# P9: Time scales in current-current correlations

## Project Description

Current-current correlations (CCC) contain information on fluctuations, particle statistics, and time scales, which can not be extracted solely from the average current through a mesoscopic sample. This project deals with the investigation of CCC in time-dependently driven nanoscale systems (e.g. due to the driving with laser fields or time-dependent gates) in which the onsite Coulomb interaction between electrons plays an important role. These investigations will be conducted with the help of an extended real-time technique (RTT) ^{(1)} and in the context of a current density functional theory (CDFT).

In the first part of this project we will deal with a model for a quantum dot contacted to electronic reservoirs and driven out of equilibrium by time-dependent gate potentials. There is currently strong interest in this type of setups since they can serve as sources of single electrons ^{(2),(3),(4)}, which are promising for metrology and for the implementation of repeated controlled quantum operations. We plan to extract information from the frequency-dependent CCC on the fluctuation in the number of emitted particles and on the statistics of their emission times. These can be directly measured in experiment as has recently been shown in a weakly interacting setup ^{(5),(6)}. First signatures of the impact of Coulomb interaction on the charge relaxation rates^{ (7)} from a quantum dot have recently been investigated in the zero-frequency CCC ^{(8)}. In this project, we will extend a perturbative RTT for a weakly tunnel-coupled quantum dot to the calculation of the frequency-dependent CCC, also giving access to the short-time behavior of the fluctuations in the emission process.

In addition to the physical insights on the time-dependently driven systems gained with the help of the frequency-dependent CCC we will also obtain insight into the general structure of the CCC in an interacting system. In the second part of the project this new insight will be used as the basis to improve a different method: In time-dependent density and current-density functional theory (CDFT) we use the correlation functions to assess the quality of available approximations to the exchange-correlation potential or vector potential. These approximations are essential in DFT and CDFT as the exact functional of the potentials is unknown and an approximation is needed in order to map the interacting many-body system onto an effective non-interacting system. We intent to improve the currently

available approximations since they are usually adiabatic, i.e. frequency independent, which is a fundamental

deficiency of the approximation in time-dependently driven systems ^{(9),(10),(11)}. By using the CCC instead of the density-density correlation function we profit from the fact that the current itself already contains a time-dependent change of the density. Hence, the desired non-local time-dependence of the functional can be easier realized using a current density functional instead of a density functional^{(12),(13)}.

This project has connections to P8 and P14.

(1) J. Splettstoesser, M. Governale, J. König and R. Fazio, Phys. Rev. B **74**, 085305 (2006)

(2) G. Fève, A. Mahé, J.-M. Berroir, T. Kontos, B. Plaçais, C. Glattli, A. Cavanna, B. Etienne and Y. Jin,

Science **316**, 1169 (2007)

(3) B. Kaestner, V. Kashcheyevs, S. Amakawa, L. Li, M. D. Blumenthal, T. J. B. M. Janssen, G. Hein, K. Pierz,

T. Weimann, U. Siegner and H. W. Schumacher, Phys. Rev. B **77**, 153301 (2008)

(4) V. F. Maisi, Yu. A. Pashkin, S. Kafanov, J. S. Tsai and J. P. Pekola, New J. Phys. **11**, 113057 (2009)

(5) A. Mah*é et al.*, Phys. Rev. B **82**, 201309(R) (2010)

(6) F. D. Parmentier, E. Bocquillon, J.-M. Berroir, D. C. Glattli, B. Plaçais and G. Fève,

Phys. Rev. B **85**, 165438 (2012)

(7) J. Splettstoesser, M. Governale, J. König and M. Büttiker, Phys. Rev. B. **81**, 165318 (2010)

(8) R. Riwar, J. Splettstoesser and J. König, Phys. Rev. B. **87**, 195407 (2013)

(9) N. Helbig, J. I. Fuks, M. Casula, M. J. Verstraete, M. A. L. Marques, I. V. Tokatly and A. Rubio,

Phys. Rev. A **83**, 032503 (2011)

(10) J. I. Fuks, N. Helbig, I. V. Tokatly and A. Rubio, Phys. Rev. B **84**, 75107 (2011)

(11) N. T. Maitra, *Memory: History, Initial-State Dependence, and Double-Excitations* in *Fundamentals of Time-Dependent Density Functional Theory*, M. A. L. Marques, N. T. Maitra, F. Nogueira, E. K. U. Gross and A. Rubio (eds.) (Springer-Verlag, Berlin-Heidelberg, 2011)

(12) G. Vignale and W. Kohn, Phys. Rev. Lett. **77**, 2037 (1996)

(13) M. Gatti, J. Chem. Phys.** 134**, 084102 (2011)