Chirality-induced spin selectivity (CISS) is a general term denoting the interplay between the chiral structure of molecules and the electron spin. CISS has been studied for over two decades, leading to a consistent picture of experimental phenomena. In this thesis, we focus on t
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Chirality-induced spin selectivity (CISS) is a general term denoting the interplay between the chiral structure of molecules and the electron spin. CISS has been studied for over two decades, leading to a consistent picture of experimental phenomena. In this thesis, we focus on transport experiments exhibiting CISS. In spite of the efforts of many scientists, there is no theoretical explanation for the high degrees of CISS that have been measured in electron transport experiments. In general, it is agreed upon by theorists that the effect is caused by the interplay between the electronic spin-orbit interaction and the helical molecule geometry, in combination with phase-breaking effects such as electron-electron or electron-phonon interactions. As of yet, no theoretical model has achieved realistic degrees of SOC without drastic inflation of the spin-orbit interaction strength.
In this thesis we explore the possibility of using matrix product states (MPS) to study spin-selectivity in boundary-driven electron transport through tight-binding models of chiral molecules, a novel approach in the field of CISS. To this end, we use a model proposed by Fransson in 2019, which considers interacting electrons in a Hubbard model with a spin-orbit interaction adapted from the Kane-Mele model. In this thesis work, the fermionic Hubbard model is mapped to a double spin chain using the Jordan-Wigner transformation. The state of the system is described by a matrix product density operator (MPDO) which is vectorised to a matrix product state (MPS). The system dynamics are described by a vectorised Lindblad equation. The advantage of this approach lies in the fact that it does not require the use of any systematic approximations to the Hamiltonian, in contrast to previous studies. The developed method is validated against the results of previous works studying the boundary-driven Heisenberg-XXZ model and the boundary-driven Hubbard model.
The method is shown to be capable of reproducing chirality-induced spin-selective effects for short chains. The results of this study show a finite magnetocurrent that is odd in bias voltage with an associated magnetoresistance of less than 1%. This is in line with previous studies of this model, but two orders of magnitude lower than experimentally measured values. However, these results are obtained using highly inflated values for the spin-orbit interaction strength. In multiple cases, the results do not satisfy the Onsager-Casimir and Büttiker reciprocity principles, which state that the magnetocurrent should vanish in the low-driving and in the non-interacting regimes. Moreover, the continuity of the current in the steady state was not fully satisfied.
We provide evidence that indicates these problems result from the time-integration error introduced by the Suzuki-Trotter decomposition. We expect that these can be mitigated using higher order time-integration schemes. From the results of this study we can conclude that matrix product states are a viable tool to study CISS in bound-electron transport. However, the method presented in this thesis suffer from numerical errors. We present several suggestions for improvement which address these shortcomings.
