Zero-frequency noise in adiabatically driven interacting quantum systems

Abstract

We investigate current-current correlations of adiabatic charge pumping through interacting quantum dots weakly coupled to reservoirs. To calculate the zero-frequency noise for a time-dependently driven system, possibly in the presence of an additional dc bias, we perform within a real-time diagrammatic approach a perturbative expansion in the tunnel coupling to the reservoirs in leading and next-to-leading orders. We apply this formalism to study the adiabatic correction to the zero-frequency noise, i.e., the pumping noise, in the case of a single-level quantum dot charge pump. If no stationary bias is applied, the adiabatic correction shows Coulomb-interaction-induced deviations from the fluctuation-dissipation theorem. Furthermore, we show that the adiabatic correction to the Fano factor carries information about the coupling asymmetry and is independent of the choice of the pumping parameters. When including a time-dependent finite bias, we find that there can be pumping noise even if there is zero adiabatically pumped charge. The pumping noise also indicates the respective direction of the bias-induced current and the pumping current.

Interaction-induced charge and spin pumping through a quantum dot at finite bias

“…In Ref. 44, the zero-frequency pumping noise in adiabatically driven quantum dots is discussed for time-dependent bias, revealing further information on the tunnel coupling asymmetry in cases where the pumped charge is zero.…”

“…Several studies addressed interaction effects in specific setups and regimes. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] In Ref. 29, pumping is investigated in interacting quantum wires.…”

“…36 and 37. A diagrammatic real-time approach, 38 was used to investigate several aspects of adiabatic pumping through weakly coupled interacting quantum-dot systems [39][40][41][42][43][44][45] and served as the basis for nonequilibrium renormalization-group studies that treat the tunneling nonperturbatively. 46 Among the above mentioned studies, only a few discuss the modulation of the applied bias.…”

Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias

“…The equivalence of this picture to the Landauer-Büttiker theory in the noninteracting case is well known [69,70]. However, it can also be extended to perturbative calculations of noise in systems with a Coulombic interaction [63,71] and to the derivation of steady-state fluctuation-dissipation relations involving the current-current correlation functions of quantum dots coupled to a single-phonon mode [72]. Crucially for this work, it involves the propagation of Green's functions along a complex time contour that means the effects of the equilibrium preparation of the system are automatically taken into account in the dynamics resulting from the switch-on of a bias in the leads [68].…”

“…In recent experiments, these quantized voltage pulses, known as levitons, have been experimentally realized [58] and approximated by a biharmonic driving field [59]. Even given the restriction of periodic time dependence, one can study a rich range of phenomena, such as photon-assisted tunneling (PAT) [35,54,60,61], quantum pumping [62,63], and the interplay of external driving field parameters with Fabry-Pérot conductance oscillations in graphene nanoribbon (GNR) and carbon nanotube (CNT) systems [64].…”