Tomonaga–Luttinger physics in electronic quantum circuits

Abstract

In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga–Luttinger liquids is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances are suppressed at low energy, a phenomenon called dynamical Coulomb blockade. Here we investigate the conductance of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance, and demonstrate a proposed link to Tomonaga–Luttinger physics. We reformulate and establish experimentally a recently derived phenomenological expression for the conductance using a wide range of circuits, including carbon nanotube data obtained elsewhere. By confronting both conductance data and phenomenological expression with the universal Tomonaga–Luttinger conductance curve, we demonstrate experimentally the predicted mapping between dynamical Coulomb blockade and the transport across a Tomonaga–Luttinger liquid with an impurity.

Transport across an impurity in one-dimensional quantum liquids far from equilibrium

“…While the clean system would display, despite interactions, ideal conductance quantization in the presence of metallic leads [1][2][3][4] , the impurity at zero temperature is capable of turning the perfect conductor into an insulating link, giving rise to power law corrections to transport coefficients at finite temperature or finite voltage bias [5][6][7] . The physics of a single impurity in a Luttinger liquid has attracted enormous attention in the past decades [8][9][10] and still finds beautiful applications in systems such as the edges of a quantum spin Hall insulator 11,12 or in electronic quantum circuits [13][14][15] . Traditional condensed matter transport settings involve a system initially in thermal equilibrium which is perturbed away from it by the action of some external field conjugate to a conserved current.…”

Quantum sweeps, synchronization, and Kibble-Zurek physics in dissipative quantum spin systems

“…A large collection of harmonic oscillators (bosons) can simulate dissipation, resulting in the celebrated Caldeira-Leggett model 5 , giving rise to dissipation-induced quantum phase transitions observed in various contexts 6,7 . For example, a ohmic bosonic bath can be engineered through a long transmission line or a one-dimensional Luttinger liquid 8,9 .…”

Giant magnetoelectric effect in magnetic tunnel junctions coupled to an electromagnetic environment

“…Finally, let us give some realistic estimates for the induced voltage based on numbers utilized for observing the DCB in normal (ultra-small) tunnel junctions 24,25 and Josephson (superconducting) junctions 26 . Since we are considering ferromagnetic metals, we believe that such estimates are also appropriate for ultra-small MTJs, such as those investigated here.…”