The introduction of foreign atoms, such as nitrogen, into the hexagonal network an sp(2)-hybridized carbon atom monolayer has been demonstrated and constitutes effective tool for tailoring intrinsic properties graphene. Here, we report that boron atoms can be efficiently substituted in Single-layer graphene substitutionally doped with was prepared by mechanical exfoliation boron-doped graphite. X-ray photoelectron spectroscopy amount substitutional graphite ~0.22 %. Raman were spaced 4.76 nm...

The Zak phase $\gamma$, the generalization of Berry to Bloch wave functions in solids, is often used characterize inversion-symmetric 1D topological insulators; however, since its value can depend on choice real-space origin and unit cell, only difference between two regions believed be relevant. Here, we show that one extract an origin-independent part so-called inter-cellular $\gamma^{\mathrm{inter}}$, which as a bulk quantity predict number surface modes follows: neutral finite...

Surface codes—leading candidates for quantum error correction (QEC)—and entanglement phases—a key notion many-body dynamics—have heretofore been unrelated. Here we establish a link between the two. We map two-dimensional (2D) surface codes under class of incoherent or coherent errors (bit flips uniaxial rotations) to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>(</a:mo><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mo>)</a:mo><a:mi...

Statistical mechanics mappings provide key insights on quantum error correction. However, existing assume incoherent noise, thus ignoring coherent errors due to, e.g., spurious gate rotations. We map the surface code with errors, taken as X or Z rotations (replacing bit phase flips), to a two-dimensional (2D) Ising model complex couplings, and further 2D Majorana scattering network. Our reveal both commonalities qualitative differences in correcting errors. For both, error-correcting maps,...

Quantum anomalies are the breaking of a classical symmetry by quantum fluctuations. They dictate how physical systems diverse nature, ranging from fundamental particles to crystalline materials, respond topologically external perturbations, insensitive local details. The anomaly paradigm was triggered discovery chiral that contributes decay pions into photons and influences motion superfluid vortices in $^{3}\mathrm{He}$-A. In solid state, it also fundamentally affects properties topological...

Condensed matter systems realizing Weyl fermions exhibit striking phenomenology derived from their topologically protected surface states as well chiral anomalies induced by electromagnetic fields. More recently, inhomogeneous strain or magnetization were predicted to result in electric ${\mathbf{E}}_{5}$ and magnetic ${\mathbf{B}}_{5}$ fields, which modify enrich the anomaly with additional terms. In this Rapid Communication, we develop a lattice-based approach describe anomaly, involves...

Type Ia supernovae (SNe Ia) play a crucial role as standardizable cosmological candles, though the nature of their progenitors is subject active investigation. Recent observational and theoretical work has pointed to merging white dwarf binaries, referred double-degenerate channel, possible progenitor systems for some SNe Ia. Additionally, recent suggests that mergers which fail detonate may produce magnetized, rapidly rotating dwarfs. In this paper, we present first multidimensional...

Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline superconductors, we establish a bulk-boundary correspondence linking the presence of such to bulk invariants introduced by Benalcazar et al. [Phys. Rev. B 89, 224503 (2014)]. We thus when superconductor protected rotational symmetry displays superconductivity. Our approach is based stacked Dirac Hamiltonians, using...

Berry phases strongly affect the properties of crystalline materials, giving rise to modifications semiclassical equations motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations connection have been analyzed characterize topology these systems. While topological classification systems is being developed, little attention has paid impact new geometric on dynamics and transport. this work, we derive full set for in a system governed by Hamiltonian, including...

Supersymmetry is a powerful concept in quantum many-body physics. It helps to illuminate ground-state properties of complex systems and gives relations between correlation functions. In this Letter, we show that the Sachdev--Ye--Kitaev model, its simplest form Majorana fermions with random four-body interactions, supersymmetric. contrast existing explicitly supersymmetric extensions supersymmetry find requires no couplings. The type structure supercharges are entirely set by number...

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion for many-body quantum chaos and the holographic correspondence. Here we construct fermionic Floquet circuits of random four-body gates designed to capture key features SYK dynamics. Our can be built using local ingredients in devices, namely, charging-mediated interactions braiding zero modes. This offers analog-digital route simulations that reconciles with topological protection modes, a feature missing...

The Sachdev-Ye-Kitaev (SYK) model, in its simplest form, describes $k$ Majorana fermions with random all-to-all four-body interactions. We consider the SYK model framework of a many-body Altland-Zirnbauer classification that sees system as belonging to one eight (real) symmetry classes depending on value $k\mod 8$. show that, class, may support exact zero modes symmetries also dictating whether these have nonzero contribution fermions, i.e., single-particle weight. These appear all but two...

The chiral anomaly in Weyl semimetals states that the left- and right-handed fermions, constituting low energy description, are not individually conserved, resulting, for example, a negative magnetoresistance such materials. Recent experiments see strong indications of an anomalous resistance response; however, with response at fields is more sharply peaked parallel magnetic electric than expected from simple theoretical considerations. Here, we uncover mechanism, arising interplay between...

The existence and topological classification of lower-dimensional Fermi surfaces is often tied to the crystal symmetries underlying lattice systems. Artificially engineered lattices, such as heterostructures other superlattices, provide promising avenues realize desired that protect surface, nodal lines. In this work, we investigate a Weyl semimetal subjected spatially periodic onsite potential, giving rise several phases, including nodal-line phase. contrast proposals purely focus on...

Magnetotransport provides key experimental signatures in Weyl semimetals. The longitudinal magnetoresistance is linked to the chiral anomaly and transversal dominant charge relaxation mechanism. Axial magnetic fields that act with opposite sign on chiralities facilitate new transport experiments probe low-energy nodes. As recently realized, these axial can be achieved by straining samples or adding inhomogeneities them. Here, we identify a robust signature of fields: an anomalous scaling...

Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of nodes. If transport direction is perpendicular to applied magnetic field, have shown a large positive magnetoresistance. In this work we present theoretical scattering matrix approach transversal magnetotransport in node. Our numerical method confirms goes beyond existing perturbative analytical by treating disorder exactly. It formulated real space...

The complex Sachdev-Ye-Kitaev (cSYK) model is a charge-conserving of randomly interacting fermions. interaction term can be chosen such that the exhibits chiral symmetry. Then, depending on charge sector and number fermions, level spacing statistics suggests fourfold categorization into three Wigner-Dyson symmetry classes. In this work, inspired by previous findings for Majorana model, we embed classes cSYK in Altland-Zirnbauer framework identify consequences originating from correlations...

Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion many-body dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we establish a link between the two. We map two-dimensional (2D) surface codes under class of incoherent or coherent errors (bit flips uniaxial rotations) to $(1+1)$D free-fermion circuits via Ising models. show that error-correcting phase implies topologically...

The surface code, one of the leading candidates for quantum error correction, is known to protect encoded information against stochastic, i.e., incoherent errors. protection coherent errors, such as from unwanted gate rotations, however understood only special cases, rotations about $X$ or $Z$ axes. Here we consider generic single-qubit errors in by angle $\alpha$ an axis that can be chosen arbitrarily. We develop a statistical mechanical mapping and perform entanglement analysis transfer...

Transport plays a key role in characterizing topological insulators and semimetals. Understanding the effect of disorder is crucial to assess robustness experimental signatures for topology. In this work, we find absence localization nodal line semimetals long-range scalar large range strengths. Using continuum transfer matrix approach, that conductivity plane out increases with system size strength. We substantiate these findings by perturbative calculation show strength using Kubo formula...

Transport plays a key role in characterizing topological insulators and semimetals. Understanding the effect of disorder is crucial to assess robustness experimental signatures for topology. In this work, we find absence localization nodal-line semimetals long-range scalar large range strengths. Using continuum transfer matrix approach, that conductivity plane out nodal line increases with system size strength. We substantiate these findings perturbative calculation show strength using Kubo...

We study the surface code under most general single-qubit $X$-error channel, encompassing both coherent and incoherent errors. develop a statistical mechanics mapping for decoding problem represent partition function as transfer-matrix, i.e., (1+1)$D$ hybrid quantum circuit. The relevant circuit evolution, we show, has an efficient matrix product state approximation, using which algorithm large-scale syndrome sampling, thus enabling simulation of these non-Pauli errors away from limits...