## Final Report Summary - NANOSPEC (Novel Out-of-Equilibrium Spectroscopy Techniques to Explore and Control Quantum Phenomena in Nanocircuits)

The NANOSPEC project is devoted to the investigation of quantum phenomena in electronic nanocircuits.

New knowledge is unveiled regarding the quantum transport of heat, the correlated Kondo and Luttinger physics, the quantum laws of electricity in mesoscopic circuits (charge quantization, conductance renormalization) and the quantum Hall physics.

On a technical level, we have demonstrated the record-low electronic temperature of 6 mK for micron-scale quantum circuits, and developed a cryogenic noise measurement setup which sets the international state of the art for quantum circuits (with a sensitivity below 10^{-31} A^2/Hz).

The three main international firsts of the project are:

(i) the measurement of the quantum limit of heat flow along a single electronic channel,

(ii) the demonstration that the Kondo effect also applies to the macroscopic quantum charge states of electronic circuits,

(iii) the characterization of the quantum collapse of charge quantization in mesoscopic circuits.

(i) At the quantum scale, particles in a conductor flow across independent modes or channels. The quantum of thermal conductance sets a maximum fundamental limit to the heat flow across a single transport channel. Remarkably, this quantum bound is predicted to be broadly universal, independent of the type of particles carrying heat. From the deep relationship between heat, entropy and information, this signals a general limit on information transfer. Up to now the quantum of thermal conductance was only measured for bosons, across as few as 16 phonon channels. We have performed the first measurement for Fermi particles (electrons) and across a single transport channel. This experiment paves the way for the quantum manipulation of heat at the nanoscale.

(ii) The Kondo effect usually results from the coupling of a magnetic impurity with the conduction electrons in a metal. Collectively, the electrons attempt to screen the spin of the impurity when cooled down below a characteristic temperature called Kondo temperature. In the so-called “charge” Kondo effect, the spin of the magnetic impurity is replaced by a pseudo-spin constituted by two degenerate charge states of a small metallic island. The major interest of the charge Kondo effect is for exploring the physics of quantum phase transitions on a completely characterized device allowing for an exact theoretical description. Quantum phase transitions are induced par quantum fluctuations, at zero temperature, when a parameter is varied. For the charge Kondo effect, this parameter is the coupling between conduction electrons and charge pseudo-spin. We have realized the charge Kondo effect using a hybrid metal-semiconductor implementation of the single-electron transistor. With this device, completely adjustable in-situ by field effect, we have determined the relationship between coupling strength and Kondo temperature, and observed the arising of the predicted quantum phase transition.

(iii) We address the very fundamental problem of charge quantization in the nodes of electrical circuits: how does charge quantization evolve when one progressively connects the node? This elemental question is also central for the development of functional `single-electronics’ devices, based on the manipulation of single electrons in circuits. In weakly coupled small conductors the charge is quantized, as evidenced with the emblematic single-electron transistor. As the coupling is increased, theory predicts that the quantization of charge is progressively destroyed by quantum fluctuations. The charge is expected to be completely unquantized when such a circuit node is connected through one perfectly ballistic electrical channel, and to scale as the square root of the residual reflection probability near the ballistic critical point. We have performed the first experimental characterization of the quantum collapse of charge quantization. With a hybrid metal-semiconductor single-electron transistor, we establish quantitatively and expand the theoretical predictions regarding one of the most basic problems, the quantized character of the charge in circuits.

New knowledge is unveiled regarding the quantum transport of heat, the correlated Kondo and Luttinger physics, the quantum laws of electricity in mesoscopic circuits (charge quantization, conductance renormalization) and the quantum Hall physics.

On a technical level, we have demonstrated the record-low electronic temperature of 6 mK for micron-scale quantum circuits, and developed a cryogenic noise measurement setup which sets the international state of the art for quantum circuits (with a sensitivity below 10^{-31} A^2/Hz).

The three main international firsts of the project are:

(i) the measurement of the quantum limit of heat flow along a single electronic channel,

(ii) the demonstration that the Kondo effect also applies to the macroscopic quantum charge states of electronic circuits,

(iii) the characterization of the quantum collapse of charge quantization in mesoscopic circuits.

(i) At the quantum scale, particles in a conductor flow across independent modes or channels. The quantum of thermal conductance sets a maximum fundamental limit to the heat flow across a single transport channel. Remarkably, this quantum bound is predicted to be broadly universal, independent of the type of particles carrying heat. From the deep relationship between heat, entropy and information, this signals a general limit on information transfer. Up to now the quantum of thermal conductance was only measured for bosons, across as few as 16 phonon channels. We have performed the first measurement for Fermi particles (electrons) and across a single transport channel. This experiment paves the way for the quantum manipulation of heat at the nanoscale.

(ii) The Kondo effect usually results from the coupling of a magnetic impurity with the conduction electrons in a metal. Collectively, the electrons attempt to screen the spin of the impurity when cooled down below a characteristic temperature called Kondo temperature. In the so-called “charge” Kondo effect, the spin of the magnetic impurity is replaced by a pseudo-spin constituted by two degenerate charge states of a small metallic island. The major interest of the charge Kondo effect is for exploring the physics of quantum phase transitions on a completely characterized device allowing for an exact theoretical description. Quantum phase transitions are induced par quantum fluctuations, at zero temperature, when a parameter is varied. For the charge Kondo effect, this parameter is the coupling between conduction electrons and charge pseudo-spin. We have realized the charge Kondo effect using a hybrid metal-semiconductor implementation of the single-electron transistor. With this device, completely adjustable in-situ by field effect, we have determined the relationship between coupling strength and Kondo temperature, and observed the arising of the predicted quantum phase transition.

(iii) We address the very fundamental problem of charge quantization in the nodes of electrical circuits: how does charge quantization evolve when one progressively connects the node? This elemental question is also central for the development of functional `single-electronics’ devices, based on the manipulation of single electrons in circuits. In weakly coupled small conductors the charge is quantized, as evidenced with the emblematic single-electron transistor. As the coupling is increased, theory predicts that the quantization of charge is progressively destroyed by quantum fluctuations. The charge is expected to be completely unquantized when such a circuit node is connected through one perfectly ballistic electrical channel, and to scale as the square root of the residual reflection probability near the ballistic critical point. We have performed the first experimental characterization of the quantum collapse of charge quantization. With a hybrid metal-semiconductor single-electron transistor, we establish quantitatively and expand the theoretical predictions regarding one of the most basic problems, the quantized character of the charge in circuits.