Flat bands with higher Chern number in pyrochlore slabs

A large number of recent works point to the emergence of intriguing analogs of fractional quantum Hall states in lattice models due to effective interactions in nearly flat bands with Chern number C=1. Here, we provide an intuitive and efficient construction of almost dispersionless bands with higher Chern numbers. Inspired by the physics of quantum Hall multilayers and pyrochlore-based transition-metal oxides, we study a tight-binding model describing spin-orbit coupled electrons in N parallel kagome layers connected by apical sites forming N-1 intermediate triangular layers (as in the pyrochlore lattice). For each N, we find finite regions in parameter space giving a virtually flat band with C=N. We analytically express the states within these topological bands in terms of single-layer states and thereby explicitly demonstrate that the C=N wave functions have an appealing structure in which layer index and translations in reciprocal space are intricately coupled. This provides a promising arena for new collective states of matter.Comment: 5+3 pages. Title extended, as publishe

Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices

The hallmark of topological phases is their robust boundary signature whose intriguing properties---such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals---are impossible to realize on the surface alone. Yet, despite the glaring simplicity of non-interacting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension without the need for fine-tuning of hopping amplitudes. Our solutions derive from local constraints tantamount to destructive interference between neighboring layer lattices perpendicular to the surface and provide microscopic insights into the structure of the surface states that enable analytical calculation of many desired properties. We illustrate our general findings on a large number of examples in two and three spatial dimensions. Notably, we derive exact chiral Chern insulator edge states on the spin orbit-coupled kagome lattice, and Fermi arcs relevant for various recently synthesized pyrochlore iridate slabs. Remarkably, each of the pyrochlore slabs exhibit Fermi arcs although only the ones with a magnetic one-in-three-out configuration feature bulk Weyl nodes in realistic parameter regimes. Our approach furthermore signal the absence of topological surface states, which we illustrate for a class of models akin to the trivial surface of Hourglass materials KHg$X$.Comment: 24 pages, 17 figure

Effect of a field-induced charge density wave

Recent experiments on type-II Weyl semimetals such as WTe2, MoTe2, MoxW1−xTe2, and WP2 reveal remarkable transport properties in the presence of a strong magnetic field, including an extremely large magnetoresistance and an unusual temperature dependence. Here, we investigate magnetotransport via the Kubo formula in a minimal model of a type-II Weyl semimetal taking into account the effect of a charge density wave (CDW) transition, which can arise even at weak coupling in the presence of a strong magnetic field because of the special Landau level dispersion of type-II Weyl systems. Consistent with experimental measurements we find an extremely large magnetoresistance with close to B2 scaling at particle-hole compensation, while in the extreme quantum limit there is a transition to a qualitatively new scaling with approximately B0.75. We also investigate the Shubnikov-de Haas effect and find that the amplitude of the resistivity quantum oscillations are greatly enhanced below the CDW transition temperature which is accompanied by an unusual nonmonotonous (non-Lifshitz-Kosevich) temperature dependence

Exact solutions from destructive interference on frustrated lattices

The hallmark of topological phases is their robust boundary signature whose intriguing properties—such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals—are impossible to realize on the surface alone. Yet, despite the glaring simplicity of noninteracting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension without the need for fine-tuning of hopping amplitudes. Our solutions derive from local constraints tantamount to destructive interference between neighboring layer lattices perpendicular to the surface and provide microscopic insights into the structure of the surface states that enable analytical calculation of many desired properties including correlation functions, surface dispersion, Berry curvature, and the system size dependent gap closing, which necessarily occurs when the spatial localization switches surface. This further provides a deepened understanding of the bulk-boundary correspondence. We illustrate our general findings on a large number of examples in two and three spatial dimensions. Notably, we derive exact chiral Chern insulator edge states on the spin-orbit-coupled kagome lattice, and Fermi arcs relevant for recently synthesized slabs of pyrochlore-based Eu2Ir2O7 and Nd2Ir2O7, which realize an all-in-all-out spin configuration, as well as for spin-ice-like two-in-two-out and one-in-three-out configurations, which are both relevant for Pr2Ir2O7. Remarkably, each of the pyrochlore examples exhibit clearly resolved Fermi arcs although only the one-in-three-out configuration features bulk Weyl nodes in realistic parameter regimes. Our approach generalizes to symmetry protected phases, e.g., quantum spin Hall systems and Dirac semimetals with time-reversal symmetry, and can furthermore signal the absence of topological surface states, which we illustrate for a class of models akin to the trivial surface of Hourglass materials KHgX where the exact solutions apply but, independently of Hamiltonian details, yield eigenstates delocalized over the entire sample

Statistical mechanics approach to the electric polarization and dielectric constant of band insulators

We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbation-like expression of the Wannier-Stark energy spectrum of electrons and a modified statistical mechanics approach involving a local chemical potential in order to deal with the unbounded spectrum and impose the physically relevant electronic filling. At first order in the field, we recover the result of King-Smith, Vanderbilt, and Resta for the electric polarization in terms of a Zak phase—albeit at finite temperature—and, at second order, deduce a general formula for the electric susceptibility, or equivalently for the dielectric constant. Advantages of our method are the validity of the formalism both at zero and finite temperature and the easy computation of higher order derivatives of the free energy. We verify our findings on two different one-dimensional tight-binding models

Comparison of transport and density of states calculations

Double Weyl nodes are topologically protected band crossing points which carry chiral charge ±2. They are stabilized by C4 point-group symmetry and are predicted to occur in SrSi2 or HgCr2Se4. We study their stability and physical properties in the presence of a disorder potential. We investigate the density of states and the quantum transport properties at the nodal point. We find that, in contrast to their counterparts with unit chiral charge, double Weyl nodes are unstable to any finite amount of disorder and give rise to a diffusive phase, in agreement with the predictions of Goswami and Nevidomskyy [Phys. Rev. B 92, 214504 (2015)] and Bera, Sau, and Roy [Phys. Rev. B 93, 201302 (2016)]. However, for finite system sizes a crossover between pseudodiffusive and diffusive quantum transport can be observed

Charge density wave instabilities of type-II Weyl semimetals in a strong magnetic field

Shortly after the discovery of Weyl semimetals, properties related to the topology of their bulk band structure have been observed, e.g., signatures of the chiral anomaly and Fermi arc surface states. These essentially single particle phenomena are well understood, but whether interesting many-body effects due to interactions arise in Weyl systems remains much less explored. Here, we investigate the effect of interactions in a microscopic model of a type-II Weyl semimetal in a strong magnetic field. We identify a charge density wave (CDW) instability even for weak interactions stemming from the emergent nesting properties of the type-II Weyl Landau level dispersion. We map out the dependence of this CDW on magnetic field strength. Remarkably, as a function of decreasing temperature, a cascade of CDW transitions emerges and we predict characteristic signatures for experiments.This work was supported by Emmy Noether program (BE 5233/1-1) of the Deutsche Forschungs- gemeinschaft, the Swedish Research Council (VR), and the Wallenberg Academy Fellows program of the Knut and Alice Wallenberg Foundation. J.K. is supported by the Marie Curie Programme under EC Grant Agreement No. 703697