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Journal of Physics Condensed Matter

Nematic order in a degenerate Hubbard model with spin–orbit coupling

Giuseppe Guarnaccia, Canio Noce

Published Jul 29, 2013• 1 citation
Publisher

Abstract

Using Bogoliubov's inequality we rigorously show that the multiorbital Hubbard model with narrow bands, even in the presence of spin-orbit coupling, does not exhibit long-range nematic order, in low dimensions. This result holds at any finite temperature for both repulsive and attractive Coulomb interactions, with and without spin-orbit coupling.

DOI
10.1088/0953-8984/25/34/345602

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Using Bogoliubov's inequality we rigorously show that the multiorbital Hubbard model with narrow bands, even in the presence of spin-orbit coupling, does not exhibit long-range nematic order, in low dimensions. This result holds at any finite temperature for both repulsive and attractive Coulomb interactions, with and without spin-orbit coupling.
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In this paper we explore the low-dimension long-range superfluid order in the trapped Bose-Einstein condensate driven by spin-orbit coupling at any finite temperature. With the help of the Bogoliubov inequality we give rigorous proofs in both one and two dimensions. For one dimension, no long-range superfluid order can be found, even if spin-orbit coupling exists. For two dimensions, we find that the long-range superfluid order cannot be ruled out in the presence of the unequal Rashba-Dresselhaus-type spin-orbit coupling. However, this long-range superfluid order disappears for the equal case, which has been achieved in recent experiments.
We study the symmetry properties of the Hubbard model with spin-orbit interactions of Rashba and Dresselhaus type. These interactions break the rotational symmetry in spin space, so that the magnetic order cannot be excluded by using the Bogoliubov inequality method. Nevertheless, we rigorously show that the existence of the magnetic long-range orders may be ruled out when the Rashba and Dresselhaus coupling constants are equal in modulus, whereas the $\ensuremath{\eta}$ pairing can be always ruled out, regardless of the microscopic parameters of the model. These results are obtained by imposing locally the SU(2) gauge symmetry on the lattice, and rewriting the spin-orbit interactions in such a way that they are included in the path order of the gauge field on the lattice.
It is rigorously shown that the two-dimensional Hubbard model with narrow bands (including next-nearest-neighbor hopping, etc.) does not exhibit ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing long-range order at any nonzero temperature. This kind of pairing long-range order will also be excluded at zero temperature if an excited energy gap opens in the charge excitation spectrum of the system. These results hold true for both repulsive and attractive Coulomb interactions and for any electron fillings, and are consistent with quantum Monto Carlo calculations.
We solve the orbitally degenerate two-band Hubbard model within dynamical mean field theory and map out the instabilities to various symmetry-broken phases based on an analysis of the corresponding lattice susceptibilities. Phase diagrams as a function of the Hund coupling parameter JJJ are obtained both for the model with rotationally invariant interaction and for the model with Ising-type anisotropy. For negative JJJ, an intraorbital spin-singlet superconducting phase appears at low temperatures, while the normal state properties are characterized by an orbital-freezing phenomenon. This is the negative-J\text{negative-}Jnegative-J analog of the recently discovered fluctuating-moment induced s-waves\text{-wave}s-wave spin-triplet superconductivity in the spin-freezing regime of multiorbital models with J>0J>0J>0.