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We show through both theoretical arguments and numerical calculations thatgraphene discerns an unconventional sequence of quantized Hall conductivity,when subject to both magnetic fields (B) and strain. The latter producestime-reversal symmetric pseudo/axial magnetic fields (b). The single-electronspectrum is composed of two interpenetrating sets of Landau levels (LLs),located at $\pm \sqrt{2 n |b \pm B|}$, $n=0, 1, 2, \cdots$. For $b>B$, thesetwo sets of LLs have opposite \emph{chiralities}, resulting in {\emoscillating} Hall conductivity between 0 and $\mp 2 e^2/h$ in electron and holedoped system, respectively, as the chemical potential is tuned in the vicinityof the neutrality point. The electron-electron interactions stabilize variouscorrelated ground states, e.g., spin-polarized, quantum spin-Hall insulators atand near the neutrality point, and possibly the anomalous Hall insulating phaseat incommensurate filling $\sim B$. Such broken-symmetry ground states havesimilarities as well as significant differences from their counterparts in theabsence of strain. For realistic strength of magnetic fields and interactions,we present scaling of the interaction-induced gap for various Hall stateswithin the zeroth Landau level.

Theory of unconventional quantum Hall effect in strained graphene