Cumulants associated with geometric phases

The Berry phase can be obtained by taking the continuous limit of a cyclic product -\mbox{Im} \ln \prod_{I=0}^{M-1} \langle \Psi_0({\boldsymbol \xi}_I)|\Psi_0({\boldsymbol \xi}_{I+1})\rangle, resulting in the circuit integral i \oint \mbox{d}{\boldsymbol \xi} \cdot \langle \Psi_0({\boldsymbol \xi})|\nabla_{\boldsymbol \xi}|\Psi_0({\boldsymbol \xi}\rangle. Considering a parametrized curve ${\boldsymbol \xi}(\chi)$ we show that the product $\prod_{I=0}^{M-1} \langle \Psi_0(\chi_I)|\Psi_0( \chi_{I+1})\rangle$ can be equated to a cumulant expansion. The first contributing term of this expansion is the Berry phase itself, the other terms are the associated spread, skew, kurtosis, etc. The cumulants are shown to be gauge invariant. It is also shown that these quantities can be expressed in terms of an operator.Comment: text + 1 figur

Extended Creutz ladder with spin-orbit coupling: a one-dimensional analog of the Kane-Mele model

We construct a topological ladder model, one-dimensional, following the steps which lead to the Kane-Mele model in two dimensions. Starting with a Creutz ladder we modify it so that the gap closure points can occur at either $k = \pi / 2$ or $-\pi/2$. We then couple two such models, one for each spin channel, in such a way that time-reversal invariance is restored. We also add a Rashba spin-orbit coupling term. The model falls in the CII symmetry class. We derive the relevant $2\mathbb{Z}$ topological index, calculate the phase diagram and demonstrate the existence of edge states. We also give the thermodynamic derivation of the quantum spin Hall conductance (St\v{r}eda-Widom). Approximate implementation of this result indicates that this quantity is sensitive to the topological behavior of the model.Comment: to appear in EPL (reference will be added later

Topological chiral kagome lattice

Chirality, a fundamental structural property of crystals, can induce many unique topological quantum phenomena. In kagome lattice, unconventional transports have been reported under tantalizing chiral charge order. Here, we show how by deforming the kagome lattice to obtain a three-dimensional (3D) chiral kagome lattice in which the key band features of the non-chiral 2D kagome lattice - flat energy bands, van Hove singularities (VHSs), and degeneracies - remain robust in both the $k_z$ = 0 and $\pi$ planes in momentum space. Given the handedness of our kagome lattice, degenerate momentum points possess quantized Chern numbers, ushering in the realization of Weyl fermions. Our 3D chiral kagome lattice surprisingly exhibits 1D behavior on its surface, where topological surface Fermi arc states connecting Weyl fermions are dispersive in one momentum direction and flat in the other direction. These 1D Fermi arcs open up unique possibilities for generating unconventional non-local transport phenomena at the interfaces of domains with different handedness, and the associated enhanced conductance as the separation of the leads on the surface is increased. Employing first-principles calculations, we investigate in-depth the electronic and phononic structures of representative materials within the ten space groups that can support topological chiral kagome lattices. Our study opens a new research direction that integrates the advantages of structural chirality with those of a kagome lattice and thus provides a new materials platform for exploring unique aspects of correlated topological physics in chiral lattices.Comment: 7 pages, 4 figure

Sovereign Wealth Funds, Sovereign Risk, and External Financing Costs of Financial Intermediaries

This paper takes a novel perspective in analyzing theoretically how the sovereign wealth funds (SWFs) would impact on the sovereign risk, and thereby, the financial sector and, due to some frictions, the real sector of its owner economy. This happens as we suggest SWFs could help in mitigating the extant financial markets incompleteness. In a standard dynamic (continuous time) stochastic partial equilibrium model, it is shown how the SWFs would, under certain conditions, mitigate its owner sovereign risk, in which case it leads to the possibility of impacting on external financing costs of financial intermediaries and corporate sector. In particular, we explore how the sensitivity of default and/or financial distress and/or debt restructuring against (domestic and/or foreign) adverse shocks to the economy would be less, when there is a SWF in the economy in comparison with when the economy lacks it. This is investigated for two sources of financing the SWF. Further, we argue how the costs and benefits of establishing the SWF would be affected by the (relative) size of SWF, its type, and the state of the financial (surplus) capacity in time of setting up the SWF. The externality associated with the establishment of the SWF for the sovereign risk and formation of the new channel for the transmission of monetary and fiscal policies have been examined too. Mutual interactions between the SWF and the monetary and fiscal policy within the analytical framework have been analyzed as well