We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contain Chern-Simons-like terms. Finally, we write down a fermionic dual of the gauged Ising model (the Fradkin-Shenker model).1 2D here means "two Euclidean space-time dimensions." arXiv:1711.00515v2 [cond-mat.str-el]

We report high quality graphene and WSe2 devices encapsulated between two hexagonal boron nitride (hBN) flakes using a pick-up method with etched hBN flakes. Picking up prepatterned hBN flakes to be used as a gate dielectric or mask for other 2D materials opens new possibilities for the design and fabrication of 2D heterostructures. In this Letter, we demonstrate this technique in two ways: first, a dual-gated graphene device that is encapsulated between an hBN substrate and prepatterned hBN strips. The conductance of the graphene device shows pronounced Fabry-Pérot oscillations as a function of carrier density, which implies strong quantum confinement and ballistic transport in the locally gated region. Second, we describe a WSe2 device encapsulated in hBN with the top hBN patterned as a mask for the channel of a Hall bar. Ionic liquid selectively tunes the carrier density of the contact region of the device, while the hBN mask allows independent tunability of the contact region for low contact resistance. Hall mobility larger than 600 cm(2)/(V·s) for few-layer p-type WSe2 at 220 K is measured, the highest mobility of a thin WSe2 device reported to date. The observations of ballistic transport in graphene and high mobility in WSe2 confirm pick-up of prepatterned hBN as a versatile technique to fabricate ultraclean devices with high quality contact.

We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form Z 2 gauge theory with an unusual Gauss law. An important property of this map is that it preserves the locality of the Hamiltonian. We give examples of 3d bosonic systems dual to free fermions and describe the corresponding Euclidean lattice models.

We extend the previous results of exact bosonization, mapping from fermionic operators to Pauli matrices, in 2D and 3D to arbitrary dimensions. This bosonization map gives a duality between any fermionic system in arbitrary n spatial dimensions and a class of (n − 1)-form Z 2 gauge theories in n dimensions with a modified Gauss's law. This map preserves locality and has an explicit dependence on the second Stiefel-Whitney class and a choice of spin structure on the spatial manifold. A formula for Stiefel-Whitney homology classes on lattices is derived. In the Euclidean path integral, this exact bosonization map is equivalent to introducing a topological Steenrod square term to the space-time action.

A perpendicular electric field breaks the layer symmetry of Bernal-stacked bilayer graphene, resulting in the opening of a band gap and a modification of the effective mass of the charge carriers. Using scanning tunneling microscopy and spectroscopy, we examine standing waves in the local density of states of bilayer graphene formed by scattering from a bilayer/trilayer boundary. The quasiparticle interference properties are controlled by the bilayer graphene band structure, allowing a direct local probe of the evolution of the band structure of bilayer graphene as a function of electric field. We extract the Slonczewski-Weiss-McClure model tight binding parameters as γ 0 = 3.1 eV, γ 1 = 0.39 eV, and γ 4 = 0.22 eV.