Observation of a pseudo-Quantum Hall effect in strained graphene

The quantum Hall effect (QHE) is a cornerstone of condensed matter physics, revealing fundamental aspects of electron correlations, lattice symmetry, and topological order. Here, we report the experimental observation of the pseudo-quantum Hall effect (pQHE), a QHE analogue predicted to occur in systems with a pseudo magnetic field (PMF). Using non-uniformly strained graphene, we break inversion symmetry and induce a valley contrasting PMF. Transport measurements under the PMF reveal different edge state values along opposite channel boundaries—a phenomenon that has remained experimentally elusive. A global PMF of approximately 3.6 T produces distinctly different transport responses under positive and negative magnetic field, where the competition of real and pseudo magnetic fields leads to asymmetric edge current.  Moreover, we observe the splitting of Landau levels into pseudo-Landau levels, to our knowledge the first direct evidence of strain engineered valley splitting in a transport experiment. These results demonstrate that non-uniform strain engineering in graphene can host asymmetric, valley-polarized edge states. Our work expands the conventional picture of the QHE and opens new opportunities to explore how symmetry breaking reshapes topological order.