Abstract
Topologically quantized response is one of the focal points of contemporary condensed matter
physics. While it directly results in quantized response coefficients in quantum systems, there
has been no notion of quantized response in classical systems thus far. This is because quantized
response has always been connected to topology via linear response theory that assumes a quantum
mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode,
even while possessing the same number of measurable edge modes as their topological winding. In
this work, we discover the totally new paradigm of quantized classical response, which is based on
the spectral winding number in the complex spectral plane, rather than the winding of eigenstates
in momentum space. Such quantized response is classical insofar as it applies to phenomenological
non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function,
and shows up in steady-state response, without invoking a conventional linear response theory.
Specifically, the ratio of the change in one quantity depicting signal amplification to the variation
in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized
values given by the spectral winding numbers as the topological invariants.
Graphene: A New Paradigm in Condensed Matter and Device Physics E.L. Wolf