arXiv subjects

K. Kyriakou

Publications and source records attributed to K. Kyriakou.

2 recordsLinked to original sources

arXiv2021

Emergent non-Hermitian boundary contributions to charge pumping and electric polarization

The phenomenon of charge pumping and the modern theory of electric polarization are reconsidered by analytically taking into account emergent non-Hermitian contributions. These are accounted for through the use of an extended definition of the velocity operator and are determined by means of a dynamic Hellmann-Feynman theorem (DHFT) that we derive here for the first time. The DHFT introduces generalized Berry curvatures and it is valid for calculating observables nonperturbatively, hence with results valid to all orders of the external fields. By using the extended velocity operator we rigorously show how the charge pumping is linked up with the boundaries of the material (with the non-Hermiticity being essential for this connection), and by means of the DHFT we show that the well-known topological quantization of the pumped charge breaks down due to a nonintegrable Aharonov-Anandan phase in driven non-equilibrium processes whenever the periodic gauge cannot be applied to the Floquet-Bloch states. Likewise, we show that the electronic polarization change has an additional non-Hermitian contribution, which is overlooked in the modern theory of electric polarization. The non-Hermitian contribution is by definition a bulk quantity that may equally be evaluated as a boundary quantity due to a symmetric structure that allows the bulk integration to be transformed into a boundary one. This non-Hermitian contribution is very sensitive to the realistic boundary conditions imposed on the wavefunctions and it is therefore expected to be significant in biased insulators where charge accumulation over their boundaries is present during the process that causes the polarization change. Finally, we show how a well-defined surface-charge theorem can be formulated in terms of the boundary non-Hermitian contribution.

cond-mat.mes-hall↗

arXiv2020

Orbital Magnetization in Solids: Boundary contributions as a non-Hermitian effect

The theory of orbital magnetization is reconsidered by defining additional quantities that incorporate a non-Hermitian effect due to anomalous operators that break the domain of definition of the Hermitian Hamiltonian. As a result, boundary contributions to the observable are rigorously and analytically taken into account. In this framework, we extend the standard velocity operator definition in order to incorporate an anomaly of the position operator that is inherent in band theory, which results in an explicit boundary velocity contribution. Using the extended velocity, we define the electrons' intrinsic orbital circulation and we argue that this is the main quantity that captures the orbital magnetization phenomenon. As evidence of this assertion, we demonstrate the explicit relation between the nth band electrons' collective intrinsic circulation and the approximated, evaluated with respect to Wannier states, local and itinerant circulation contributions that are frequently used in the modern theory of orbital magnetization. A quantum mechanical formalism for the orbital magnetization of extended and periodic topological solids (insulators or metals) is redeveloped without any Wannier localization approximation or heuristic extension [Caresoli, Thonhauser, Vanderbilt and Resta, Phys. Rev. B 74, 024408 (2006)]. It is rigorously shown that, as a result of the non-Hermitian effect, an emerging covariant derivative enters the one-band (adiabatically deformed) approximation k-space expression for the orbital magnetization. In the corresponding many-band (unrestricted) k-space formula, the non-Hermitian effect contributes an additional boundary quantity which is expected to give locally (in momentum space) giant contributions whenever band crossings occur along with Hall voltage due to imbalance of electron accumulation at the opposite boundaries of the material.

cond-mat.mes-hall↗