Summation of Path Integrals for Resonant Transport through an Interacting Quantum-Dot Spin Valve

Abstract

The field of spintronics, where the electron spin is used next to the electron charge as an additional degree of freedom for information transfer, shows huge promise for future developments in the area of information processing and storage. Of particular importance to this field is the spin valve, a device that allows control of spin transport via external means, basically a `spin transistor'. Continued miniaturization of the spin valve motivates the proposition of a quantum-dot spin valve, the analog to a single-electron transistor. Such a device can be constructed from a quantum dot coupled to ferromagnetic leads and allows for individual control over single spins by tuning the tunnel magnetoresistance effect that defines the spin valve. In this work, we aim to give a thorough theoretical picture of spin-dependent electronic transport through an interacting quantum-dot spin valve. Transport through quantum-dot systems is often pictured as well-separated tunneling events, where a single electron tunnels from the source electrode to the quantum dot and then on to the drain electrode. This sequential description of electronic transport, however, has proven to be lacking in the low-temperature regime and at strong coupling to the leads. In reality, infinitely many different processes contribute to the procedure of moving electrons from the source through the quantum dot and to the drain. To receive a complete picture of the electronic transport and the spin dynamics of the quantum-dot spin valve, it is crucial to include all of these resonant tunneling effects, which is the main goal of this work. We especially focus on the generic regime, where all relevant energy scales within the system are of equal order of magnitude, and thus perturbative approaches severely fail. To achieve a characterization of this regime including resonant tunneling, we employ the numerically exact technique of iterative summation of path integrals (ISPI) and generalize it to account for spin-dependent transport. To be able to study the impact of spin dynamics on the electronic transport we expand the pool of observables within this technique to include quantum-dot based quantities like the occupation number and spin projection. In addition, we advance the method itself by mapping it to a transfer-matrix approach. This leads to a novel implementation of the ISPI technique, which increases its performance and versatility. With the two implementations of the technique at our disposal, we demonstrate that resonant effects are crucial to reach a reasonable theoretical description of the tunnel magnetoresistance of the interacting quantum-dot spin valve. When investigating noncollinear setups of the quantum-dot spin valve we show how particle-hole symmetry of the system is broken via the interplay between Coulomb interactions and a local magnetic field, leading to asymmetries in the conductance and in components of the spin projection as a function of the gate voltage.