>Γ</sup>out,i. While only more complicated structures, for example see the double gate structure, as discussed later on in this review paper, may offer the possibility for an independent control of the position of the quantum states and of the transparency of <sup>Γ</sup>in,i and of <sup>Γ</sup>out,i, even a simple structure like the one described in Figure 2, it is possible to observe many-body effects at sufficient low-temperatures [8–12]. In this review paper, I will often use this geometry as a platform for the description of the interesting effects that can be observed in silicon nano-devices, since the said platform has already demonstrated the capability to offer access to the quantum systems, as illustrated in Figure 1.

The most typical first order regimes of transport, i.e., non-involving virtual states [4,8,9], which can be observed in three terminal nano-devices at low temperatures are the sequential and the coherent regimes of transport [4]. A typical Coulomb Blockade differential conductance (G = dI*SD*/dV*SD*) signature is shown inside the areas delimitated by the pink dashed lines in Figure 3. In this typical Coulomb Blockade situation, only first order transport is expected to arise, and only within those regions limited by the pink lines, while everywhere else no transport should be allowed [4].

However, from Figure 3, it is also clear that, for these systems, it can be affected by many higher order body effects. As such transport can arise in regions represented by the stability diagram in Figure, where it is not expected to, if only first order results are taken into consideration [4]. In fact, in this section, we are mainly interested in discussing in more detail some of these unexpected effects. These involve coherent and incoherent second order charge transitions, such as the ones related to the apparent violation of Heisenberg uncertainty principle and indeed can arise outside the conventional Coulomb Blockade picture. The Kondo, see References [8,9] and references therein, and the co-tunneling, see References [4,31], regimes of transport become observable when the temperature of the system is below a certain critical temperature (e.g., the Kondo Temperature) and when quantum fluctuations in the spin or in the pseudo-spin degrees of freedom, as opposed to temperature ones, become the leading fluctuation effects [4,8–11,32–34].
