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arXiv:1005.1857 · Physical Review B

Paired states of interacting electrons in a two-dimensional lattice

D. Souza, Francisco H. Claro

Published Nov 30, 2010• 14 citations
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Abstract

We show that two tight-binding electrons that repel may form a bounded pair in two dimensions. The paired states form a band with energies that scale like the strength of the interaction potential. By applying an electric field we show that the dynamics of such states is that of a composite particle of charge $2e$. The system still sustains Bloch-type states so that if the two bands overlap single and paired states might coexist allowing for a bosonic fluid component that, if condensed, would decrease the resistance at low temperatures. The presence of two bands allows for new oscillations whose experimental detection would permit a direct measurement of the interaction potential strength.

DOI
10.1103/physrevb.82.205437

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We show that two tight-binding electrons that repel may form a bounded pair in two dimensions. The paired states form a band with energies that scale like the strength of the interaction potential. By applying an electric field we show that the dynamics of such states is that of a composite particle of charge 2e2e2e. The system still sustains Bloch-type states so that if the two bands overlap single and paired states might coexist allowing for a bosonic fluid component that, if condensed, would decrease the resistance at low temperatures. The presence of two bands allows for new oscillations whose experimental detection would permit a direct measurement of the interaction potential strength.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
When atoms are organized into a crystal, the single-electron energy levels of individual atoms form energy bands. However, there also exist electron-pair states in atoms. We found previously that the counterpart of these electron-pair states of individual atoms may survive in a two-dimensional square-lattice crystal. When the amplitude of the crystal potential is larger than a certain value, a metastable electron-pair band arises between the two lowest single-electron energy bands. In this paper, we demonstrate that the many-particle exchange-correlation corrections renormalize the energy bands and may stabilize the electron pairs for certain hole and electron-pair densities in the two-dimensional crystal. Therefore, depending upon the crystal potential and free carrier densities, there may exist a new many-particle system consisting of electron pairs and holes. Furthermore, we calculate the charge-density excitation spectrum in this new many-particle system.
We study two correlated electrons in a nearest-neighbour tight-binding chain, with both on-site and nearest-neighbour interaction. Both the cases of parallel and antiparallel spin are considered. In addition to the free electron band for two electrons, there are correlated bands with positive or negative energy, depending on whether the interaction parameters are repulsive or attractive. Electrons form bound states, with amplitudes that decay exponentially with separation. Conditions for such states to be filled at low temperatures are discussed.
The correlated motion of electrons in a one-dimensional system with an externally applied longitudinal electric field is discussed. Within the tight-binding model we show that in addition to the well-known Bloch oscillations, the electron-electron interaction induces time-dependent oscillations of the mobility whose period depends on the strength and range of the coupling only. The oscillations involve transitions between bands of bound and unbound states. The case of two electrons is solved in detail and an extension of the results to more particles is discussed.
We study possible quantum states of two correlated electrons in a two-dimensional periodic potential and find a metastable energy band of electron pairs between the two lowest single-electron bands. These metastable states result from interplay of the electron-electron Coulomb interaction and the strength of the crystal potential. The paired electrons are bound in the same unit cell in relative coordinates with an average distance between them of approximately one third of the crystal period. Furthermore, we discuss how such electron pairs can possibly be stabilized in a many-electron system.