  Recently synthesized novel phase of germanium selenide ({\gamma}-GeSe) adopts
a hexagonal lattice and a surprisingly high conductivity than graphite. This
triggers great interests in exploring its potential for thermoelectric
applications. Herein, we explored the thermoelectric performance of monolayer
{\gamma}-GeSe and other isostructural {\gamma}-phase of group-IV
monochalcogenides {\gamma}-GeX (X = S, Se and Te) using the density functional
theory and the Boltzmann transport theory. A superb thermoelectric performance
of monolayer {\gamma}-GeSe is revealed with figure of merit ZT value up to
1.13-2.76 for n-type doping at a moderate carrier concentration of
4.73-2.58x10^12 cm-2 between 300 and 600 K. This superb performance is rooted
in its rich pocket states and flat plateau levels around the electronic band
edges, leading to promoted concentrations and electronic conductivity, and
limited thermal conductivity. Our work suggests that monolayer {\gamma}-GeSe is
a promising candidate for high performance medium-temperature thermoelectric
applications.
