Quantum transport in strongly interacting one-dimensional nanostructures

In this thesis we study quantum transport in several one-dimensional systems with strong electronic interactions. The first chapter contains an introduction to the concepts treated throughout this thesis, such as the Aharonov-Bohm effect, the Kondo effect, the Fano effect and quantum state transfer. It also includes a brief historical introduction to these phenomena. The next three chapters discuss electronic transport in strongly interacting systems with a focus on the transport produced by the Kondo effect. The final chapter deals with spin quantum state transfer, where we analytically address the idea of having a one-dimensional spin chain as a quantum data bus in a quantum computer. In chapter 2 we model a system of coupled donors to explain experimental data of conductance, and use this model to investigate coherence and correlation effects. The two donors are strongly coupled to two leads in a parallel configuration embedded in a nano-wire field effect transistor. We then model the system as an Aharonov-Bohm ring with a strongly interacting quantum dot in each arm, and calculate the conductance in the middle of the Coulomb diamond when the system is in the Kondo regime. In the experimental data, interference was observed when a magnetic field was applied [Fig. 2.3(a)]. This interference shows a dependence on the Aharonov-Bohm phase picked up by electrons traversing the structure. This means that donors can be coupled coherently through a many-body state (the Kondo state). Calculations show the non-monotonic behavior of the conductance that was seen in the experimental data [Fig. 2.4(a)]. The conductance decreases since the Kondo effect is destroyed by the magnetic field, and at the same time an oscillatory behavior appears due to the magnetic phase picked up by the electrons going through the parallel structure. Our results improve the general understanding of possible interference effects in an atomic system, especially in the regime where strong interactions take over. Non-symmetric conductance resonances were observed in the data used in chapter 2 when the transport regime of one of the quantum dots changes from Coulomb blockade to sequential tunneling. We model this situation in chapter 3 and arrive at an analytical expression of conductance which we rewrite as a Fano equation. We demonstrate that the strongly interacting quantum dot creates a Kondo scattering channel which serves as a continuum and interferes with the resonant quantum dot, hence producing a non-symmetric Fano like shape in the conductance. Simulations were done using experimental parameters and good agreement with the data is found [Fig. 3.3]. Furthermore, we predict that even if the interacting channel is fully in the Kondo regime, we can use the magnetic flux to diminish its contribution by lowering the characteristic Kondo temperature (Kondo state broadening), producing an alteration in the electron’s path preference. The next challenge consisted of modeling a strongly-interacting chain of atoms, and study the impact of disorder on the Kondo conductance. In chapter 4 we model the energy levels of the quantum dots to be in the middle of the Coulomb blockade region without disorder. Transport calculations of the atomic chains show that in the weak disorder regime conductance drops with increasing disorder, which is surprising and not expected as the disorder is screened by the pinning of the Kondo state at the Fermi level. We demonstrate that the cause of this decrease is an induced non-screened disorder due to the local distribution of Kondo temperatures along the chain. We also show that weak disorder increases the Kondo temperature of a chain without disorder. We propose two experimental scanning tunneling microscopy setups where the impact of local Kondo temperatures can be observed [Fig. 4.5]. It has been reported that quantum state transfer (QST) can be achieved in a Heisenberg spin chain consisting of three spins. Then it might also be possible to achieve QST in longer spin chains if they can be modeled by an effective three-spin system during the complete quantum state transfer. This idea is formally discussed in chapter 5. We propose simple protocols to achieve quantum state transfer across a spin bus with high accuracy. We propose an effective toy model and apply our findings to a spin chain with a sender and a receiver qubit. We find that within the scope of the effective model the control of only the couplings of the spin bus to the sender and receiver qubits yield high fidelity. We also find an interesting high fidelity region that cannot be described by the effective toy model, and predict the high fidelities to be a consequence of a time-independent first excited state energy. We apply the socalled superadiabatic formalism, which makes the evolution 100% adiabatic, and find fidelities that are equal to one. We derive an approximate Hamiltonian containing parameters that correspond to physical (experimental) knobs, and demonstrate that this Hamiltonian improves the fidelity in both of the treated protocols [Fig. 5.9].Quantum NanoscienceApplied Science