In semiconductors that break inversion symmetry,
a bulk photocurrent can be generated by applying light with frequency larger than the gap.
During the project, we have shown that for a gap centered at a mirror-invariant k-point,
two classes of band-edge responses are possible depending
on the relative parity of conduction and valence bands.
When the relative parity is even, as for example in GeS,
the current flows parallel to the electric field polarization.
With odd relative parities, however, the current flows instead
purely perpendicular to the electric field and its
strength is proportional to the Berry curvature dipole.
This remarkable quantum-mechanical effect had been overlooked in the literature up to now.
As a proof of principle,
we have validated our prediction via ab initio calculations on graphitic BC2N,
which exhibits a extraordinarily large transverse shift current
that ranks amongst the strongest nonlinear responses reported.
As a complementary outcome of the project, we have proposed
the measurement of this sizable effect as a benchmark test to clarify
the longstanding debate concerning the atomic structure of this promising material.
In order to understand the nonlinear shift-current response in depth, we have
performed a study of the position operator
in describing optical properties of acentric materials.
This is important, as tight-binding models often employed for studies of nonlinear responses
implicitly assume a rather drastic approximation
concerning the position operator, which
amounts to discarding all of its off-diagonal matrix elements.
In turn, our ab initio analysis is based on a Wannier-interpolation scheme that naturally
incorporates such matrix elements into the formalism, hence it is particularly well suited for the task.
Our results show that while the linear dielectric
function is mildly affected by the approximation,
it can induce serious numerical errors in the case of the shift current.
This is confirmed in two separate ways; i) by explicitly assessing the impact of
off-diagonal position matrix elements in ab-initio calculations and,
ii) by means of a two-band k.p model that assumes implicitly the diagonal
tight-binding approximation. For the latter, we have developed a
numerical scheme for extracting k.p coefficients using quasi-degenerate (Lowding) perturbation
theory, a tool that we have implemented into the free-software package Wannier90 and we expect it will be useful for
researchers in the field.
In summary, this part of the project has highlighted the strong sensitivity of the shift-current mechanism to
wavefunction localization.
Finally, the project has also contributed in a nearby field where the PI has previous experience, namely studying the response of magnetic
materials and, more precisely, magnetic nanostructures. In this field, we have studied the impact of
quantum spin-fluctuations on the magnetic exchange interactions, i.e. the fundamental physical quantities that
define how magnetic atoms interact with each other. By developing an appropriate theoretical scheme and performing
ab-initio calculations, we have shown that quantum fluctuations are needed in order to explain previous
experimental results based on scanning tunneling microscope (STM).
