Coherent oscillations of current due to nuclear spins

Abstract

We propose a mechanism for very slow coherent oscillations of current and nuclear spins in a quantum dot system, that may qualitatively explain some recent experimental observations. We concentrate on an experimentally relevant double dot setup where hyperfine interaction lifts the spin blockade. We study the dependence of the magnitude and period of the oscillations on magnetic field and anisotropy. DOI: 10.1103/PhysRevB.72.033301 PACS number͑s͒: 73.63.Kv, 73.23.Ϫb, 71.70.Jp There are significant experimental and theoretical efforts aimed to utilize and manipulate the electron spin in the context of electronic transport; these are commonly referred to as spintronics.1,2 Some of them involve nuclear spins as well. Many efforts concern GaAs semiconductor structures where the hyperfine interaction between electron and nuclear spin is relatively strong.3 Furthermore, the nuclear spin relaxation times are much longer than the time scales related to electron dynamics. 4,5 This time scale separation has facilitated experiments where a quasistationary polarization of the nuclear system was achieved and its effect on the electronic transport was observed.6-8 Recent experiments implement interesting ways of controlling the interaction of electron and nuclear spin, 9,10 whereby the coherent oscillations between "up" and "down" polarized nuclear systems have been observed. 11Transport experiments with quantum dots allow for a detailed study and control of the quantum dot energy spectrum, both in the regime of linear transport and in the nonlinear regime of excitation spectroscopy.12,13 They reveal interesting regimes where unusual mechanisms of electron transport are the dominant ones. For instance, in the Coulomb blockade regime the direct charging of the quantum dot is forbidden by energy conservation and the residual current is due to cotunneling.14,15 The effect of Coulomb blockade on the nuclear spin-relaxation time was considered in Ref.16. Another regime is the so-called spin blockade where the direct electron transfers are blocked by virtue of spin conservation.17 Spin blockade may be achieved in various ways, e.g., with spin polarized leads.18 Recent experiment realizes the spin blockade in a double dot system, where the absence of transitions between spin-singlet and spin-triplet states in the dots explains the current rectification observed.19 Any spin-flip mechanism facilitates these transitions, giving rise to a small residual current.The same group has recently reported 20 an unexpected and unusual result. They have observed coherent oscillations of the residual current in this regime with a period in the range of seconds. This extremely long time scale together with the fact that the oscillation period and amplitude can be modified by resonant excitation of the nuclear spins strongly suggests that the origin of the oscillations may be traced to the hyperfine interaction. 20In this paper we propose a concrete mechanism for these oscillations that can at least qualitatively explain the observation made in ...

Solution for the dynamics of the BCS and central spin problems

“…For example, it emerged in the studies of electron spin dynamics in disordered insulators 17 and of coherent spin tunnelling in ferromagnetic grains 18 . More recently, it attracted considerable attention as a model for decoherence of qubits 19,20,21,22 . In particular, it can be used to model 19,20 the hyperfine interaction of a localized electron spin with nuclear spins and the spin-dependent transport 23 in GaAs quantum dots.…”

“…More recently, it attracted considerable attention as a model for decoherence of qubits 19,20,21,22 . In particular, it can be used to model 19,20 the hyperfine interaction of a localized electron spin with nuclear spins and the spin-dependent transport 23 in GaAs quantum dots. In these cases, it provides an adequate description of spin dynamics at times shorter than the nuclear spin relaxation time in the regime where the orbital level spacing in the dot is much larger than the temperature and typical interaction energies.…”

Temperature-dependent dynamical nuclear polarization bistabilities in double quantum dots in the spin-blockade regime

“…10,51,64 Other experimental findings like long-lived current oscillations in time 6,10 and transient phenomena in the leakage current 44 have also been attributed to the nuclear spin environment. [95][96][97] Furthermore, it has been shown Leakage Current Feedback Scheme…”

Integrable dynamics of coupled Fermi-Bose condensates

“…In these problems the goal is to describe the dynamics of a many-body system following a sudden perturbation that drove the system out of an equilibrium. The system in question can be a BCS superconductor [1,2,3,4,5,6,7,8,9,10,11], coupled FermiBose condensates [12,13], or a single electronic spin interacting with many nuclear spins (the central spin model) [14,15,16,17,18,19,20]. A common feature of all these problems is that they can be formulated in terms of spin Hamiltonians, which belong to a class of integrable systems known as Gaudin magnets [21,22,23].…”