Non-Orthogonality and Electron Correlations in Nanotransport: Spin- and Time-Dependent Currents

The concept of the transfer Hamiltonian formalism has been reconsidered and generalized to include the non-orthogonality between the electron states in an interacting region, e.g. quantum dot (QD), and the states in the conduction bands in the attached contacts. The electron correlations in the QD are described by means of a diagram technique for Hubbard operator Green functions for non-equilibrium states.It is shown that the non-orthogonality between the electrons states in the contacts and the QD is reflected in the anti-commutation relations for the field operators of the subsystems. The derived forumla for the current contains corrections from the overlap of the same order as the widely used conventional tunneling coefficients.It is also shown that kinematic interactions between the QD states and the electrons in the contacts, renormalizes the QD energies in a spin-dependent fashion. The structure of the renormalization provides an opportunity to include a spin splitting of the QD levels by polarizing the conduction bands in the contacts and/or imposing different hybridizations between the states in the contacts and the QD for the two spin channels. This leads to a substantial amplification of the spin polarization in the current, suggesting applications in magnetic sensors and spin-filters.


1 Electric current
1.1 General formulation of charge current
1.2 Tunneling phenomenon
1.2.1 Penetration of a barrier
1.2.2 Transmission resonances
2 Transport in mesoscopic systems
2.1 Boltzmann equation
2.2 Kubo formula
2.3 Landauer formula
3 Transfer Hamiltonian formalism
3.1 Generalization of the formalism
4 Current through quantum dots
4.1 Non-equilibrium Green function approach
4.2 Non-orthogonality and many-body states
4.2.1 Commutation relations
4.2.2 Dynamics of the conduction electrons
4.3 Current in the non-orthogonal framework
5 Focusing on the quantum dot
5.1 Single-particle picture
5.1.1 Non-interacting resonant level
5.1.2 Weak-coupling mean-field approximation
5.1.3 Further perturbation expansion
5.1.4 Simple model of a Coulomb island
5.1.5 The retarded and lesser quantum dot Green functions
5.2 Many-body picture
5.2.1 Diagram technique in brief
5.2.2 Hubbard I approximation
5.2.3 Loop correction
5.2.4 The retarded and lesser quantum dot Green functions
5.3 Non-orthogonality in the many-body picture
5.3.1 The retarded and lesser quantum dot Green functions
5.4 Comparison of the different approaches
6 Some recent results
6.1 Alternative opportunity to induce spin-dependent transport
6.2 Cluster approach to transport in nanostructures
What’s next?
A Diagram technique

Author: Fransson, Jonas

Source: Uppsala University Library

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