Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

Abstract

Interacting quantum many-body systems constitute a fascinating research field because they form quantum liquids with remarkable properties and universal behaviour The idea is that they behave as an ensemble of non-interacting 'quasi-particles'. However, non-equilibrium properties have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi liquid theory extended to the non-equilibrium regime in a zero-dimensional system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) (ref. The Kondo effect19 is a typical example of a quantum manybody effect, where a localized spin is screened by the surrounding conduction electrons at low temperature to form a unique correlated ground state. The Kondo state is described well by the Fermi liquid theory at equilibrium 1,9 , which makes it an ideal testbed to go beyond equilibrium. To unveil the universal behaviour of nonequilibrium Fermi liquid 11 , we have used the current fluctuations or shot noise in a Kondo-correlated nanotube quantum dot 18 . When electrons are transmitted through this system, the scattering induces the shot noise, which sensitively reflects the nature of the quasi-particles 20 , as shown in the upper panel of Fig. 1a. A remarkable prediction of the non-equilibrium Fermi liquid theory is that the residual interaction between quasi-particles creates an additional scattering of two quasi-particles which enhances the noise (see the lower panel of Fig. 1a) 10,12-15 . This two-particle scattering is characterized by an effective charge e * larger than e (electron charge). This value, closely related to the Wilson ratio, is universal for the Fermi liquid in the Kondo regime as it depends only on the symmetry group of the system [13][14][15] . Although some aspects of Kondo-associated noise have been reported 8,16,17 , a rigorous, selfconsistent treatment in a regime where universal results apply is at the core of the present work. Actually, by investigating the same nanotube quantum dot in the spin degenerate SU(2) Kondo regime and in the spin-orbit degenerate SU(4) regime, the noise is proved to contain distinct signatures of these two symmetries, confirming theoretical developments of Fermi liquid theory out of equilibrium.In our experiment, we measured the conductance and current noise through a carbon nanotube quantum dot grown by chemical vapour deposition 21 . Iron catalyst was deposited on an oxidized undoped silicon wafer and exposed to 10 mbar of acetylene for 9 s at 900• C. The nanotube was connected with a Pd(6 nm)/Al(70 nm) bilayer deposited by e-gun evaporation. The distance between the contacts is 400 nm and a side gate electrode is deposited to tune the potential of the quantum dot (see Fig. 1b). A magnetic field of 0.08 T is applied to suppress superconductivity of the contacts. To measure accurately the shot noise, our sample is connected to a resonant (2.58 MHz) LC circuit thermalized at the mixing chambe...

Intra- and inter-shell Kondo effects in carbon nanotube quantum dots

“…The first report on the appearance of the exotic many-body state in CNTs was the result of Jarillo-Herrero et al indicating the occurrence of Kondo effect of spin-orbital SU(4) symmetry [14]. Later appeared similar reports also evidencing the occurrence of SU(4) Kondo effect in carbon nanotubes [15][16][17][18][19]. Since it is hardly possible from the conductance to distinguish between SU(2) and SU(4) symmetries, of importance are ultra-sensitive current noise measurements reported in [18][19][20].…”

“…Later appeared similar reports also evidencing the occurrence of SU(4) Kondo effect in carbon nanotubes [15][16][17][18][19]. Since it is hardly possible from the conductance to distinguish between SU(2) and SU(4) symmetries, of importance are ultra-sensitive current noise measurements reported in [18][19][20]. The problem of simultaneous screening of orbital and spin degrees of freedom has been also discussed from theoretical point of view in several publications .…”

“…1b). In odd valleys on the other hand, the observed half transmission of spin-orbital channels corresponds to strong partition, what means strong shot noise (F = 1/2) [18,20,37]. Total conductance curve and noise Fano factor are symmetric vs E 0 = −(3/2)U line (symmetry of 1e and 3e regions), as they reflect transmission values at E F for T = 0 or transmissions averaged over the thermal energy k B T for higher temperatures.…”

Noise of a Chargeless Fermi Liquid

“…For example, the noise of back-scattered current in quantum-Hall devices has been used, e.g., to extract the fractional charge e * of excitations at fillings ν = 1/3 [15,16] or ν = 2/3 [17]. Furthermore, in a strongly interacting local Fermi liquid, realized, e.g., in a quantum dot (QD) attached to normal electrodes at very low temperatures, the noise of the back-scattered current is induced by interactions, and the corresponding effective charge, e * = 5e/3 turns out to reflect the structure of local interactions rather than that of elementary excitations [4,18,19].Superconductors, from this perspective, are of particular interest; while they obviously carry current, elementary excitations in a superconductor do not have a definite charge, and possess only spin. In particular, attaching a superconductor to normal electrodes destroys the charge of electrons in its neighborhood by proximity effect [20], and makes charge ill-defined, there too.…”

“…For example, the noise of back-scattered current in quantum-Hall devices has been used, e.g., to extract the fractional charge e * of excitations at fillings ν = 1/3 [15,16] or ν = 2/3 [17]. Furthermore, in a strongly interacting local Fermi liquid, realized, e.g., in a quantum dot (QD) attached to normal electrodes at very low temperatures, the noise of the back-scattered current is induced by interactions, and the corresponding effective charge, e * = 5e/3 turns out to reflect the structure of local interactions rather than that of elementary excitations [4,18,19].…”