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Graphene antidot lattices (GALs) are two-dimensional (2D) monolayers withperiodically placed holes in otherwise pristine graphene. We investigate theelectronic properties of symmetric and asymmetric GAL structures havinghexagonal holes, and show that anisotropic 2D GALs can display a dimensionalcrossover such that effectively one-dimensional (1D) electronic structures canbe realized in two-dimensions around the charge neutrality point. Weinvestigate the transport and thermoelectric properties of these 2D GALs byusing non-equilibrium Green function (NEGF) method. Dimensional crossovermanifests itself as transmission plateaus, a characteristic feature of 1Dsystems, and enhancement of thermoelectric efficiency, where thermoelectricfigure of merit, $zT$, can be as high as 0.9 at room temperature. We also studythe transport properties in the presence of Anderson disorder and find thatmean free paths of effectively 1D electrons of anisotropic configuration aremuch longer than their isotropic counterparts. We further argue thatdimensional crossover due to broken symmetry and enhancement of thermoelectricefficiency can be nanostructuring strategy virtually for all 2D materials.

Dimensional crossover and enhanced thermoelectric efficiency due to broken symmetry in graphene antidot lattices