Abstract
We use the Hartree-Fock method to study an interacting one-dimensional electron system on a finite wire, partially depleted at the center by a smooth potential barrier. A uniform one-Tesla Zeeman field is applied throughout the system. We find that with the increase in the potential barrier, the low density electrons under it go from a non-magnetic state to an antiferromagnetic state, and then to a state with a well-localized spin-aligned region isolated by two antiferromagnetic regions from the high density leads. At this final stage, in response to a continuously increasing barrier potential, the system undergoes a series of abrupt density changes, corresponding to the successive expulsion of a single electron from the spin-aligned region under the barrier. Motivated by the recent momentum-resolved tunneling experiments in a parallel wire geometry, we also compute the momentum resolved tunneling matrix elements. Our calculations suggest that the eigenstates being expelled are spatially localized, consistent with the experimental observations. However, additional mechanisms are needed to account for the experimentally observed large spectral weight at near $k=0$ in the tunneling matrix elements.
Highlights
One-dimensional1Delectronic systems have been proven to be a very fruitful field in the studies of interacting many-body systems
We find that with the increase in the potential barrier, the low density electrons under it go from a nonmagnetic state to an antiferromagnetic state and to a state with a well-localized spin-aligned region isolated by two antiferromagnetic regions from the high density leads
In order to better understand the results of our calculations, it will be helpful to recall some features of HartreeFock calculations for an infinite homogeneous onedimensional electron system
Summary
One-dimensional1Delectronic systems have been proven to be a very fruitful field in the studies of interacting many-body systems. Steinberg and co-workers used a negatively charged metal gate to partially deplete the central region of a finite quasione-dimensional wire and studied the low density region by means of momentum-conserved tunneling from a parallel “semi-infinite” wire with higher electron density They found a striking transition from a regime of extended electronic states to a regime of apparently localized states, as the electron density at the center of the wire is lowered by the negative gate voltage. Mueller explored the crossover from the nonmagnetic state to the Wigner crystal antiferromagnetic state when reducing the electronic density in a finite wire using a restricted Hartree-Fock method He mostly considered a finite wire that is relatively uniform in the center region, under no external magnetic field.
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