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A fundamental idea in wave mechanics is that propagation in a periodic medium can be described by Bloch waves whose conserved crystal momenta define their transformations when displaced by the set of discrete lattice translations. In ordered materials where incommensurate spatial periods compete, this general principle is rendered ineffective, often with dramatic consequences. Examples are crystals with broken symmetries from charge or spin density waves, quasiperiodic lattices that produce diffraction patterns with crystallographically forbidden point symmetries, and stacks of two-dimensional lattices with a relative rotation (twist) between layers. In special cases when there is a small difference between the competing periods, a useful work-around is a continuum description where a periodic long-wavelength field produces Bragg scattering that coherently mixes short-wavelength carrier waves. In this work, we advocate an alternative approach to study three-dimensional twisted crystals that replaces their spectrally congested momentum-space Bloch band structures with a representation using squeezed coherent states in a Fock space of free-particle vortex states. This reorganization of the Hilbert space highlights the crucial role of the Coriolis force in the equations of motion that leads to unconventional phase space dynamics and edge state structure generic to a family of complex crystals., Comment: 9 + 16 pages; 4 + 6 figures. Comments are very appreciated!

Lattice deformations in graphene couple to the low-energy electronic degrees of freedom as pseudo scalar and gauge fields. Using molecular dynamics simulations, we show that the optical component of the displacement field, i.e., the relative motion of different sublattices, contributes at equal order as the acoustic component and effectively screens the pseudo gauge fields. In particular, we consider twisted bilayer graphene and corrugated monolayer graphene. In both cases, optical lattice displacement significantly reduce the overall magnitude of the pseudo magnetic fields. For corrugated graphene, we further show that the corresponding electronic bands are significantly modified by the screened pseudo magnetic field. Previous studies based on continuum elasticity, which ignores this effect, have therefore systematically overestimated the strength of the strain-induced pseudo magnetic field. Our results have important consequences for the interpretation of experiments and design of straintronic applications., Comment: 7 + 14 pages, 4 + 11 figures

The multi-staged XENON program at INFN Laboratori Nazionali del Gran Sasso aims to detect dark matter with two-phase liquid xenon time projection chambers of increasing size and sensitivity. The XENONnT experiment is the latest detector in the program, planned to be an upgrade of its predecessor XENON1T. It features an active target of 5.9 tonnes of cryogenic liquid xenon (8.5 tonnes total mass in cryostat). The experiment is expected to extend the sensitivity to WIMP dark matter by more than an order of magnitude compared to XENON1T, thanks to the larger active mass and the significantly reduced background, improved by novel systems such as a radon removal plant and a neutron veto. This article describes the XENONnT experiment and its sub-systems in detail and reports on the detector performance during the first science run., Comment: 32 pages, 19 figures

We develop the Floquet-Bloch theory of noninteracting fermions on a periodic lattice in the presence of a constant electric field. As long as the field lies along a reciprocal lattice vector, time periodicity of the Bloch Hamiltonian is inherited from the evolution of momentum in the Brillouin zone. The corresponding Floquet quasienergies yield the Wannier-Stark ladder with interband couplings included to all orders. These results are compared to perturbative results where the lowest-order interband correction gives the field-induced polarization shift in terms of the electric susceptibility. Additionally, we investigate electronic transport by coupling the system to a bath within the Floquet-Keldysh formalism. We then study the breakdown of the band-projected theory from the onset of interband contributions and Zener resonances in the band-resolved currents. In particular, we consider the transverse quantum-geometric response in two spatial dimensions due to the Berry curvature. In the strong-field regime, the semiclassical theory predicts a plateau of the geometric response as a function of field strength. Here, we scrutinize the conditions under which the semiclassical results continue to hold in the quantum theory., Comment: 15 + 8 pages, 12 + 1 figures

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moir\'e materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe$_2$ bilayers using large-scale molecular dynamics simulations. Our theory is valid in graphene bilayers for twist angles $\theta \gtrsim 1^\circ$, and in twisted transition metal dichalcogenides for $\theta \gtrsim 4^\circ$. We also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

Artificial crystals such as moir\'e superlattices can have a real-space periodicity much larger than the underlying atomic scale. This facilitates the presence of Bloch oscillations in the presence of a static electric field. We demonstrate that the optical response of such a system, when dressed with a static field, becomes resonant at the frequencies of Bloch oscillations, which are in the terahertz regime when the lattice constant is of the order of 10 nm. In particular, we show within a semiclassical band-projected theory that resonances in the dressed Hall conductivity are proportional to the lattice Fourier components of the Berry curvature. We illustrate our results with a low-energy model on an effective honeycomb lattice., Comment: 6 + 4 pages, 3 figures. Published version

In two-dimensional artificial crystals with large real-space periodicity, the nonlinear current response to a large applied electric field can feature a strong angular dependence, which encodes information about the band dispersion and Berry curvature of isolated electronic Bloch minibands. Within the relaxation-time approximation, we obtain analytic expressions up to infinite order in the driving field for the current in a band-projected theory with time-reversal and trigonal symmetry. For a fixed field strength, the dependence of the current on the direction of the applied field is given by rose curves whose petal structure is symmetry constrained and is obtained from an expansion in real-space translation vectors. We illustrate our theory with calculations on periodically-buckled graphene and twisted double bilayer graphene, wherein the discussed physics can be accessed at experimentally-relevant field strengths., Comment: 8 + 22 pages, 4 + 12 figures. Published version

Two-dimensional van der Waals heterostructures can be engineered into artificial superlattices that host flat bands with significant Berry curvature and provide a favorable environment for the emergence of novel electron dynamics. In particular, the Berry curvature can induce an oscillating trajectory of an electron wave packet transverse to an applied static electric field. Though analogous to Bloch oscillations, this novel oscillatory behavior is driven entirely by quantum geometry in momentum space instead of band dispersion. While the orbits of Bloch oscillations can be localized by increasing field strength, the size of the geometric orbits saturates to a nonzero plateau in the strong-field limit. In non-magnetic materials, the geometric oscillations are even under inversion of the applied field, whereas the Bloch oscillations are odd, a property that can be used to distinguish these two co-existing effects., Comment: 6 + 7 pages, 2 figures. Comments are greatly appreciated!

The long-wavelength physics of monolayer graphene in the presence of periodic strain fields has a natural chiral scattering network description. When the strain field varies slowly compared to the graphene lattice and the effective magnetic length of the induced valley pseudomagnetic field, the low-energy physics can be understood in terms of valley-polarized percolating domain-wall modes. Inspired by a recent experiment, we consider a strain field with threefold rotation and mirror symmetries but without twofold rotation symmetry, resulting in a system with the connectivity of the oriented kagome network. Scattering processes in this network are captured by a symmetry-constrained phenomenological $S$ matrix. We analyze the phase diagram of the kagome network, and show that the bulk physics of the strained graphene can be qualitatively captured by the network when we account for a percolation transition at charge neutrality. We also discuss the limitations of this approach to properly account for boundary physics., Comment: 13 pages; 11 figures

Single-layer graphenes subject to periodic lateral strains are artificial crystals that can support boundary spectra with an intrinsic polarity. These are analyzed by comparing the effects of periodic magnetic fields and strain-induced pseudomagnetic fields that respectively break and preserve time-reversal symmetry. In the former case, a Chern classification of the superlattice minibands with zero total magnetic flux enforces {\it single} counter-propagating modes traversing each bulk gap on opposite boundaries of a nanoribbon. For the pseudomagnetic field, pairs of counter-propagating modes migrate to the {\it same} boundary where they provide well-developed valley-helical transport channels on a single zigzag edge. We discuss possible schemes for implementing this situation and their experimental signatures., Comment: 5+12 pages; 3+6 figures; version accepted to Physical Review Letters

Non-reciprocal plasmons in current-driven, isotropic, and homogenous graphene with proximal metallic gates is theoretically explored. Nearby metallic gates screen the Coulomb interactions, leading to linearly dispersive acoustic plasmons residing close to its particle-hole continuum counterpart. We show that the applied bias leads to spectral broadband focused plasmons whose resonance linewidth is dependent on the angular direction relative to the current flow due to Landau damping. We predict that forward focused non-reciprocal plasmons are possible with accessible experimental parameters and setup.

The family of monolayer two-dimensional (2D) materials hosts a wide range of interesting phenomena, including superconductivity, charge density waves, topological states and ferromagnetism, but direct evidence for antiferromagnetism in the monolayer has been lacking. Nevertheless, antiferromagnets have attracted enormous interest recently in spintronics due to the absence of stray fields and their terahertz resonant frequency. Despite the great advantages of antiferromagnetic spintronics, controlling and detecting N\'eel vectors have been limited in bulk materials. In this work, we developed a sensitive second harmonic generation (SHG) microscope and detected long-range N\'eel antiferromagnetic (AFM) order and N\'eel vector switching down to the monolayer in MnPSe$_3$. Temperature-dependent SHG measurement in repetitive thermal cooling surprisingly collapses into two curves, which correspond to the switching of an Ising type N\'eel vector reversed by the time-reversal operation, instead of a six-state clock ground state expected from the threefold rotation symmetry in the structure. We imaged the spatial distribution of the N\'eel vectors across samples and rotated them by an arbitrary angle irrespective of the lattice in the sample plane by applying strain. By studying both a Landau theory and a microscopic model that couples strain to nearest-neighbor exchange, we conclude that the phase transition of the XY model in the presence of strain falls into the Ising universality class instead of the XY one, which could explain the extreme strain tunability. Finally, we found that the 180{\deg} AFM domain walls are highly mobile down to the monolayer after thermal cycles, paving the way for future control of the antiferromagnetic domains by strain or external fields on demand for ultra-compact 2D AFM terahertz spintronics., Comment: Submitted version; To appear in Nature Nanotechnology

Graphene bilayers with layer antisymmetric strains are studied using the Dirac-Harper model for a pair of single layer Dirac Hamiltonians coupled by a one-dimensional moir\'e-periodic interlayer tunneling amplitude. This model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of its charge multipole distributions. These are analyzed introducing a generalized Berry curvature that encodes the field-induced dynamics of multipole fields allowed in a chiral medium with time reversal symmetry. The formulation identifies a reciprocity relation between responses to layer-symmetric and layer-antisymmetric in-plane electric fields and reveals momentum-space quantum oscillations produced by a spatial pattern of band inversions on the moir\'e scale., Comment: 11 pages, 10 figures

We study the Fermi surface contribution to the nonlinear DC photocurrent at quadratic order in a spatially uniform optical field in the ultra-clean limit. In addition to shift and injection current, we find that polarized light incident on a metallic system generates an intrinsic contribution to the bulk photovoltaic effect deriving from photoinduced electronic transitions on the Fermi surface. In {velocity} gauge, this contribution originates in both the coherent band off-diagonal and diagonal parts of the density matrix, describing respectively, the coherent wave function evolution and the carrier dynamics of an excited population. We derive a formula for the intrinsic Fermi surface contribution for a time-reversal invariant chiral Weyl semimetal illuminated with circularly-polarized light. At low frequency, this response is proportional to the frequency of the driving field, with its sign determined by the topological charge of the Weyl nodes and with its magnitude being comparable to the recently discovered quantized circular photogalvanic effect. Our work presents a complete derivation for all contributions to nonlinear DC photocurrent and classify them according to the polarization of light in the presence and absence of TRS.

The distribution of string tension on the contact line between an ideal string and a massive pulley is a frequently-discussed but incompletely-posed problem that confronts students in introductory mechanics. We highlight ambiguities in the usual presentation of this problem by the massive Atwood's machine and discuss two compact resolutions that treat situations where the pulley or the string elastically deform. We propose experiments that can be developed in an intermediate laboratory to determine the tension profile., Comment: American Journal of Physics (in press): pdfLaTeX: 8 pages, 6 figures

We study a Dirac Harper model for moir\'e bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For sufficiently long moir\'e period the we find low energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position dependent mass inversions. We analyze their charge distributions, mode count and valley-coherence using exact symmetries of the lattice model and approximate symmetries of a four-flavor version of the Jackiw-Rebbi one dimensional solution., Comment: 10 pages, 9 figures

The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light's polarization, known as the circular photogalvanic effect, is predicted to depend only on fundamental constants. The conditions to observe quantization are non-universal, and depend on material parameters and the incident frequency. In this work, we perform terahertz emission spectroscopy with tunable photon energy from 0.2 eV - 1.1 eV in the chiral topological semimetal CoSi. We identify a large longitudinal photocurrent peaked at 0.4 eV reaching $\sim$ 550 $\mu A/V^{2}$, which is much larger than the photocurrent in any chiral crystal reported in the literature. Using first-principles calculations we establish that the peak originates from topological band crossings, reaching 3.3$\pm$0.3 in units of the quantization constant. Our calculations indicate that the quantized CPGE is within reach in CoSi upon doping and increase of the hot-carrier lifetime. The large photo-conductivity suggests that topological semimetals could potentially be used as novel mid-infrared detectors., Comment: Fig.4 color updated

We develop a theory for the nonlinear time domain response of a Weyl semimetal driven by an ultrafast optical pulse. At quadratic order in the driving field we find that the response near a band inversion transition contains a coherent oscillating component proportional field intensity and with a frequency that can be tuned over a wide range (from THz to the near IR) selected by the chemical potential. We illustrate the effect by calculating the induced current as a function of time for a model of a parity broken Weyl semimetal where large Berry curvature near the band inversion transition promotes this nonlinear response., Comment: 7 pages, 3 figures

We report the optical conductivity in high-quality crystals of the chiral topological semimetal CoSi, which hosts exotic quasiparticles known as multifold fermions. We find that the optical response is separated into several distinct regions as a function of frequency, each dominated by different types of quasiparticles. The low-frequency intraband response is captured by a narrow Drude peak from a high-mobility electron pocket of double Weyl quasi-particles, and the temperature dependence of the spectral weight is consistent with its Fermi velocity. By subtracting the low-frequency sharp Drude and phonon peaks at low temperatures, we reveal two intermediate quasi-linear inter-band contributions separated by a kink at 0.2 eV. Using Wannier tight-binding models based on first-principle calculations, we link the optical conductivity above and below 0.2 eV to interband transitions near the double Weyl fermion and a threefold fermion, respectively. We analyze and determine the chemical potential relative to the energy of the threefold fermion, revealing the importance of transitions between a linearly dispersing band and a flat band. More strikingly, below 0.1 eV our data are best explained if spin-orbit coupling is included, suggesting that at these energies the optical response is governed by transitions between a previously unobserved four-fold spin-3/2 node and a Weyl node. Our comprehensive combined experimental and theoretical study provides a way to resolve different types of multifold fermions in CoSi at different energy. More broadly our results provide the necessary basis to interpret the burgeoning set of optical and transport experiments in chiral topological semimetals.

The electronic bands of twisted bilayer graphene (TBLG) with a large-period moir\'e superlattice fracture to form narrow Bloch minibands that are spectrally isolated by forbidden energy gaps from remote dispersive bands. When these gaps are sufficiently large, one can study a band-projected Hamiltonian that correctly represents the dynamics within the minibands. This inevitably introduces nontrivial geometrical constraints that arise from the assumed form of the projection. Here we show that this choice has a profound consequence in a low-energy experimentally-observable signature which therefore can be used to tightly constrain the analytic form of the appropriate low-energy theory. We find that this can be accomplished by a careful analysis of the electron density produced by backscattering of Bloch waves from an impurity potential localized on the moir\'e superlattice scale. We provide numerical estimates of the effect that can guide experimental work to clearly discriminate between competing models for the low-energy band structure., Comment: 6 + 29 pages; 3 + 13 figures

The propagation of electrons in an orbital multiplet dispersing on a lattice can support anomalous transport phenomena deriving from an orbitally-induced Berry curvature. In striking contrast to the related situation in graphene, we find that anomalous transport for an $L=1$ multiplet on the primitive 2D triangular lattice is activated by easily implemented on-site and optically-tunable potentials. We demonstrate this for dynamics in a Bloch band where point degeneracies carrying opposite winding numbers are generically offset in energy, allowing both an anomalous charge Hall conductance with sign selected by off-resonance coupling to circularly-polarized light and a related anomalous orbital Hall conductance activated by layer buckling., Comment: 5 + 4 pages, 4 + 1 figures, version accepted to Physical Review Letters

We propose that the noncentrosymmetric LiGaGe-type hexagonal $ABC$ crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space. The symmetry-protected Dirac points arise due to a band inversion and are located on the sixfold rotation $z$-axis, whereas the six pairs of Weyl points related by sixfold symmetry are located on the perpendicular $k_z=0$ plane. By studying the electronic structure as a function of the buckling of the HgPb layer, which is the origin of inversion symmetry breaking, we establish that the coexistence of Dirac and Weyl fermions defines a phase separating two topologically distinct Dirac semimetals. These two Dirac semimetals are distinguished by the $\mathbb{Z}_2$ index of the $k_z=0$ plane and the corresponding presence or absence of 2D Dirac fermions on side surfaces. We formalize our first-principles calculations by deriving and studying a low-energy model Hamiltonian describing the Dirac-Weyl semimetal phase. We conclude by proposing several other materials in the non-centrosymmetric $ABC $ material class, in particular SrHgSn and CaHgSn, as candidates for realizing the Dirac-Weyl semimetal., Comment: 6 pages, 4 figures + 5 pages of supplemental material

Domain walls separating regions of AB and BA interlayer stacking in bilayer graphene have attracted attention as novel examples of structural solitons, topological electronic boundaries, and nanoscale plasmonic scatterers. We show that strong coupling of domain walls to surface plasmons observed in infrared nanoimaging experiments is due to topological chiral modes confined to the walls. The optical transitions among these chiral modes and the band continua enhance the local ac conductivity, which leads to plasmon reflection by the domain walls. The imaging reveals two kinds of plasmonic standing-wave interference patterns, which we attribute to shear and tensile domain walls. We compute the electronic structure of both wall varieties and show that the tensile wall contain additional confined bands which produce a structure-specific contrast of the local conductivity. The calculated plasmonic interference profiles are in quantitative agreement with our experiments., Comment: 14 pages, 5 figures

Weyl and Dirac semimetals are three dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and -- despite their gaplessness -- to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. Here we review the theoretical foundations of these phases, their proposed realizations in solid state systems, recent experiments on candidate materials, as well as their relation to other states of matter., Comment: 63 pages, 38 figures; Comprehensive review on Weyl and Dirac Semimetals first submitted to Reviews of Modern Physics December 2016; Accepted July 5th, 2017; Minor corrections and additions in this version

We study the frequency-dependent conductivity of nodal line semimetals (NLSMs), focusing on the effects of carrier density and energy dispersion on the nodal line. We find that the low-frequency conductivity has a rich spectral structure which can be understood using scaling rules derived from the geometry of their Dupin cyclide Fermi surfaces. We identify different frequency regimes, find scaling rules for the optical conductivity in each, and demonstrate them with numerical calculations of the inter- and intraband contributions to the optical conductivity using a low-energy model for a generic NLSM., Comment: 5 pages, 5 figures + supplementary material (8 pages)

Low-energy excitations in graphene exhibit relativistic properties due to the linear dispersion relation close to the Dirac points in the first Brillouin zone. Two of the Dirac points located at opposite corners of the first Brillouin zone can be chosen as inequivalent, representing a new valley degree of freedom, in addition to the charge and spin of an electron. Using the valley degree of freedom to encode information has attracted significant interest, both theoretically and experimentally, and gave rise to the field of valleytronics. We study a graphene $p$-$n$ junction in a uniform out-of-plane magnetic field as a platform to generate and controllably manipulate the valley polarization of electrons. We show that by tuning the external potential giving rise to the $p$-$n$ junction we can switch the current from one valley polarization to the other. We also consider the effect of different types of edge terminations and present a setup, where we can partition an incoming valley-unpolarized current into two branches of valley-polarized currents. The branching ratio can be chosen by changing the location of the $p$-$n$ junction using a gate., Comment: 8 pages, 7 figures

Multi-Weyl semimetals (m-WSMs) are a new type of Weyl semimetal that have linear dispersion along one symmetry direction but anisotropic non-linear dispersion along the two transverse directions with a topological charge larger than one. Using the Boltzmann transport theory and fully incorporating the anisotropy of the system, we study the DC conductivity as a function of carrier density and temperature. We find that the characteristic density and temperature dependence of the transport coefficients at the level of Boltzmann theory are controlled by the topological charge of the multi-Weyl point and distinguish m-WSMs from their linear Weyl counterparts., Comment: 5 pages, 4 figures + supplementary material (10 pages)

We study charge and spin transport along grain boundaries in single layer graphene in the presence of a quantizing magnetic field. Transport states in a grain boundary are produced by hybridization of Landau zero modes with interfacial states. In selected energy regimes quantum Hall edge states can be deflected either fully or partially into grain boundary states. The degree of edge state deflection is studied in the nonlocal conductance and in the shot noise. We also consider the possibility of grain boundaries as gate-switchable spin filters, a functionality enabled by counterpropagating transport channels laterally confined in the grain boundary., Comment: 4 pages, 5 figures; includes 5 page Supplemental Material

Multi-Weyl semimetals are new types of Weyl semimetals which have anisotropic non-linear energy dispersion and a topological charge larger than one, thus exhibiting a unique quantum response. Using a unified lattice model, we calculate the optical conductivity numerically in the multi-Weyl semimetal phase and in its neighboring gapped states, and obtain the characteristic frequency dependence of each phase analytically using a low-energy continuum model. The frequency dependence of longitudinal and transverse optical conductivities obeys scaling relations that are derived from the winding number of the parent multi-Weyl semimetal phase and can be used to distinguish these electronic states of matter., Comment: 5 pages, 4 figures + supplementary material (14 pages)

Snake states are open trajectories for charged particles propagating in two dimensions under the influence of a spatially varying perpendicular magnetic field. In the quantum limit they are protected edge modes that separate topologically inequivalent ground states and can also occur when the particle density rather than the field is made nonuniform. We examine the correspondence of snake trajectories in single-layer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric field profile and (b) antisymmetric carrier distribution in a uniform field. These families support different internal symmetries but the same pattern of boundary and interface currents. We demonstrate that these physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p-wave paired state. A variational model is introduced to interpret the interfacial solutions of both domain wall problems.

We combine large-scale atomistic modelling with continuum elastic theory to study the shapes of graphene sheets embedding nanoscale kirigami. Lattice segments are selectively removed from a flat graphene sheet and the structure is allowed to close and reconstruct by relaxing in the third dimension. The surface relaxation is limited by a nonzero bending modulus which produces a smoothly modulated landscape instead of the ridge-and-plateau motif found in macroscopic lattice kirigami. The resulting surface shapes and their interactions are well described by a new set of microscopic kirigami rules that resolve the competition between the bending and stretching energies., Comment: 5 pages, 4 jpeg figures

Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the inter-layer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) ($\mu_1,\mu_2$) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) monolayer/h-BN heterostructure and can be tuned by mechanical strain. Our results shed light on the role of the MCNs on inequivalent mirror-symmetric planes in reciprocal space and open new possibilities for finding new topological materials.

Electronic states confined to zero angle grain boundaries in single layer graphene are analyzed using topological band theoretic arguments. We identify a hidden chiral symmetry which supports symmetry protected zero modes in projected bulk gaps. These branches occupy a finite fraction of the interface-projected Brillouin zone and terminate at bulk gap closures, manifesting topological transitions in the occupied manifolds of the bulk systems that are joined at an interface. These features are studied by numerical calculations on a tight binding lattice and by analysis of the geometric phases of the bulk ground states., Comment: 5 pages, 4 jpeg figures

We show that valley degeneracy in rotationally faulted multilayer graphene may be broken in the presence of a magnetic field and interlayer commensurations. This happens due to a simultaneous breaking of both time-reversal and inversion symmetries leading to a splitting of Landau levels linear in the field. Our theoretical work is motivated by an experiment [Y. J. Song et al., Nature 467, 185 (2010)] on epitaxially grown multilayer graphene where such linear splitting of Landau levels was observed at moderate fields. We consider both bilayer and trilayer configurations and, although a linear splitting occurs in both cases, we show that the latter produces a splitting that is in quantitative agreement with the experiment.

Mirror symmetric surfaces of a topological crystalline insulator host even number of Dirac surface states. A surface Zeeman field generically gaps these states leading to a quantized anomalous Hall effect. Varying the direction of Zeeman field induces transitions between different surface insulating states with any two Chern numbers between -4 and 4. In the crystal frame the phase boundaries occur for field orientations which are great circles with (111)-like normals on a sphere., Comment: 4 pages, 2 figures

We report on a Dirac-like Fermi surface in three-dimensional bulk materials in a distorted spinel structure on the basis of density functional theory (DFT) as well as tight-binding theory. The four examples we provide in this paper are BiZnSiO4, BiCaSiO4, BiMgSiO4, and BiAlInO4. A necessary characteristic of these structures is that they contain a Bi lattice which forms a hierarchy of chain-like substructures, with consequences for both fundamental understanding and materials design.

We study a family of globally smooth spatially varying two dimensional stacking textures in bilayer graphene. We find that the strain-minimizing stacking patterns connecting inequivalent ground states with local $AB$ and $BA$ interlayer registries are two dimensional twisted textures of an interlayer displacement field. We construct and display these topological stacking textures for bilayer graphene, examine their interactions and develop the composition rules that allow us to represent other more complex stacking textures, including globally twisted graphenes and extended one dimensional domain walls., Comment: 4 pages, 4 color figures

Selection rules and interference effects in angle resolved photoemission spectra from twisted graphene bilayers are studied within a long wavelength theory for the electronic structure. Using a generic model for the interlayer coupling, we identify features in the calculated ARPES momentum distributions that are controlled by the singularities and topological character of its long wavelength spectrum. We distinguish spectral features that are controlled by single-layer singularities in the spectrum, their modification by gauge potentials in each layer generated by the interlayer coupling, and new energy-dependent interference effects that directly probe the interlayer coherence. The results demonstrate how the energy- and polarization- dependence of ARPES spectra can be used to characterize the interlayer coupling in twisted bilayer graphenes., Comment: RevTex4: 17 pages, 12 figures

We show that the probability of electric field induced interband tunneling in solid state systems is generically a non-monotonic (oscillatory) function of the applied field. This unexpected behavior can be understood as arising due to a common path interference between two distinct tunneling solutions. The phenomenon is insensitive to magnetic field, and arises whenever the low energy dispersion relation contains higher order terms in addition to the usual $p^2$ term. Such higher order terms are generically present, albeit with small co-efficient, so that the oscillatory Zener tunneling is a universal phenomenon. However, the first `Zener oscillation' occurs at a transmission probability which is exponentially small when the co-efficient of the higher order terms is small. This explains why this oscillatory aspect of Zener tunneling has been hitherto overlooked, despite its universality. The common path interference is also destroyed by the presence of odd powers of $p$ in the low energy dispersion relation. Since odd powers of $p$ are strictly absent only when the tunneling barrier lies along an axis of mirror symmetry, it follows that the robustness of the oscillatory behavior depends on the orientation of the tunneling barrier. Bilayer graphene is identified as a particularly good material for observation of common path interference, due to its unusual nearly isotropic dispersion relation, where the $p^4$ term makes the leading contribution.

We demonstrate the existence of topological superconductors (SC) protected by mirror and time reversal (TR) symmetries. D-dimensional (D=1,2,3) crystalline SCs are characterized by 2^(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z_2 index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa, and that a DIII SC with a mirror plane is always TR trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out., Comment: 5 pages, 2 figures, 1 table, published version