*Article* **Current Correlations in a Quantum Dot Ring: A Role of Quantum Interference**

### **Bogdan R. Bułka \* and Jakub Łuczak**

Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Pozna ´n, Poland; jakub.luczak@ifmpan.poznan.pl

**\*** Correspondence: bogdan.bulka@ifmpan.poznan.pl

Received: 29 April 2019; Accepted: 22 May 2019; Published: 24 May 2019

**Abstract:** We present studies of the electron transport and circular currents induced by the bias voltage and the magnetic flux threading a ring of three quantum dots coupled with two electrodes. Quantum interference of electron waves passing through the states with opposite chirality plays a relevant role in transport, where one can observe Fano resonance with destructive interference. The quantum interference effect is quantitatively described by local bond currents and their correlation functions. Fluctuations of the transport current are characterized by the Lesovik formula for the shot noise, which is a composition of the bond current correlation functions. In the presence of circular currents, the cross-correlation of the bond currents can be very large, but it is negative and compensates for the large positive auto-correlation functions.

**Keywords:** quantum interference; shot noise; persistent current
