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Due to linearly vanishing density of states, emergent massless Diracquasiparticle resulting from the free fermion motion on a family oftwo-dimensional half-filled bipartite hyperbolic lattices feature dynamic massgeneration through quantum phase transitions only for sufficiently strongfinite-range Coulomb repulsion. As such, strong nearest-neighbor Coulombrepulsion ($V$) is conducive to the nucleation of a charge-density-wave (CDW)order with a staggered pattern of average fermionic density between twosublattices of bipartite hyperbolic lattices. Considering a collection ofspinless fermions (for simplicity), here we show that application of strongexternal magnetic fields by virtue of producing a \emph{finite} density ofstates near the zero energy triggers the condensation of the CDW order even for\emph{infinitesimal} $V$. The proposed magnetic catalysis mechanism isoperative for uniform as well as inhomogeneous (bell-shaped) magnetic fields.We present scaling of the CDW order with the total flux enclosed by hyperbolicDirac materials for a wide range of (especially subcritical) $V$.

Magnetic catalysis in weakly interacting hyperbolic Dirac materials