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Quantum transport in gapped graphene 10.17863/CAM.48578 Li, Yang Robinson, Jason This thesis focuses on investigating local and nonlocal transport properties in hexagonal boron nitride (hBN)/graphene superlattice Hall bars and graphene Hall bars proximity coupled to the ferrimagnetic insulator yttrium iron garnet ($\text{Y}_{3}\text{Fe}_{5}\text{O}_{12}$ or YIG). The first part describes in detail the pulse laser deposition of atomically flat YIG thin films onto single crystal gadolinium gallium garnet with a magnetization of 144 emu cm$^{-3}$. This part also outlines device fabrication procedures including graphene exfoliation and dry transfer, electron beam lithography and metallization of side-contacts, and finally the electrical setup for measuring local and nonlocal transport in graphene. The second part investigates transport properties in hBN/graphene/hBN superlattice Hall bars with a field-effect mobility of up to 220,000 cm$^{2}$ V$^{-1}$ s$^{-1}$ at 9 K with low charge impurities. By aligning hBN and graphene, a ∼33.7 meV band gap at 9 K is demonstrated at the primary Dirac point in zero magnetic field. Furthermore, the nonlocal resistances approach $h/2e^{2}$, where $h$ is Planck’s constant and e is the electron charge. Nonlocal measurements demonstrate that, below 60 K a spin-degenerate ballistic counter-propagating edge state forms and dominates with a possible secondary contribution from a network of one-dimensional conducting channels with soliton-like domain walls. The spin-degenerate ballistic edge states offer possibilities for electronic applications beyond quantum spin and anomalous Hall effects since a quantized resistance is observed through valley coupling. The third part reports a proximity-induced magnetic exchange field in graphene of the order 60 T by placing graphene on the ferrimagnetic insulator YIG. From electrical transport measurements, the magnetic order and energy gap of the edge modes in graphene are tunable, and a transition between the canted antiferromagnetic and spin-polarized ferromagnetic $ν = 0$ quantum Hall states can be achieved with relatively low magnetic fields ($> 6$ T) at 2.7 K. The fourth part summarizes the key results of the thesis. University of Cambridge 2020-05-16 Thesis Doctoral Doctor of Philosophy (PhD) en Cambridge Trust and China Scholarship Committee https://www.repository.cam.ac.uk/handle/1810/301509 https://www.repository.cam.ac.uk/bitstreams/a0675f87-06ca-4b0e-a580-28862a68cb20/download 2597238f74d2682e0d12b1074eaa4dba https://www.repository.cam.ac.uk/bitstreams/837f6e32-e5bd-4b6b-81fc-011301190621/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ Graphene Quantum effect Edge state Nonlocal transport Proximity effect