2021Physical review. B./Physical review. BOpen access

Spatial and magnetic confinement of massless Dirac fermions

Ya-Ning Ren, Qiang Cheng, Si-Yu Li, Chao Yan, Yi-Wen Liu, Ke Lv, Mohan Zhang, Qing‐Feng Sun, Lin He

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Abstract

The massless Dirac fermions and the ease to introduce spatial and magnetic confinement in graphene provide us unprecedented opportunity to explore confined relativistic matter in this condensed-matter system. Here we report the interplay between the confinement induced by external electric fields and magnetic fields of the massless Dirac fermions in graphene. When the magnetic length ${l}_{B}$ is larger than the characteristic length of the confined electric potential ${l}_{V}$, the spatial confinement dominates and a relatively small critical magnetic field splits the spatial-confinement induced atomiclike shell states by switching on a \ensuremath{\pi} Berry phase of the quasiparticles. When the ${l}_{B}$ becomes smaller than the ${l}_{V}$, the transition from spatial confinement to magnetic confinement occurs and the atomiclike shell states condense into Landau levels (LLs) of the Fock-Darwin states in graphene. Our experiment demonstrates that the spatial confinement dramatically changes the energy spacing between the LLs and generates large electron-hole asymmetry of the energy spacing between the LLs. These results shed light on puzzling observations in previous experiments, which hitherto remained unaddressed.

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The massless Dirac fermions and the ease to introduce spatial and magnetic confinement in graphene provide us unprecedented opportunity to explore confined relativistic matter in this condensed-matter system. Here we report the interplay between the confinement induced by external electric fields and magnetic fields of the massless Dirac fermions in graphene. When the magnetic length ${l}_{B}$ is larger than the characteristic length of the confined electric potential ${l}_{V}$, the spatial confinement dominates and a relatively small critical magnetic field splits the spatial-confinement induced atomiclike shell states by switching on a \ensuremath{\pi} Berry phase of the quasiparticles. When the ${l}_{B}$ becomes smaller than the ${l}_{V}$, the transition from spatial confinement to magnetic confinement occurs and the atomiclike shell states condense into Landau levels (LLs) of the Fock-Darwin states in graphene. Our experiment demonstrates that the spatial confinement dramatically changes the energy spacing between the LLs and generates large electron-hole asymmetry of the energy spacing between the LLs. These results shed light on puzzling observations in previous experiments, which hitherto remained unaddressed.

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Available abstract

The massless Dirac fermions and the ease to introduce spatial and magnetic confinement in graphene provide us unprecedented opportunity to explore confined relativistic matter in this condensed-matter system. Here we report the interplay between the confinement induced by external electric fields and magnetic fields of the massless Dirac fermions in graphene. When the magnetic length ${l}_{B}$ is larger than the characteristic length of the confined electric potential ${l}_{V}$, the spatial confinement dominates and a relatively small critical magnetic field splits the spatial-confinement induced atomiclike shell states by switching on a \ensuremath{\pi} Berry phase of the quasiparticles. When the ${l}_{B}$ becomes smaller than the ${l}_{V}$, the transition from spatial confinement to magnetic confinement occurs and the atomiclike shell states condense into Landau levels (LLs) of the Fock-Darwin states in graphene. Our experiment demonstrates that the spatial confinement dramatically changes the energy spacing between the LLs and generates large electron-hole asymmetry of the energy spacing between the LLs. These results shed light on puzzling observations in previous experiments, which hitherto remained unaddressed.

Key concepts: Physics, Condensed matter physics, Dirac fermion, Massless particle, Graphene, Fermion, Magnetic field, Quasiparticle

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