During this seminar, we present the study of screening effects caused by a STM tip in a quantum wire. With the help of a bosonization procedure, we are able to determine non perturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interaction in the wire.

In our approach, we justify that the working Hamiltonian of the whole system is quadratic in given conditions and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function as well as the tunnel density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength.

Then, we study the effects of this electrostatic coupling on the tunneling current and noise. For a local interaction potential, we derive the Green's functions associated to the wire and to the tip. The electrostatic coupling leads to the existence of new correlators, called mixed Green's functions, which are correlators between bosonic fields of the wire and the tip. We calculate the transport properties up to second order with the amplitude of the tunnel transfert: the tunnel current is strongly reduced by the presence of screening. The zero-frequency noise is modified in a similar way, but the Fano factor remains unchanged.