arXiv subjects

Titus Neupert

Publications and source records attributed to Titus Neupert.

At least 127 records · Page 7Linked to original sources

arXiv2020

Topological Quantum Liquids with Long-Range Couplings

Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological properties. We demonstrate that, even though topological phases are intimately linked to the notion of locality, the infinite-range couplings give rise to topological zero and non-zero energy Majorana end modes depending on the boundary conditions of the system. We show that the analytically derived properties are to a large degree stable against modifications to decaying long-range couplings. Our work opens new frontiers for topological states of matter that are relevant to current experiments where suitable interactions can be designed.

cond-mat.str-el↗

arXiv2020

Learning-based Defect Recognition for Quasi-Periodic Microscope Images

Controlling crystalline material defects is crucial, as they affect properties of the material that may be detrimental or beneficial for the final performance of a device. Defect analysis on the sub-nanometer scale is enabled by high-resolution (scanning) transmission electron microscopy [HR(S)TEM], where the identification of defects is currently carried out based on human expertise. However, the process is tedious, highly time consuming and, in some cases, yields ambiguous results. Here we propose a semi-supervised machine learning method that assists in the detection of lattice defects from atomic resolution microscope images. It involves a convolutional neural network that classifies image patches as defective or non-defective, a graph-based heuristic that chooses one non-defective patch as a model, and finally an automatically generated convolutional filter bank, which highlights symmetry breaking such as stacking faults, twin defects and grain boundaries. Additionally, we suggest a variance filter to segment amorphous regions and beam defects. The algorithm is tested on III-V/Si crystalline materials and successfully evaluated against different metrics, showing promising results even for extremely small training data sets. By combining the data-driven classification generality, robustness and speed of deep learning with the effectiveness of image filters in segmenting faulty symmetry arrangements, we provide a valuable open-source tool to the microscopist community that can streamline future HR(S)TEM analyses of crystalline materials.

cond-mat.mtrl-sci↗

arXiv2020

Theory for the negative longitudinal magnetoresistance in the quantum limit of Kramers Weyl semimetals

Negative magnetoresistance is rare in non-magnetic materials. Recently, a negative magnetoresistance has been observed in the quantum limit of $β$-Ag$_2$Se, where only one band of Landau levels is occupied in a strong magnetic field parallel to the applied current. $β$-Ag$_2$Se is a material that host a Kramers Weyl cone with band degeneracy near the Fermi energy. Kramers Weyl cones exist at time-reversal invariant momenta in all symmorphic chiral crystals, and at a subset of these momenta, including the $Γ$ point, in non-symmorphic chiral crystals. Here, we present a theory for the negative magnetoresistance in the quantum limit of Kramers Weyl semimetals. We show that, although there is a band touching similar to those in Weyl semimetals, negative magnetoresistance can exist without a chiral anomaly. We find that it requires screened Coulomb scattering potentials between electrons and impurities, which is naturally the case in $β$-Ag$_2$Se.

cond-mat.mes-hall↗

arXiv2020

Fermion-boson many-body interplay in a frustrated kagome paramagnet

Kagome-net, appearing in areas of fundamental physics, materials, photonic and cold-atom systems, hosts frustrated fermionic and bosonic excitations. However, it is extremely rare to find a system to study both fermionic and bosonic modes to gain insights into their many-body interplay. Here we use state-of-the-art scanning tunneling microscopy and spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet. Our results reveal the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through a combination of self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice analog of kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials.

cond-mat.mtrl-sci↗

arXiv2020

Pairing Obstructions in Topological Superconductors

The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor, we show that the wave function of an individual Cooper pair decays exponentially with separation in the trivial phase and polynomially in the topological phase. For the position-space Majorana representation, we show that the topological phase is characterized by a nonzero Majorana polarization, which captures an irremovable and quantized separation of Majorana Wannier centers from the atomic positions. We apply our results to diagnose second-order topological superconducting phases in two dimensions. Our work establishes a vantage point for the generalization of Topological Quantum Chemistry to superconductivity.

cond-mat.supr-con↗

arXiv2020

Many-body Resonance in a Correlated Topological Kagome Antiferromagnet

We use scanning tunneling microscopy/spectroscopy (STM/S) to elucidate the atomically resolved electronic structure in strongly correlated topological kagome magnet Mn$_3$Sn. In stark contrast to its broad single-particle electronic structure, we observe a pronounced resonance with a Fano line shape at the Fermi level resembling the many-body Kondo resonance. We find that this resonance does not arise from the step edges or atomic impurities, but the intrinsic kagome lattice. Moreover, the resonance is robust against the perturbation of a vector magnetic field, but broadens substantially with increasing temperature, signaling strongly interacting physics. We show that this resonance can be understood as the result of geometrical frustration and strong correlation based on the kagome lattice Hubbard model. Our results point to the emergent many-body resonance behavior in a topological kagome magnet.

cond-mat.str-el↗

arXiv2020

The fine structure of heating in a quasiperiodically driven critical quantum system

We study the heating dynamics of a generic one dimensional critical system when driven quasiperiodically. Specifically, we consider a Fibonacci drive sequence comprising the Hamiltonian of uniform conformal field theory (CFT) describing such critical systems and its sine-square deformed counterpart. The asymptotic dynamics is dictated by the Lyapunov exponent which has a fractal structure embedding Cantor lines where the exponent is exactly zero. Away from these Cantor lines, the system typically heats up fast to infinite energy in a non-ergodic manner where the quasiparticle excitations congregate at a small number of select spatial locations resulting in a build up of energy at these points. Periodic dynamics with no heating for physically relevant timescales is seen in the high frequency regime. As we traverse the fractal region and approach the Cantor lines, the heating slows enormously and the quasiparticles completely delocalise at stroboscopic times. Our setup allows us to tune between fast and ultra-slow heating regimes in integrable systems.

cond-mat.str-el↗

arXiv2020

Discovery of a quantum limit Chern magnet TbMn6Sn6

The quantum level interplay between geometry, topology, and correlation is at the forefront of fundamental physics. Owing to the unusual lattice geometry and breaking of time-reversal symmetry, kagome magnets are predicted to support intrinsic Chern quantum phases. However, quantum materials hosting ideal spin-orbit coupled kagome lattices with strong out-of-plane magnetization have been lacking. Here we use scanning tunneling microscopy to discover a new topological kagome magnet TbMn6Sn6, which is close to satisfying the above criteria. We visualize its effectively defect-free purely Mn-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state exhibits distinct Landau quantization upon the application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn6Sn6, opening up an avenue for discovering topological quantum phenomena in the RMn6Sn6 (R = rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real and momentum space demonstrates a proof-of-principle method revealing topological magnets.

cond-mat.mtrl-sci↗

arXiv2020

Reciprocal skin effect and its realization in a topolectrical circuit

A system is non-Hermitian when it exchanges energy with its environment and non-reciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and non-reciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but reciprocal systems in two or more dimensions: Eigenmodes with opposite longitudinal momentum exhibit opposite transverse anomalous localization. We experimentally demonstrate the reciprocal skin effect in a passive RLC circuit, suggesting convenient alternative implementations in optical, acoustic, mechanical, and related platforms. Skin mode localization brings forth potential applications in directional and polarization detectors for electromagnetic waves.

cond-mat.mes-hall↗

arXiv2020

Transport across twist angle domains in moiré graphene

Many of the experiments in twisted bilayer graphene (TBG) differ from each other in terms of the details of their phase diagrams. Few controllable aspects aside, this discrepancy is largely believed to be arising from the presence of a varying degree of twist angle inhomogeneity across different samples. Real space maps indeed reveal TBG devices splitting into several large domains of different twist angles. Motivated by these observations, we study the quantum mechanical tunneling across a domain wall (DW) that separates two such regions. We show that the tunneling of the moiré particles can be understood by the formation of an effective step potential at the DW. The height of this step potential is simply a measure of the difference in twist angles. These computations lead us to identify the global transport signatures for detecting and quantifying the local twist angle variations. In particular, Using Landauer-Büttiker formalism we compute single-channel conductance ($dI/dV$) and Fano factor for shot noise (ratio of noise power and mean current). A zero-bias, sub-meV transport gap is observed in the conductance which scales with the height of the step potential. One of the key findings of our work is that transport in presence of twist angle inhomogeneity is "noisy", though sub-Poissonian. In particular, the differential Fano factor peaks near the van Hove energies corresponding to the domains in the sample. The location and the strength of the peak is simply a measure of the degree of twist angle inhomogeneity.

cond-mat.mes-hall↗

arXiv2020

`Unhinging' the surfaces of higher-order topological insulators and superconductors

We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting $\mathsf{C}_{2n}\mathcal T$ symmetry upon the introduction of non-Abelian surface topological order. In both cases, the topological order on a single side surface breaks time reversal symmetry, but appears with its time-reversal conjugate on alternating sides in a $\mathsf{C}_{2n}\mathcal T$ preserving pattern. In the absence of the HOTI/HOTSC bulk, such a pattern necessarily involves gapless chiral modes on hinges between $\mathsf{C}_{2n}\mathcal T$-conjugate domains. However, using a combination of $K$-matrix and anyon condensation arguments, we show that on the boundary of a 3D HOTI/HOTSC these topological orders are fully gapped and hence `anomalous'. Our results suggest that new patterns of surface and hinge states can be engineered by selectively introducing topological order only on specific surfaces.

cond-mat.str-el↗

arXiv2019

Higher-Order Topology in Bismuth

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.

cond-mat.mtrl-sci↗

arXiv2019

Competing orders in the Hofstadter t-J model

The Hofstadter model describes non-interacting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model including a Hubbard repulsion U. We investigate this model in the large-U limit corresponding to a t-J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly co-existing) charge, bond and superconducting orders. Topological properties of the states are also investigated and some of our results are compared to related experiments involving ultra-cold atoms loaded on optical lattices in the presence of a synthetic gauge field.

cond-mat.str-el↗

arXiv2019

Fractional corner charges in spin-orbit coupled crystals

We study two-dimensional spinful insulating phases of matter that are protected by time-reversal and crystalline symmetries. To characterize these phases we employ the concept of corner charge fractionalization: Corners can carry charges that are fractions of even multiples of the electric charge. The charges are quantized and topologically stable as long as all symmetries are preserved. We classify the different corner charge configurations for all point groups, and match them with the corresponding bulk topology. For this we employ symmetry indicators and (nested) Wilson loop invariants. We provide formulas that allow for a convenient calculation of the corner charge from Bloch wavefunctions and illustrate our results using the example of arsenic and antimony monolayers. Depending on the degree of structural buckling, these materials can exhibit two distinct obstructed atomic limits. We present density functional theory calculations for open flakes to support our findings.

cond-mat.str-el↗

arXiv2019

Slave-Boson analysis of the 2D Hubbard model

We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\boldsymbol Q = (π, π), (0, π)$, and $(0, 0)$ we find incommensurate phases where the ordering wave vectors $\boldsymbol Q = (Q, Q)$, and $(Q, π)$ vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the $(Q, Q)$ and $(Q, π)$ phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.

cond-mat.str-el↗

arXiv2019

Topology and Magnetism in the Kondo Insulator Phase Diagram

Topological Kondo insulators are a rare example of an interaction-enabled topological phase of matter in three-dimensional crystals - making them an intriguing but also hard case for theoretical studies. Here, we aim to advance their theoretical understanding by solving the paradigmatic two-band model for topological Kondo-insulators using a fully spin-rotation invariant slave-boson treatment. Within a mean-field approximation, we map out the magnetic phase diagram and characterize both antiferromagnetic and paramagnetic phases by their topological properties. Among others, we identify an antiferromagnetic insulator that shows, for suitable crystal terminations, topologically protected hinge modes. Furthermore, Gaussian fluctuations of the slave boson fields around their mean-field value are included in order to establish the stability of the mean-field solution through computation of the full dynamical susceptibility.

cond-mat.str-el↗

arXiv2019

Emergent Black Hole Dynamics in Critical Floquet Systems

While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. We study such an exceptional class in periodically driven critical (1 + 1)-dimensional systems with a spatially modulated, but disorder-free time evolution operator. Instead of complete scrambling, the excitations of the system remain well-defined. Their propagation is analogous to the evolution along light cones in a curved space-time obtained by two Schwarzschild black holes. The Hawking temperature serves as an order parameter which distinguishes between heating and non-heating phases. Beyond a time scale determined by the inverse Hawking temperature, excitations are absorbed by the black holes resulting in a singular concentration of energy at their center. We obtain these results analytically within conformal field theory, capitalizing on a mapping to sine-square deformed field theories. Furthermore, by means of numerical calculations for an interacting XXZ spin-1/2 chain, we demonstrate that our findings survive lattice regularization.

cond-mat.str-el↗

arXiv2019

An exactly soluble model for a fractionalized Weyl semimetal

We construct an exactly solvable lattice model of a fractional Weyl semimetal (FWS). The low energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect (CPGE) and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function they provide strong experimental signatures for this exotic gapless state of matter.

cond-mat.str-el↗