arXiv subjects

Stepan S. Tsirkin

Publications and source records attributed to Stepan S. Tsirkin.

29 records · Page 2Linked to original sources

arXiv2021

Flat bands with fragile topology through superlattice engineering on single-layer graphene

'Magic'-angle twisted bilayer graphene has received a lot of interest due to its flat bands with potentially non-trivial topology that lead to intricate correlated phases. A spectrum with flat bands, however, does not require a twist between multiple sheets of van der Waals materials, but rather can be realized with the application of an appropriate periodic potential. Here, we propose the imposition of a tailored periodic potential onto a single graphene layer through local perturbations that could be created via lithography or adatom manipulation, which also results in an energy spectrum featuring flat bands. Our first-principle calculations for an appropriate decoration of graphene with adatoms indeed show the presence of flat bands in the spectrum. Furthermore, we reveal the topological nature of the flat bands through a symmetry-indicator analysis. This non-trivial topology manifests itself in corner-localized states with a filling anomaly as we show using a tight-binding model. Our proposal of a single decorated graphene sheet provides a new versatile route to study correlated phases in topologically non-trivial, flat band structures.

cond-mat.mes-hall↗

arXiv2020

High performance Wannier interpolation of Berry curvature and related quantities: WannierBerri code

Wannier interpolation is a powerful tool for performing Brillouin zone integrals over dense grids of $\mathbf{k}$ points, which are essential to evaluate such quantities as the intrinsic anomalous Hall conductivity or Boltzmann transport coefficients. However, new physical problems and new materials create new numerical challenges, and computations with the existing codes become very expensive, which often prevents reaching the desired accuracy. In this article, I present a series of methods that boost the speed of Wannier interpolation by several orders of magnitude. They include a combination of fast and slow Fourier transforms, explicit use of symmetries and recursive adaptive grid refinement among others. The proposed methodology has been implemented in the new python code WannierBerri, which also aims to serve as a convenient platform for the future development of interpolation schemes for novel phenomena.

cond-mat.mtrl-sci↗

arXiv2020

IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures

We present IrRep - a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with state-of-the-art Density Functional Theory codes such as VASP, Quantum Espresso, or Abinit, as well as any other code that has an interface to Wannier90. Our code is applicable to materials in any of the 230 space groups and double groups preserving time-reversal symmetry with or without spin-orbit coupling included, for primitive or conventional unit cells. This makes IrRep a powerful tool to systematically analyze the connectivity and topological classification of bands, as well as to detect insulators with non-trivial topology, following the Topological Quantum Chemistry formalism: IrRep can generate the input files needed to calculate the (physical) elementary band representations and the symmetry-based indicators using the CheckTopologicalMat routine of the Bilbao Crystallographic Server. It is also particularly suitable for interfaces with other plane-waves based codes, due to its flexible structure.

cond-mat.mtrl-sci↗

arXiv2020

Non-Abelian chiral spin liquid on a simple non-Archimedean lattice

We extend the scope of Kitaev spin liquids to non-Archimedean lattices. For the pentaheptite lattice, which results from the proliferation of Stone-Wales defects on the honeycomb lattice, we find an exactly solvable non-Abelian chiral spin liquid with spontaneous time reversal symmetry breaking due to lattice loops of odd length. Our findings call for potential extensions of exact results for Kitaev models which are based on reflection positivity, which is not fulfilled by the pentaheptite lattice. We further elaborate on potential realizations of our chiral spin liquid proposal in strained $α$-RuCl$_3$.

cond-mat.str-el↗

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↗

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

Wannier90 as a community code: new features and applications

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

cond-mat.mtrl-sci↗

arXiv2018

Ab initio calculation of the shift photocurrent by Wannier interpolation

We describe and implement a first-principles algorithm based on maximally-localized Wannier functions for calculating the shift-current response of piezoelectric crystals in the independent-particle approximation. The proposed algorithm presents several advantages over existing ones, including full gauge invariance, low computational cost, and a correct treatment of the optical matrix elements with nonlocal pseudopotentials. Band-truncation errors are avoided by a careful formulation of $k\cdot p$ perturbation theory within the subspace of wannierized bands. The needed ingredients are the matrix elements of the Hamiltonian and of the position operator in the Wannier basis, which are readily available at the end of the wannierization step. If the off-diagonal matrix elements of the position operator are discarded, our expressions reduce to the ones that have been used in recent tight-binding calculations of the shift current. We find that this `diagonal' approximation can introduce sizeable errors, highlighting the importance of carefully embedding the tight-binding model in real space for an accurate description of the charge transfer that gives rise to the shift current.

cond-mat.mtrl-sci↗

arXiv2018

Gyrotropic effects in trigonal tellurium studied from first principles

We present a combined ab initio study of several gyrotropic effects in p-doped trigonal tellurium (effects that reverse direction with the handedness of the spiral chains in the atomic structure). The key ingredients in our study are the k-space Berry curvature and intrinsic orbital magnetic moment imparted on the Bloch states by the chirality of the crystal structure. We show that the observed sign reversal with temperature of the circular photogalvanic effect can be explained by the presence of Weyl points near the bottom of the conduction band acting as sources and sinks of Berry curvature. The passage of a current along the trigonal axis induces a rather small parallel magnetization, which can nevertheless be detected by optical means (Faraday rotation of transmitted light) due to the high transparency of the sample. In agreement with experiment, we find that when infrared light propagates antiparallel to the current at low doping the current-induced optical rotation enhances the natural optical rotation. According to our calculations the plane of polarization rotates in the opposite sense to the bonded atoms in the spiral chains, in agreement with a recent experiment that contradicts earlier reports.

cond-mat.mtrl-sci↗

arXiv2017

Composite Weyl nodes stabilized by screw symmetry with and without time reversal

We classify the band degeneracies in 3D crystals with screw symmetry $n_m$ and broken $\mathcal P*\mathcal T$ symmetry, where $\mathcal P$ stands for spatial inversion and $\mathcal T$ for time reversal. The generic degeneracies along symmetry lines are Weyl nodes: Chiral contact points between pairs of bands. They can be single nodes with a chiral charge of magnitude $|χ|=1$ or composite nodes with $|χ|=2$ or $3$, and the possible $χ$ values only depend on the order $n$ of the axis, not on the pitch $m/n$ of the screw. Double Weyl nodes require $n=4$ or 6, and triple nodes require $n=6$. In all cases the bands split linearly along the axis, and for composite nodes the splitting is quadratic on the orthogonal plane. This is true for triple as well as double nodes, due to the presence in the effective two-band Hamiltonian of a nonchiral quadratic term that masks the chiral cubic dispersion. If $\mathcal T$ symmetry is present and $\mathcal P$ is broken there may exist on some symmetry lines Weyl nodes pinned to $\mathcal T$-invariant momenta, which in some cases are unavoidable. In the absence of other symmetries their classification depends on $n$, $m$, and the type of $\mathcal T$ symmetry. With spinless $\mathcal T$ such $\mathcal T$-invariant Weyl nodes are always double nodes, while with spinful $\mathcal T$ they can be single or triple nodes. $\mathcal T$-invariant triples nodes can occur not only on 6-fold axes but also on 3-fold ones, and their in-plane band splitting is cubic, not quadratic as in the case of generic triple nodes. These rules are illustrated by means of first-principles calculations for hcp cobalt, a $\mathcal T$-broken, $\mathcal P$-invariant crystal with $6_3$ symmetry, and for trigonal tellurium and hexagonal NbSi$_2$, which are $\mathcal T$-invariant, $\mathcal P$-broken crystals with 3-fold and 6-fold screw symmetry respectively.

cond-mat.mtrl-sci↗

arXiv2015

Unfolding spinor wavefunctions and expectation values of general operators: Introducing the unfolding-density operator

We show that the spectral weights $W_{m\vec K}(\vec k)$ used for the unfolding of two-component spinor eigenstates $| {ψ_{m\vec K}^\mathrm{SC}} > = | α> | {ψ_{m\vec{K}}^\mathrm{SC, α}} > + | β> | {ψ_{m\vec{K}}^\mathrm{SC, β}} >$ can be decomposed as the sum of the partial spectral weights $W_{m\vec{K}}^μ(\vec k)$ calculated for each component $μ= α, β$ independently, effortlessly turning a possibly complicated problem involving two coupled quantities into two independent problems of easy solution. Furthermore, we define the unfolding-density operator $\hatρ_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)$, which unfolds the primitive cell expectation values $φ^{pc}(\vec{k}; \varepsilon)$ of any arbitrary operator $\mathbf{\hatφ}$ according to $φ^{pc}(\vec{k}_{i}; \varepsilon) = \mathit{Tr}(\hatρ_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)\,\,\hatφ)$. As a proof of concept, we apply the method to obtain the unfolded band structures, as well as the expectation values of the Pauli spin matrices, for prototypical physical systems described by two-component spinor eigenfunctions.

cond-mat.mtrl-sci↗