Breaking reciprocity of the electron wave function in chiral materials with nonlocal interactions - the chiral-induced spin selectivity case.

The breaking of time reversal symmetry (TRS) is commonly discussed in relation to the chiral-induced spin selectivity (CISS) effect. Here, we define the conditions under which TRS breaks and discuss two complementary mechanisms: the delocalization of the electron's wave function and dissipation. The delocalization of the electron wave function generates non-local interactions that change the angular momentum of the electron while preserving the total angular momentum in the system at room temperature. This process is associated with the interaction of the electron spin with chiral phonons as well as dissipation to an open system. Frequency-dependent conduction through chiral and achiral gold indicates that at frequencies up to about 100 MHz, there is enhancement of the second harmonic in the chiral gold, indicating a dominant non-linear dissipative behavior in the chiral case. The compelling conclusion is that in most of the past experiments in which the CISS effect was measured, indeed, TRS broke.