Towards a bulk theory of flexoelectricity

Flexoelectricity is the linear response of polarization to a strain gradient. Here we address the simplest class of dielectrics, namely elemental cubic crystals, and we prove that therein there is no extrinsic (i.e. surface) contribution to flexoelectricity in the thermodynamic limit. The flexoelectric tensor is expressed as a bulk response of the solid, manifestly independent of surface configurations. Furthermore, we prove that the flexoelectric responses induced by a long-wavelength phonon and by a uniform strain gradient are identical.Comment: 5 pages, 1 figure (2 panels

Theory of Orbital Magnetization in Solids

In this review article, we survey the relatively new theory of orbital magnetization in solids-often referred to as the "modern theory of orbital magnetization"-and its applications. Surprisingly, while the calculation of the orbital magnetization in finite systems such as atoms and molecules is straight forward, in extended systems or solids it has long eluded calculations owing to the fact that the position operator is ill-defined in such a context. Approaches that overcome this problem were first developed in 2005 and in the first part of this review we present the main ideas reaching from a Wannier function approach to semi-classical and finite-temperature formalisms. In the second part, we describe practical aspects of calculating the orbital magnetization, such as taking k-space derivatives, a formalism for pseudopotentials, a single k-point derivation, a Wannier interpolation scheme, and DFT specific aspects. We then show results of recent calculations on Fe, Co, and Ni. In the last part of this review, we focus on direct applications of the orbital magnetization. In particular, we will review how properties such as the nuclear magnetic resonance shielding tensor and the electron paramagnetic resonance g-tensor can elegantly be calculated in terms of a derivative of the orbital magnetization

Berry phases in superconducting transitions

I generalize the concept of Berry's geometrical phase for quasicyclic Hamiltonians to the case in which the ground state evolves adiabatically to an excited state after one cycle, but returns to the ground state after an integer number of cycles. This allows to extend the charge Berry phase gamma_c related to the macroscopic polarization, to many-body systems with fractional number of particles per site. Under certain conditions, gamma_c and the spin Berry phase gamma_s jump in pi at the boundary of superconducting phases. In the extended Hubbard chain with on-site attraction U and nearest-neighbor interaction V at quarter filling, the transitions detected agree very well with exact results in two limits solved by the Bethe ansatz, and with previous numerical studies. In chains with spin SU(2) symmetry, gamma_s jumps when a spin gap opens.Comment: 5 pages, 3 figures, accepted in Europhys. Let

Multiferroic BiFeO3-BiMnO3 Nanocheckerboard From First Principles

We present a first principles study of an unusual heterostructure, an atomic-scale checkerboard of BiFeO3-BiMnO3, and compare its properties to the two bulk constituent materials, BiFeO3 and BiMnO3. The "nanocheckerboard" is found to have a multiferroic ground state with the desired properties of each constituent: polar and ferrimagnetic due to BiFeO3 and BiMnO3, respectively. The effect of B-site cation ordering on magnetic ordering in the BiFeO3-BiMnO3 system is studied. The checkerboard geometry is seen to give rise to a a novel magnetostructural effect that is neither present in the bulk constituent materials, nor in the layered BiFeO3-BiMnO3 superlattice.Comment: 15 pages, 14 figure

Density-functional theory of polar insulators

We examine the density-functional theory of macroscopic insulators, obtained in the large-cluster limit or under periodic boundary conditions. For polar crystals, we find that the two procedures are not equivalent. In a large-cluster case, the exact exchange-correlation potential acquires a homogeneous ``electric field'' which is absent from the usual local approximations, and the Kohn-Sham electronic system becomes metallic. With periodic boundary conditions, such a field is forbidden, and the polarization deduced from Kohn-Sham wavefunctions is incorrect even if the exact functional is used

Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators

Non-linear transport of electrons in strong electric fields, as typified by dielectric breakdown, is re-formulated in terms of the ground-state decay rate originally studied by Schwinger in non-linear QED. We discuss the effect of electron interaction on Zener tunneling by comparing the dielectric breakdown of the band insulator and the Mott insulator, where the latter is studied by the time-dependent density-matrix renormalization group (DMRG). The relation with the Berry's phase theory of polarization is also established.Comment: 5 pages 2 figures, revised text, version to appear in Phys. Rev. Let