10 research outputs found

### Quasiclassical theory for the superconducting proximity effect in Dirac materials

We derive the quasiclassical non-equilibrium Eilenberger and Usadel equations
to first order in quantities small compared to the Fermi energy, valid for
Dirac edge and surface electrons with spin-momentum locking, as relevant for
topological insulators. We discuss in detail several of the key technical
points and assumptions of the derivation, and provide a Riccati-parametrization
of the equations. Solving first the equilibrium equations for S/N and S/F
bilayers and Josephson junctions, we study the superconducting proximity effect
in Dirac materials. Similarly to related works, we find that the effect of an
exchange field depends strongly on the direction of the field. Only components
normal to the transport direction lead to attenuation of the Cooper pair
wavefunction inside the F. Fields parallel to the transport direction lead to
phase-shifts in the dependence on the superconducting phase difference for both
the charge current and density of states in an S/F/S-junction. Moreover, we
compute the differential conductance in S/N and S/F bilayers with an applied
voltage bias, and determine the dependence on the length of the N and F regions
and the exchange field.Comment: 13 pages, 5 figures. Accepted for publication in Phys. Rev.

### Possible odd-frequency Amperean magnon-mediated superconductivity in topological insulator -- ferromagnetic insulator bilayer

We study the magnon-mediated pairing between fermions on the surface of a
topological insulator (TI) coupled to a ferromagnetic insulator with a tilted
mean field magnetization. Tilting the magnetization towards the interfacial
plane reduces the magnetic band gap and leads to a shift in the effective TI
dispersions. We derive and solve the self-consistency equation for the
superconducting gap in two different situations, where we neglect or include
the frequency dependence of the magnon propagator. Neglecting the frequency
dependence results in p-wave Amperean solutions. We also find that tilting the
magnetization into the interface plane favors Cooper pairs with center of mass
momenta parallel to the magnetization vector, increasing $T_c$ compared to the
out-of-plane case. Including the frequency dependence of the magnon propagator,
and solving for a low number of Matsubara frequencies, we find that the
eigenvectors of the Amperean solutions at the critical temperature are
dominantly odd in frequency and even in momentum, thus opening the possibility
for odd-frequency Amperean pairing.Comment: 11 pages, 8 figures, updated versio

### Inverse proximity effect in $s$-wave and $d$-wave superconductors coupled to topological insulators

We study the inverse proximity effect in a bilayer consisting of a thin $s$-
or $d$-wave superconductor (S) and a topological insulator (TI). Integrating
out the topological fermions of the TI, we find that spin-orbit coupling is
induced in the S, which leads to spin-triplet $p$-wave ($f$-wave) correlations
in the anomalous Green's function for an $s$-wave ($d$-wave) superconductor.
Solving the self-consistency equation for the superconducting order parameter,
we find that the inverse proximity effect can be strong for parameters for
which the Fermi momenta of the S and TI coincide. The suppression of the gap is
approximately proportional to $e^{-1/\lambda}$, where $\lambda$ is the
dimensionless superconducting coupling constant. This is consistent with the
fact that a higher $\lambda$ gives a more robust superconducting state. For an
$s$-wave S, the interval of TI chemical potentials for which the suppression of
the gap is strong is centered at $\mu_{TI} = \pm\sqrt{2mv_F^2\mu}$, and
increases quadratically with the hopping parameter $t$. Since the S chemical
potential $\mu$ typically is high for conventional superconductors, the inverse
proximity effect is negligible except for $t$ above a critical value. For
sufficiently low $t$, however, the inverse proximity effect is negligible, in
agreement with what has thus far been assumed in most works studying the
proximity effect in S-TI structures. In superconductors with low Fermi
energies, such as high-$T_c$ cuprates with $d$-wave symmetry, we again find a
suppression of the order parameter. However, since $\mu$ is much smaller in
this case, a strong inverse proximity effect can occur at $\mu_{TI}=0$ for much
lower values of $t$. Moreover, the onset of a strong inverse proximity effect
is preceded by an increase in the order parameter, allowing the gap to be tuned
by several orders of magnitude by small variations in $\mu_{TI}$.Comment: 11 pages, 4 figures, updated versio

### High magnetic field superconductivity in a two-band superconductor

When applying an external magnetic field to a superconductor, orbital and
Pauli paramagnetic pairbreaking effects govern the limit of the upper critical
magnetic field that can be supported before superconductivity breaks down.
Experimental studies have shown that many multiband superconductors exhibit
values of the upper critical magnetic field that violate the theoretically
predicted limit, giving rise to many studies treating the underlying mechanisms
that allow this. In this work we consider spin-splitting induced by an external
magnetic field in a superconductor with two relevant bands close to the Fermi
level, and show that the presence of interband superconducting pairing produces
high-field reentrant superconductivity violating the
Pauli-Chandrasekhar-Clogston limit for the value of the upper critical magnetic
field

### Cavity-mediated superconductor\unicode{x2013}ferromagnetic insulator coupling

A recent proof of concept showed that cavity photons can mediate
superconducting (SC) signatures to a ferromagnetic insulator (FI) over a
macroscopic distance [Phys. Rev. B, 102, 180506(R) (2020)]. In contrast with
conventional proximity systems, this facilitates long-distance
FI\unicode{x2013}SC coupling, local subjection to different drives and
temperatures, and studies of their mutual interactions without proximal
disruption of their orders. Here we derive a microscopic theory for these
interactions, with an emphasis on the leading effect on the FI, namely, an
induced anisotropy field. In an arbitrary practical example, we find an
anisotropy field of 14 \unicode{x2013} 16 $\mu$T, which is expected to yield
an experimentally appreciable tilt of the FI spins for low-coercivity FIs such
as Bi-YIG. We discuss the implications and potential applications of such a
system in the context of superconducting spintronics.Comment: 17 pages, 8 figure