Violation of Onsager symmetry for a ballistic channel Coulomb coupled to a quantum ring

We investigate a scattering of electron which is injected individually into an empty ballistic channel containing a cavity that is Coulomb coupled to a quantum ring charged with a single-electron. We solve the time-dependent Schrödinger equation for the electron pair with an exact account for the electron-electron correlation. Absorption of energy and angular momentum by the quantum ring is not an even function of the external magnetic field. As a consequence we find that the electron backscattering probability is asymmetric in the magnetic field and thus violates Onsager symmetry. Introduction. – The transport properties of twodimensional mesoscopic and nano-scale conductors are usually studied in external magnetic field B applied perpendicular to the plane of electron confinement. The current / voltage (I/V ) characteristics of the device is described by its conductance (G), I(B, V ) = G(V,B)V . In the linear transport regime the conductance is independent of V , moreover it is an even function of the magnetic field [1] G(B) = G(−B) – relation that is known as the Onsager symmetry. In the Landauer approach the linear conductance G(B) is determined by the probability T (B) that a Fermi-level electron is transferred from one terminal to the other G(B) = eT (B)/h. The dependence of the transfer probability on B results from Aharonov-Bohm interference and from deflection of the electron trajectories by the Lorentz force. Due to the magnetic forces the kinetics of the electron transfer through an asymmetric channel is different for opposite magnetic field orientations. However, the backscattered trajectories are identical for ±B which results in the Onsager symmetry. In the non-linear transport regime the magnetic-field symmetry of the current can be broken [2]. The magnetic asymmetry of the non-linear current was observed in various systems, including open quantum rings [3] and dots (cavities) [4] as well as in carbon nanotubes [5]. A number of scenarios for the appearance of the asymmetric current were given, including potential landscape being not an even function of the magnetic field [2, 6], effects of the electron-electron interaction within the channel [7] or capacitive coupling of the channel to the other conductor which is driven out of equilibrium [8] by an applied bias. The studies of the magnetic field asymmetry of the current [2–8] concerned standard devices which are filled by the electron gas. Recently, Gustavsson et al. [9] studied experimentally the Aharonov-Bohm self-interference of electrons injected into the channel one by one. In the experiment single-electron injection occurs due to Coulomb blockade which allows only a single electron to move between the source and the drain. The single-electron valve applied in the device [9] is a quantum dot occupied by a single-electron with the energy below the Fermi energy of the source. The electron can be ejected from a bound quantum dot state into the channel only using the excess energy of another electron which tunnels from the source Fermi level to replace the ejected electron in the quantumdot-confined state (so called co-tunneling process). In the experiment [9] the transmission of electrons through the device is detected by a counter instead of ammeter applied in standard experiments that measure the current carried by the electron gas. The electron counter consists of a quantum point contact charge coupled to the channel. In the single-electron injection regime the counter registers transmission of only about a hundred electrons