Andrej Mesaros

Topological Defects Coupling Smectic Modulations to Intra–Unit-Cell Nematicity in Cuprates

A theoretical model explains how electronic states with different symmetries coexist and interact. We study the coexisting smectic modulations and intra–unit-cell nematicity in the pseudogap states of underdoped Bi2Sr2CaCu2O8+δ. By visualizing their spatial components separately, we identified 2π topological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra–unit-cell nematicity revealed strong empirical evidence for a coupling between them. From these observations, we propose a Ginzburg-Landau functional describing this coupling and demonstrate how it can explain the coexistence of the smectic and intra–unit-cell broken symmetries and also correctly predict their interplay at the atomic scale. This theoretical perspective can lead to unraveling the complexities of the phase diagram of cuprate high-critical-temperature superconductors.

The space group classification of topological band-insulators

Topological insulators are now shown to be protected not only by time-reversal symmetry, but also by crystal lattice symmetry. By accounting for the crystalline symmetries, additional topological insulators can be predicted.

Electronic states of graphene grain boundaries

We introduce a model for amorphous grain boundaries in graphene and find that stable structures can exist along the boundary that are responsible for local density of states enhancements both at zero and finite

Classification of symmetry enriched topological phases with exactly solvable models

(\ensuremath{\sim}0.5\text{ }\text{eV})

Universal probes of two-dimensional topological insulators: dislocation and π flux.

energies. Such zero-energy peaks, in particular, were identified in STS measurements [J. \ifmmode \check{C}\else \v{C}\fi{}ervenka, M. I. Katsnelson, and C. F. J. Flipse, Nat. Phys. 5, 840 (2009)] but are not present in the simplest pentagon-heptagon dislocation array model [O. V. Yazyev and S. G. Louie, Phys. Rev. B 81, 195420 (2010)]. We consider the low-energy continuum theory of arrays of dislocations in graphene and show that it predicts localized zero-energy states. Since the continuum theory is based on an idealized lattice scale physics it is a priori not literally applicable. However, we identify stable dislocation cores, different from the pentagon-heptagon pairs that do carry zero-energy states. These might be responsible for the enhanced magnetism seen experimentally at graphite grain boundaries.

Commensurate 4a0-period charge density modulations throughout the Bi2Sr2CaCu2O8+x pseudogap regime

Recently a new class of quantum phases of matter: symmetry protected topological states, such as topological insulators, attracted much attention. In presence of interactions, group cohomology provides a classification of these [X. Chen et al., arXiv:1106.4772v5 (2011)]. These phases have short-ranged entanglement, and no topological order in the bulk. However, when long-range entangled topological order is present, it is much less understood how to classify quantum phases of matter in presence of global symmetries. Here we present a classification of bosonic gapped quantum phases with or without long-range entanglement, in the presence or absence of on-site global symmetries. In 2+1 dimensions, the quantum phases in the presence of a global symmetry group SG, and with topological order described by a finite gauge group GG, are classified by the cohomology group H^3(SGxGG,U(1)). Generally in d+1 dimensions, such quantum phases are classified by H^{d+1}(SGxGG,U(1)). Although we only partially understand to what extent our classification is complete, we present an exactly solvable local bosonic model, in which the topological order is emergent, for each given class in our classification. When the global symmetry is absent, the topological order in our models is described by the general Dijkgraaf-Witten discrete gauge theories. When the topological order is absent, our models become the exactly solvable models for symmetry protected topological phases [X. Chen et al., arXiv:1106.4772v5 (2011)]. When both the global symmetry and the topological order are present, our models describe symmetry enriched topological phases. Our classification includes, but goes beyond the previously discussed projective symmetry group classification. Measurable signatures of these symmetry enriched topological phases, and generalizations of our classification are discussed.

Generalized Modular Transformations in(3+1)DTopologically Ordered Phases and Triple Linking Invariant of Loop Braiding

We show that the π flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that π flux hosts a Kramers pair of zero modes in the topological Γ (Berry phase Skyrmion at the zero momentum) and M (Berry phase Skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a π flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.

Interplay between electronic topology and crystal symmetry : Dislocation-line modes in topological band insulators

Significance Strong Coulomb interactions between electrons on adjacent Cu atoms result in charge localization in the cuprate Mott-insulator state. When a few percent of electrons are removed, both high-temperature superconductivity and exotic charge density modulations appear. Identifying the correct fundamental theory for superconductivity requires confidence on whether a particle-like or a wave-like concept of electrons describes this physics. To address this issue, here we take the approach of using the phase of charge modulations, available only from atomic-scale imaging. It reveals a universal periodicity of the charge modulations of four crystal unit cells. These results indicate that the particle-like concept of strong interactions in real-space provides the intrinsic organizational principle for cuprate charge modulations, implying the equivalent for the superconductivity. Theories based upon strong real space (r-space) electron–electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4a0) periodicity should occur in the hole-doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector QA of the CDM to evolve continuously as if driven primarily by momentum-space (k-space) effects. Here we introduce phase-resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this technique reveals a virtually doping-independent locking of the local CDM wavevector at |Q0|=2π/4a0 throughout the underdoped phase diagram of the canonical cuprate Bi2Sr2CaCu2O8. These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi-surface)–based picture of the cuprate CDMs but are consistent with strong-coupling r-space–based theories. Our findings imply that it is the latter that provides the intrinsic organizational principle for the cuprate CDM state.

Changing topology by topological defects in three-dimensional topologically ordered phases

In topologically ordered quantum states of matter in 2+1D (space-time dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property which is directly related to global transformations of the ground-state wavefunctions on a torus (the modular transformations). On the other hand, there are theoretical descriptions of various topologically ordered states in 3+1D, which exhibit both point-like and loop-like excitations, but systematic understanding of the fundamental physical distinctions between phases, and how these distinctions are connected to quantum statistics of excitations, is still lacking. One main result of this work is that the three-dimensional generalization of modular transformations, when applied to topologically ordered ground states, is directly related to a certain braiding process of loop-like excitations. This specific braiding surprisingly involves three loops simultaneously, and can distinguish different topologically ordered states. Our second main result is the identification of the three-loop braiding as a process in which the worldsheets of the three loops have a non-trivial triple linking number, which is a topological invariant characterizing closed two-dimensional surfaces in four dimensions. In this work we consider realizations of topological order in 3+1D using cohomological gauge theory in which the loops have Abelian statistics, and explicitly demonstrate our results on examples with

Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems

Z_2\times Z_2