  Traditional electronic devices rely on electron's intrinsic degrees of
freedom (d.o.f.) to process information. However, additional d.o.f. like the
valley, can emerge in the low-energy states of certain systems. Here, we show
that the quantum dots (QDs) constructed from two-dimensional (2D) second-order
topological insulator (SOTI) posses a new kind of d.o.f., namely corner
freedom, related to the topological corner states that reside at different
corners of the systems. Since the corner states are well separated in real
space, they can be intuitively addressed and manipulated individually, giving
rise to the concept of cornertronics. Via symmetry analysis and material
search, we identify the TiSiCO-family monolayers as the first prototype of
cornertronics materials, where the corner states can be controlled by both
electric and optical fields, due to the novel corner-layer coupling (CLC)
effect and the corner-contrasted optical selection rules. Furthermore, we find
that the band gap of the TiSiCO nanodisk lies in the terahertz region and is
robust to size reduction. These results indicate that the TiSiCO nanodisks can
be used to design terahertz devices with ultrasmall size, electric-field
tunable band gap, and the ability to simultaneously detect the strength and
polarization of terahertz waves, which is not possible for previously reported
QDs. Our findings not only pave the way for the cornertronics, but also open a
new direction for the research in 2D SOTI, QD and terahertz electronics.
