On the volatility of volatility

The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge," the VIX is a measure of the implied volatility of the SPX, and is observed to be correlated with the 30-day realized volatility of the SPX. Changes in the VIX are observed to be negatively correlated with changes in the SPX. However, no significant correlation between changes in the VIX and changes in the 30-day realized volatility of the SPX are observed. We investigate whether this indicates a mispricing of options following large VIX moves, and examine the relation to excess returns from variance swaps.Comment: 15 pages, 12 figures, LaTe

Chiral d-wave superconducting state in the core of a doubly quantized s-wave vortex in graphene

We show that the intrinsic chiral $d_{x^2-y^2} \pm id_{xy}$-wave superconducting pairing in doped graphene is significantly strengthened in the core region of a doubly quantized s-wave superconducting vortex produced in a graphene-superconductor hybrid structure. The chiral d-wave state is induced by proximity effect, which transfers the center-of-mass angular momentum of the s-wave vortex to the orbital angular momentum of the chiral d-wave Cooper pairs. The proximity effect is enhanced by the circular geometry of the vortex and we find a $[1 + (T-T_{c,J})^2]^{-1}$ temperature dependence for the chiral d-wave core amplitude, where $T_{c,J}$ is its intrinsic bulk transition temperature. We further propose to detect the chiral d-wave state by studying the temperature dependence of the low-energy local density of states in the vortex core, which displays a sudden radial change as function of the strength of the d-wave core state.Comment: 6 pages, 3 figures. v2 minor change

Unconventional proximity-induced superconductivity in bilayer systems

We study the proximity-induced superconducting state in a general bilayer -- conventional $s$-wave superconductor hybrid structure. For the bilayer we include a general parabolic dispersion, Rashba spin-orbit coupling, and finite layer tunneling as well as the possibility to apply a bias potential and a magnetic Zeeman field, in order to address experimentally relevant bilayer systems, ranging from topological insulator thin films to generic double quantum well systems. By extracting the proximity-induced anomalous Green's function in the bilayer we show on a very rich structure for the superconducting pairing, including different spin states and odd-frequency pairing. Equal-spin spin-triplet $p_x\pm ip_y$-wave pairing is induced in both layers in the presence of a finite spin-orbit coupling and opposite-spin spin-triplet $s$-wave pairing with odd-frequency dependence appears for an applied magnetic Zeeman field. Finite interlayer pairing is also generally present in the bilayer. The interlayer pairing can be either even or odd in the layer index, with a complete reciprocity between parity in frequency and in layer index. We also find that a bilayer offers the possibility of sign reversal of the superconducting order parameters, both between the two layers and between multiple Fermi surfaces.Comment: 10 pages, 5 figures. v2 published versio

Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor UPt3_3

We study the emergence of odd-frequency superconducting pairing in UPt$_3$. Starting from a tight-binding model accounting for the nonsymmorphic crystal symmetry of UPt$_3$ and assuming an order parameter in the $E_{2u}$ representation, we demonstrate that odd-frequency pairing arises very generally, as soon as inter-sublattice hopping or spin-orbit coupling is present. We also show that in the low temperature superconducting $B$ phase, the presence of a chiral order parameter together with spin-orbit coupling, leads to additional odd-frequency pair amplitudes not present in the $A$ or $C$ phases. Furthermore, we show that a finite Kerr rotation in the $B$ phase is only present if odd-$\omega$ pairing also exists.Comment: 8 pages, 2 figure

Probing chiral edge states in topological superconductors through spin-polarized local density of state measurements

We show that spin-polarized local density of states (LDOS) measurements can uniquely determine the chiral nature of topologically protected edge states surrounding a ferromagnetic island embedded in a conventional superconductor with spin-orbit coupling. The spin-polarized LDOS show a strong spin-polarization directly tied to the normal direction of the edge, with opposite polarizations on opposite sides of the island, and with a distinct oscillatory pattern in energy.Comment: 5 pages, 4 figures, publicly released cod