6 research outputs found
Upper bounds on the superfluid stiffness and superconducting : Applications to twisted-bilayer graphene and ultra-cold Fermi gases
Understanding the material parameters that control the superconducting
transition temperature is a problem of fundamental importance. In many
novel superconductors, phase fluctuations determine , rather than the
collapse of the pairing amplitude. We derive rigorous upper bounds on the
superfluid phase stiffness for multi-band systems, valid in any dimension. This
in turn leads to an upper bound on in two dimensions (2D), which holds
irrespective of pairing mechanism, interaction strength, or order-parameter
symmetry. Our bound is particularly useful for the strongly correlated regime
of low-density and narrow-band systems, where mean field theory fails. For a
simple parabolic band in 2D with Fermi energy , we find that , an exact result that has direct implications for the 2D BCS-BEC
crossover in ultra-cold Fermi gases. Applying our multi-band bound to
magic-angle twisted bilayer graphene (MA-TBG), we find that band structure
results constrain the maximum to be close to the experimentally observed
value. Finally, we discuss the question of deriving rigorous upper bounds on
in 3D.Comment: Revised figures, includes estimates from another model of MA-TBG,
published version of manuscrip
Triplet pairing mechanisms from Hund's-Kondo models: applications to UTe and CeRhAs
Observing that several U and Ce based candidate triplet superconductors share
a common structural motif, with pairs of magnetic atoms separated by an
inversion center, we hypothesize a triplet pairing mechanism based on an
interplay of Hund's and Kondo interactions that is unique to this structure. In
the presence of Hund's interactions, valence fluctuations generate a triplet
superexchange between electrons and local moments. The offset from the center
of symmetry allows spin-triplet pairs formed by the resulting Kondo effect to
delocalize onto the Fermi surface, precipitating superconductivity. We
demonstrate this mechanism within a minimal two-channel Kondo lattice model and
present support for this pairing mechanism from existing experiments.Comment: Comments welcome. 5pages + 4figures + 2 appendices. Typos corrected,
improved presentatio
Pair-Kondo effect: a mechanism for time-reversal broken superconductivity in UTe
An important open puzzle in the superconductivity of UTe is the emergence
of time-reversal broken superconductivity from a non-magnetic normal state.
Breaking time-reversal symmetry in a single second-order superconducting
transition requires the existence of two degenerate superconducting order
parameters, which is not natural for orthorhombic UTe. Moreover,
experiments under pressure (Braithwaite et. al., Comm. Phys. \bf{2}, 147
(2019), arXiv:1909.06074 [cond-mat.str-el]) suggest that superconductivity sets
in at a single transition temperature in a finite parameter window, in contrast
to the splitting between the symmetry breaking temperatures expected for
accidental degenerate orders. Motivated by these observations, we propose a
mechanism for the emergence of time-reversal breaking superconductivity without
accidental or symmetry-enforced order parameter degeneracies in systems close
to a magnetic phase transition. We demonstrate using Landau theory that a cubic
coupling between incipient magnetic order and magnetic moments of Cooper pairs
(pair-Kondo coupling) can drive time-reversal symmetry breaking
superconductivity that onsets in a single, weakly first order transition over
an extended region of the phase diagram. We discuss the experimental signatures
of such transition in thermodynamic and resonant ultrasound measurements. A
microscopic origin of pair-Kondo coupling is identified as screening of
magnetic moments by chiral Cooper pairs, built out of two non-degenerate order
parameters - an extension of Kondo screening to unconventional pairs.Comment: Added modeling and discussion of ultrasound experiments, removed pair
density wave discussion, includes results from a more general Landau theory
with additional allowed biquadratic terms, added discussion of earlier
literature on magnetic moment of a triplet superconductor. 9 pages, 3
figures, comments are welcom
Exact solutions of coupled Li\'enard-type nonlinear systems using factorization technique
General solutions of nonlinear ordinary differential equations (ODEs) are in
general difficult to find although powerful integrability techniques exist in
the literature for this purpose. It has been shown that in some scalar cases
particular solutions may be found with little effort if it is possible to
factorize the equation in terms of first order differential operators. In our
present study we use this factorization technique to address the problem of
finding solutions of a system of general two-coupled Li\'enard type nonlinear
differential equations. We describe a generic algorithm to identify specific
classes of Li\'enard type systems for which solutions may be found. We
demonstrate this method by identifying a class of two-coupled equations for
which the particular solution can be found by solving a Bernoulli equation.
This class of equations include coupled generalization of the modified Emden
equation. We further deduce the general solution of a class of coupled ordinary
differential equations using the factorization procedure discussed in this
manuscript.Comment: Accepted for publication in J. Math. Phy