Gauge Fields: From Chern Insulators to Higher-Order Topological Insulators*

Fermions coupled to gauge fields defined on the links of
lattices have received considerable attention due to their
importance in describing a variety of physical systems. Here,
we show how a higher-order topological insulator emerges in a
system of fermions coupled to Z_N gauge fields. By tuning the
filling of fermions and the strength of the coupling of
fermions to the gauge fields, we show that a variety of fermion
phases are stabilized for different parameter regimes. We map
out the phase diagram of this system and identify conditions
needed to generate a higher-order topological insulating
phase. This work suggests experimental routes, for example in a
cold atomic system, to obtain different topological phases of
fermions to study both the properties of these phases and the
phase transitions between them.