The rapid experimental progress of ultra-cold dipolar fermions opens
up a whole new opportunity to investigate novel many-body physics
of fermions.
We have performed a systematic study on many-body physics with
electric and magnetic dipolar fermions from the perspective of
unconventional symmetries.
Difference between electric and magnetic dipolar systems
When electric dipoles are aligned by the external electric field, their
interactions are anisotropic described by the 2nd Legendre polynomial.
On the other hand, the magnetic dipolar interaction is actually
isotropic: It is invariant under the simultaneous
rotations of both the dipole moments and the relative displacement,
but varies under either of them.
This is a feature of spin-orbit coupling:
It does not exhibit at the single-particle level
but manifests in both Fermi liquid theory and Cooper pairing
instabilities
Novel Weyl Cooper pairings from the magnetic dipolar interaction
The rare earth fermions 161Dy and 163Dy realize a novel itinerant
fermion systems characterized by magnetic dipolar interactions.
We found that the magnetic dipolar interactions lead to a robust mechanism
for the p-wave (L=1) spin triplet S=1 Cooper pairing, which is
a new mechanism independent from the spin fluctuation mechanism for
the 3He pairing superfluidity
[Ref. 4] .
Furthermore, a novel pairing symmetry appears, which, to our knowledge,
has {\it not} been studied in condensed matter systems before:
The total angular momentum of a Cooper pair is J=L+S=1.
It is different from both the 3He-B phase which corresponds
to J=0, and the 3He-A phase in which spin and orbit decouple.
The resultant states can either be in the sector of J_z=0 exhibiting a pair
of Dirac nodes as a time-reversal invariant generalization
of the 3He-A phase, or, in the sector of J_z=\pm 1, which is a Weyl Cooper
pairing with the winding number \pm 2, respectively.
Spin-orbit coupled Fermi liquid theory of magnetic
dipolar fermions
The Landau interaction matrix is calculated and is diagonalized in terms
of the spin-orbit coupled partial-wave channels of the total angular
momentum J
[Ref. 3] .
An exotic propagating collective mode is identified as the spin-orbit
coupled Fermi surface oscillations in which spin distribution on the
Fermi surface exhibits a topologically nontrivial hedgehog configuration.
Time-reversal symmetry breaking pairing from
electric dipolar interaction
The electric dipolar anisotropy provides a natural and robust mechanism
for both triplet and singlet Cooper pairing to first order in the
interaction strength
[Ref. 2] .
In collaboration with J. Hirsch,
we found the competition between the $p_z$-wave spin triplet and
the $s+d$-wave spin singlet pairings, and their coexistence
favors a relative phase of $\pm \pi/2$, which breaks time-reversal
symmetry spontaneously.
It is interesting that a simple analysis provides a novel
mechanism other than spin fluctuation for the triplet Cooper
pairing in the two-component dipolar gases.
Anisotropic Fermi liquid theory from electric dipolar interaction
For the anisotropic electric dipolar systems, all the Landau-Fermi
liquid properties, including the single-particle spectra, thermodynamic
susceptibilities and collective excitations
Ref. [1] , are all affected.
The Landau interaction parameters in the isotropic Fermi liquids
change to the tri-diagonal matrices because of the anisotropy.
The dynamic collective zero sound modes exhibit an anisotropic
dispersion with the largest sound velocity propagating along
the polarization direction.
References and talks
1. Ching-Kit Chan, Congjun Wu, Wei-cheng Lee, S. Das Sarma,
"Anisotropic Fermi liquid theory of the ultra cold fermionic polar
molecules: Landau parameters and collective modes",
Phys. Rev. A 81, 023602 (2010),
See pdf file
2. Congjun Wu, J. E. Hirsch,
"Mixed triplet and singlet pairing in ultracold multicomponent
fermion systems with dipolar interactions",
Phys. Rev. B 81, 020508 (R) (2010).
See pdf file .
3. Yi Li, Congjun Wu,
Spin-orbit coupled Fermi liquid theory with magnetic dipolar interaction,
Phys. Rev. B 85, 205126 (2012) ,
pdf file
4. Yi Li, Congjun Wu,
"The $J$-triplet Cooper pairing with magnetic dipolar interactions",
Scientific Report 2, 392 (2012) . See
pdf file .
Talk:
"Novel p-wave pairing from dipolar interactions " .
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Last modified: July 15, 2007.