Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point [1,2]. However, accessing the physics of the low density region at the Dirac point has been difficult because of the presence of disorder which leaves the graphene with local microscopic electron and hole puddles [3][4][5], resulting in a finite density of carriers even at the charge neutrality point. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult [6,7].Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance [8]. In this letter, we use scanning tunneling microscopy to show that graphene conforms to hBN, as evidenced by the presence of Moiré patterns in the topographic images. However, contrary to recent predictions [9,10], this conformation does not lead to a sizable band gap due to the misalignment of the lattices. Moreover, local spectroscopy measurements demonstrate that the electron-hole charge fluctuations are reduced by two orders of magnitude as compared to those on silicon oxide. This leads to charge fluctuations which are as small as in suspended graphene [6], opening up Dirac point physics to more diverse experiments than are possible on freestanding devices.

We use the Higgs mechanism to investigate connections between higher-rank symmetric U (1) gauge theories and gapped fracton phases. We define two classes of rank-2 symmetric U (1) gauge theories: the (m, n) scalar and vector charge theories, for integer m and n, which respect the symmetry of the square (cubic) lattice in two (three) spatial dimensions. We further provide local lattice rotor models whose low energy dynamics are described by these theories. We then describe in detail the Higgs phases obtained when the U (1) gauge symmetry is spontaneously broken to a discrete subgroup. A subset of the scalar charge theories indeed have X-cube fracton order as their Higgs phase, although we find that this can only occur if the continuum higher rank gauge theory breaks continuous spatial rotational symmetry. However, not all higher rank gauge theories have fractonic Higgs phases; other Higgs phases possess conventional topological order. Nevertheless, they yield interesting novel exactly solvable models of conventional topological order, somewhat reminiscent of the color code models in both two and three spatial dimensions. We also investigate phase transitions in these models and find a possible direct phase transition between four copies of Z2 gauge theory in three spatial dimensions and X-cube fracton order.CONTENTS arXiv:1802.10099v2 [cond-mat.str-el]

We study strained Hg1−x−yCdxMnyTe in a magnetic field using a k · p model and predict that the system is a Weyl semimetal with two nodes in an experimentally reasonable region of the phase diagram. We also predict two signatures of the Weyl semimetal phase which arise from tunability of the Weyl node splitting. First, we find that the Hall conductivity is proportional to the average Mn ion spin and thus is strongly temperature dependent. Second, we find an unusual magnetic field angle dependence of the Hall conductivity; in particular, we predict a peak in σxy as a function of field angle in the xz-plane and a finite σyz as the x-component of the field goes to 0.Introduction.-Since the connection of the Chern number to the quantum Hall effect 1 , topology has become an increasingly important ingredient in classifying phases of matter. Despite all early examples of topological states being insulators, it has recently been shown that gapless materials can also have topologically nontrivial properties, with the primary example being the Weyl semimetal (WSM) 2-5 .

We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools - semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals - we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically calculated quantum oscillations for generic Weyl semimetals with distinctly curved Fermi arcs on the two surfaces. Based on these methods, we identify a ‘magic’ magnetic-field angle where quantum oscillations become independent of sample thickness, with striking experimental implications. We also analyze the stability of these quantum oscillations to disorder, and show that the high-field oscillations are expected to persist in samples whose thickness parametrically exceeds the quantum mean free path.

Using data from the Fermi Large Area Telescope (LAT), we report the first clear γ -ray measurement of a delay between flares from the gravitationally lensed images of a blazar. The delay was detected in B0218+357, a known double-image lensed system, during a period of enhanced γ -ray activity with peak fluxes consistently observed to reach >20-50× its previous average flux. An auto-correlation function analysis identified a delay in the γ -ray data of 11.46 ± 0.16 days (1σ ) that is ∼1 day greater than previous radio measurements. Considering that it is beyond the capabilities of the LAT to spatially resolve the two images, we nevertheless decomposed individual sequences of superposing γ -ray flares/delayed emissions. In three such ∼8-10 day-long sequences within a ∼4 month span, considering confusion due to overlapping flaring emission and flux measurement uncertainties, we found flux ratios consistent with ∼1, thus systematically smaller than those from radio observations. During the first, best-defined flare, the delayed emission was detailed with a Fermi pointing, and we observed flux doubling timescales of ∼3-6 hr implying as well extremely compact γ -ray emitting regions.

We present a theoretical framework for a class of generalized U (1) gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then lead to a class of generalized Gauss law constraints. The charge and magnetic excitations in these theories have restricted, subdimensional dynamics, providing a generalization of recently studied higher-rank symmetric U (1) gauge theories to the case where arbitrary spatial rotational symmetries are broken. These theories can describe situations where charges exist at the corners of fractal operators, thus providing a continuum effective field theoretic description of Haah's code and Yoshida's Sierpinski prism model. We also present a 3 + 1-dimensional U (1) theory that does not have a non-trivial discrete Zp counterpart.3 i=1 E 1 (r + a 0 xi ), where a 0 is the lattice spacing. The action of the local operator exp(iA 1 (r)a 0 ), which acts as a raising operator for E 1 (r), modifies all ρ(r ) that contain E(r) in its Gauss law constraint. The resulting charge configuration is the tetrahedron of Fig. 1a.The Gauss Law constraint requires that

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We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity (κ) is proportional to the product of the absolute temperature (T ) and the electrical conductivity (σ) in a metal with the constant of proportionality, the so-called Lorenz number L0, being a materials-independent universal constant in all systems obeying the Fermi liquid (FL) paradigm. It has been often stated that the validity (invalidity) of the WF law is the hallmark of an FL (non-Fermi-liquid (NFL)). We consider, both in two (2D) and three (3D) dimensions, a system of conduction electrons at a finite temperature T coupled to a bath of acoustic phonons and quenched impurities, ignoring effects of electron-electron interactions. We find that the WF law is violated arbitrarily strongly with the effective Lorenz number vanishing at low temperatures as long as phonon scattering is stronger than impurity scattering. This happens both in 2D and in 3D for T < TBG, where TBG is the Bloch-Grüneisen temperature of the system. In the absence of phonon scattering (or equivalently, when impurity scattering is much stronger than the phonon scattering), however, the WF law is restored at low temperatures even if the impurity scattering is mostly small angle forward scattering. Thus, strictly at T = 0 the WF law is always valid in a FL in the presence of infinitesimal impurity scattering. For strong phonon scattering, the WF law is restored for T > TBG (or the Debye temperature TD, whichever is lower) as in usual metals. At very high temperatures, thermal smearing of the Fermi surface causes the effective Lorenz number to go below L0 manifesting a quantitative deviation from the WF law. Our work establishes definitively that the uncritical association of an NFL behavior with the failure of the WF law is incorrect. arXiv:1810.05646v2 [cond-mat.mes-hall]