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Physical Review Letters

Aharonov-Casher Effect in Exchange Interactions in a Wigner Crystal

Yaroslav Tserkovnyak, Markus Kindermann

Published Mar 23, 2009• 4 citations
Publisher

Abstract

We theoretically study the effects of spin-orbit coupling on spin exchange in a low-density Wigner crystal. In addition to the familiar antiferromagnetic Heisenberg exchange, we find general anisotropic interactions in spin space if the exchange paths allowed by the crystal structure form loops in real space. In particular, it is shown that the two-electron exchange interaction can acquire ferromagnetic character.

DOI
10.1103/physrevlett.102.126801

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We theoretically study the effects of spin-orbit coupling on spin exchange in a low-density Wigner crystal. In addition to the familiar antiferromagnetic Heisenberg exchange, we find general anisotropic interactions in spin space if the exchange paths allowed by the crystal structure form loops in real space. In particular, it is shown that the two-electron exchange interaction can acquire ferromagnetic character.
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We investigate the effect of mass anisotropy on the magnetic structure of the Wigner crystal of low-density electron systems in two dimensions at T=0T=0T=0. The multiparticle exchange frequencies are calculated with effective mass anisotropy, with and without concomitant lattice distortions. Numerical diagonalization of small lattice sizes with two-, three-, and four-spin exchange terms shows a transition from a ferromagnetic to an antiferromagnetic ground state with increasing mass anisotropy. We map out this transition at various electron densities.
Abstract. The physics of interacting quantum wires has attracted a lot of attention recently. When the density of electrons in the wire is very low, the strong repulsion between electrons leads to the formation of a Wigner crystal. We review the rich spin and orbital properties of the Wigner crystal, both in the one-dimensional and quasi-one-dimensional regime. In the one-dimensional Wigner crystal the electron spins form an antiferromagnetic Heisenberg chain with exponentially small exchange coupling. In the presence of leads the resulting inhomogeneity of the electron density causes a violation of spin-charge separation. As a consequence the spin degrees of freedom affect the conductance of the wire. Upon increasing the electron density, the Wigner crystal starts deviating from the strictly one-dimensional geometry, forming a zigzag structure instead. Spin interactions in this regime are dominated by ring exchanges, and the phase diagram of the resulting zigzag spin chain has a number of unpolarized phases as well as regions of complete and partial spin polarization. Finally we address the orbital properties in the vicinity of the transition from a onedimensional to a quasi-one-dimensional state. Due to the locking between chains in the zigzag Wigner crystal, only one gapless mode exists. Manifestations of Wigner crystal physics at weak interactions are explored by studying the fate of the additional gapped low-energy mode as a function of interaction strength. PACS numbers: 71.10.Pm2 1.
We consider a long quantum wire at low electron densities. In this strong-interaction regime a Wigner crystal may form, in which electrons comprise an antiferromagnetic Heisenberg spin chain. The coupling constant JJJ is exponentially small, as it originates from tunneling of two neighboring electrons through the segregating potential barrier. We study this exponential dependence, properly accounting for the many-body effects and the finite width of the wire.