We calculate exactly functional determinants for quantum oscillations about periodic instantons with non-trivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with non-trivial holonomy occur in the Yang-Mills partition function. The weight depends on the value of the holonomy, the temperature, ΛQCD, and the separation between the BPS monopoles (or dyons) which constitute the periodic instanton. At large separation between constituent dyons, the quantum measure factorizes into a product of individual dyon measures, times a definite interaction energy. We present an argument that at temperatures below a critical one related to ΛQCD, trivial holonomy is unstable, and that calorons "ionize" into separate dyons.

We explore a network of electronic quantum valley Hall (QVH) states in the moiré crystal of minimally twisted bilayer graphene. In our transport measurements we observe Fabry-Pérot and Aharanov-Bohm oscillations which are robust in magnetic fields ranging from 0 to 8 T, in strong contrast to more conventional 2D systems where trajectories in the bulk are bent by the Lorentz force. This persistence in magnetic field and the linear spacing in density indicate that charge carriers in the bulk flow in topologically protected, one dimensional channels. With this work we demonstrate coherent electronic transport in a lattice of topologically protected states. arXiv:1802.07317v2 [cond-mat.mes-hall]

We report the fabrication of electrostatically defined nanostructures in encapsulated bilayer graphene, with leakage resistances below depletion gates as high as R ∼ 10 GΩ. This exceeds previously reported values of R = 10-100 kΩ.1-3 We attribute this improvement to the use of a graphite back gate. We realize two split gate devices which define an electronic channel on the scale of the Fermi-wavelength. A channel gate covering the gap between the split gates varies the charge carrier density in the channel. We observe device-dependent conductance quantization of ΔG = 2e/h and ΔG = 4e/h. In quantizing magnetic fields normal to the sample plane, we recover the four-fold Landau level degeneracy of bilayer graphene. Unexpected mode crossings appear at the crossover between zero magnetic field and the quantum Hall regime.

Graphene is hailed as an ideal material for spintronics due to weak intrinsic spin-orbit interaction that facilitates lateral spin transport and tunability of its electronic properties [1-3], including a possibility to induce magnetism in graphene [4-9]. Another promising application of graphene is related to its use as a spacer separating ferromagnetic metals (FMs) in vertical magnetoresistive devices [10-20], the most prominent class of spintronic devices widely used as magnetic sensors. In particular, few-layer graphene was predicted [10-12] to act as a perfect spin filter. Here we show that the role of graphene in such devices (at least in the absence of epitaxial alignment between graphene and the FMs) is different and determined by proximity-induced spin splitting and charge transfer with adjacent ferromagnetic metals, making graphene a weak FM electrode rather than a spin filter. To this end, we report observations of magnetoresistance (MR) in vertical Co-graphene-NiFe junctions with 1 to 4 graphene layers separating the ferromagnets, and demonstrate that the dependence of the MR sign on the number of layers and its inversion at relatively small bias voltages is consistent with spin transport between weakly doped and differently spin-polarized layers of graphene. The proposed interpretation is supported by the observation of an MR sign reversal in biased Co-graphene-hBN-NiFe devices and by comprehensive structural characterization. Our results suggest a new architecture for vertical devices with electrically controlled MR. Following the successful development of graphene-based lateral spintronic structures [1-8], the implementation of graphene as a spacer in vertical magnetic tunnel junctions (MTJ) has become a subject of intense interest [13-20]. Up to now, theoretical proposals [10-12] for graphene's role in MTJs focused on the so-called 'K-point spin filtering' expected in ideally lattice-matched single-crystalline ferromagnet-graphene-ferromagnet (FM-G-FM) structures and attributed to matching spin-polarized bands in the ferromagnet and the electronic states in the graphene treated as a tunnelling barrier. This mechanism was also used to interpret the MR sign inversion observed in conventional Ni-Al 2 O 3 -Co [13] and Ni-MgO-Co [14] tunnel junctions where the Ni electrode was passivated by CVD grown (epitaxial) mono-[13] or few-layer [14] graphene. However, despite several attempts,