arXiv subjects

Robert-Jan Slager

Publications and source records attributed to Robert-Jan Slager.

At least 55 records · Page 3Linked to original sources

arXiv2024

Non-Abelian Hopf-Euler insulators

We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal ($\mathcal{PT}$) inversion symmetry. These phases may also host subdimensional topological invariants given by the Euler characteristic class, resulting in real Hopf-Euler insulators. Such systems naturally realize helical nodal structures in the three-dimensional Brillouin zone, providing a physical manifestation of the linking number described by the Hopf invariant. We show that, by opening a gap between the valence bands of these systems, one finds a fully-gapped ``flag'' phase, which displays a three-band multi-gap Pontryagin invariant. Unlike the previously reported $\mathcal{PT}$-symmetric four-band real Hopf insulator, which hosts a $\mathbb{Z} \oplus \mathbb{Z}$ invariant, these phases are not unitarily equivalent to two copies of a complex two-band Hopf insulator. We show that such uncharted phases can be obtained through dimensional extension of two-dimensional Euler insulators, and that they support (i) an optical bulk integrated circular shift effect quantized by the Hopf invariant, (ii) quantum-geometric breathing in the real space Wannier functions, and (iii) surface Euler topology on boundaries. Consequently, our findings pave the way for novel experimental realizations of real-space quantum-geometry, as these systems may be directly simulated by utilizing synthetic dimensions in metamaterials or ultracold atoms.

cond-mat.mes-hall↗

arXiv2024

Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals

We study the effect of disorder in systems having a non-trivial Euler class. As these recently proposed multi-gap topological phases come about by braiding non-Abelian charged band nodes residing between different bands to induce stable pairs within isolated band subspaces, novel properties may be expected. Namely, a~modified stability and critical phases under the unbraiding to metals can arise, when the disorder preserves the underlying $C_2\cal{T}$ or $\cal{P}\cal{T}$ symmetry on average. Employing elaborate numerical computations, we verify the robustness of associated topology by evaluating the changes in the average densities of states and conductivities for different types of disorders. Upon performing a scaling analysis around the corresponding quantum critical points we retrieve a universality for the localization length exponent of $ν= 1.4 \pm 0.1$ for Euler-protected phases, relating to two-dimensional percolation models. We generically find that quenched disorder drives Euler semimetals into critical metallic phases. Finally, we show that magnetic disorder can also induce topological transitions to quantum anomalous Hall plaquettes with local Chern numbers determined by the initial value of the Euler invariant.

cond-mat.mes-hall↗

arXiv2024

Interferometry of non-Abelian band singularities and Euler class topology

In systems with a real Bloch Hamiltonian band nodes can be characterised by a non-Abelian frame-rotation charge. The ability of these band nodes to annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps the sign of their charges can be changed. Here, we theoretically construct and numerically confirm two concrete methods to experimentally probe these non-Abelian braiding processes and charges in ultracold atomic systems. We consider a coherent superposition of two bands that can be created by moving atoms through the band singularities at some angle in momentum space. Analyzing the dependency of excitations on the frame charges, we demonstrate an interferometry scheme passing through two band nodes, which reveals the relative frame charges and allows for measuring the multi-gap topological invariant. The second method relies on a single wavepacket probing two nodes sequentially, where the frame charges can be determined from the band populations. Our results present a feasible avenue for measuring non-Abelian charges of band nodes and the direct experimental verification of braiding procedures, which can be applied in a variety of settings including the recently discovered anomalous non-Abelian phases arising under periodic driving.

cond-mat.quant-gas↗

arXiv2024

On dualities of paired quantum Hall bilayer states at $ν_T = \frac{1}{2} + \frac{1}{2}$

Density-balanced, widely separated quantum Hall bilayers at $ν_T = 1$ can be described as two copies of composite Fermi liquids (CFLs). The two CFLs have interlayer weak-coupling BCS instabilities mediated by gauge fluctuations, the resulting pairing symmetry of which depends on the CFL hypothesis used. If both layers are described by the conventional Halperin-Lee-Read (HLR) theory-based composite electron liquid (CEL), the dominant pairing instability is in the $p+ip$ channel; whereas if one layer is described by CEL and the other by a composite hole liquid (CHL, in the sense of anti-HLR), the dominant pairing instability occurs in the $s$-wave channel. Using the Dirac composite fermion (CF) picture, we show that these two pairing channels can be mapped onto each other by particle-hole (PH) transformation. Furthermore, we derive the CHL theory as the non-relativistic limit of the PH-transformed massive Dirac CF theory. Finally, we prove that an effective topological field theory for the paired CEL-CHL in the weak-coupling limit is equivalent to the exciton condensate phase in the strong-coupling limit.

cond-mat.str-el↗

arXiv2024

Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence"

We comment on the recent paper ``Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" by Tianyu Li and Haiping Hu, Nat. Comm. {\bf 14}, 6418 (2023). Apart from the fact that the authors unjustly imply to study multi-gap topology in Floquet systems for the first time, only known homotopic relations are presented. While such insights are used to present interesting Floquet phenomena and phases, which is an attractive result in itself, they cannot be used to deduce the total bulk characterization in the dynamical context without further proof. In fact, the authors essentially rephrase a Zak phase description. These results should in particular be contrasted to earlier results, arXiv:2208.12824, in which static-compatible Zak phases {\it and} dynamical Dirac strings were shown to be able to {\it distinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensional systems. As a result, the claim of a sharp multifold bulk-edge correspondence cannot be concluded from the given arguments.

cond-mat.mes-hall↗

arXiv2024

Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index

We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless $\mathcal{P}\mathcal{T}$ symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases host multi-gap topology, providing a realization of a single $\mathbb{Z}$ invariant in three spatial dimensions that is distinct from the Hopf index. We identify this invariant with the Pontryagin index, which describes BPST instantons in particle physics contexts and corresponds to a 3-sphere winding number. We study naturally arising multi-gap linked nodal rings, topologically characterized by split-biquaternion charges, which can be removed by non-Abelian braiding of nodal rings, even without closing a gap. We additionally connect the describing winding number in terms of gauge-invariant combinations of non-Abelian Berry connection elements, indicating relations to Pontryagin characteristic class in four dimensions. These topological configurations are furthermore related to fully non-degenerate multi-gap phases that are characterized by a pair of winding numbers relating to two isoclinic rotations in the case of four bands and can be generalized to an arbitrary number of bands. From a physical perspective, we also analyze the edge states corresponding to this Pontryagin index as well as their dissolution subject to the gap-closing disorder. Finally, we elaborate on the realization of these novel non-Abelian phases, their edge states and linked nodal structures in acoustic metamaterials and trapped-ion experiments.

cond-mat.mes-hall↗

arXiv2024

Photo-induced electronic and spin topological phase transitions in monolayer bismuth

Ultrathin bismuth exhibits rich physics including strong spin-orbit coupling, ferroelectricity, nontrivial topology, and light-induced structural dynamics. We use \textit{ab initio} calculations to show that light can induce structural transitions to four transient phases in bismuth monolayers. These light-induced phases exhibit nontrivial topological character, which we illustrate using the recently introduced concept of spin bands and spin-resolved Wilson loops. Specifically, we find that the topology changes via the closing of the electron and spin band gaps during photo-induced structural phase transitions, leading to distinct edge states. Our study provides strategies to tailor electronic and spin topology via ultrafast control of photo-excited carriers and associated structural dynamics.

cond-mat.mtrl-sci↗

arXiv2024

Electrical transport signatures of metallic surface state formation in the strongly-correlated insulator FeSb2

We present local and nonlocal electrical transport measurements of the correlated insulator FeSb$_2$. By employing wiring configurations that delineate between bulk- and surface-dominated conduction, we reveal the formation of a metallic surface state in FeSb$_2$ for temperatures $\lessapprox 5$~K. This result is corroborated by an angular rotation study of this material's magnetotransport, which also shows signatures of the transition from bulk- to surface-dominated conduction over the same temperature interval as the local/nonlocal transport divergence. Notable similarities with the topological Kondo insulator candidate SmB$_6$ are discussed.

cond-mat.str-el↗

arXiv2023

Exploring Kondo effect by quantum energy teleportation

We consider a quantum energy teleportation (QET) method to replicate the phase diagram of a one-dimensional $XXZ$ spin chain featuring a Kondo effect coupling. In this setup, the energy supplier and receiver are spatially separated from the point impurity and do not interact directly with it. Nonetheless, they may successfully generate phase diagrams that closely mirror those produced via exact diagonalization. This can be achieved using only local operations on their respective subsystems, supplemented by classical communication. This feat is made possible due to a critical connection between the energy obtained through the QET approach and the system's quantum entanglement entropy. To substantiate these findings, we initially demonstrate that the quantum entanglement entropy serves as the relevant order parameter for the system. Intriguingly, changes in the gap spacing of the entanglement spectra align with the locations of peaks in both entanglement entropy and energy, as determined by QET. We hypothesize that this theoretical framework could, for example, be validated experimentally using a one-dimensional chain of Rydberg atoms.

quant-ph↗

arXiv2023

Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries

We consider nontrivial topological phases in Floquet systems using unitary loops and stroboscopic evolutions under a static Floquet Hamiltonian $H_F$ in the presence of dynamical space-time symmetries $G$. While the latter has been subject of out-of-equilibrium classifications that extend the ten-fold way and systems with additional crystalline symmetries to periodically driven systems, we explore the anomalous topological zero modes that arise in $H_F$ from the coexistence of a dynamical space-time symmetry $M$ and antisymmetry $A$ of $G$, and classify them using a frequency-domain formulation. Moreover, we provide an interpretation of the resulting Floquet topological phases using a frequency lattice with a decoration represented by color degrees of freedom on the lattice vertices. These colors correspond to the coefficient $N$ of the group extension $\tilde{G}$ of $G$ along the frequency lattice, given by $N=Z\rtimes H^1[A,M]$. The distinct topological classifications that arise at different energy gaps in its quasi-energy spectrum are described by the torsion product of the cohomology group $H^{2}[G,N]$ classifying the group extension.

cond-mat.mes-hall↗

arXiv2023

Theory of polarization textures in crystal supercells

Recently, topologically nontrivial polarization textures have been predicted and observed in nanoscale systems. While these polarization textures are interesting and promising in terms of applications, their topology in general is yet to be fully understood. For example, the relation between topological polarization structures and band topology has not been explored, and polar domain structures are typically considered in topologically trivial systems. In particular, the local polarization in a crystal supercell is not well-defined, and typically calculated using approximations which do not satisfy gauge invariance. Furthermore, local polarization in supercells is typically approximated using calculations involving smaller unit cells, meaning the connection to the electronic structure of the supercell is lost. In this work, we propose a definition of local polarization which is gauge invariant and can be calculated directly from a supercell without approximations. We show using first-principles calculations for commensurate bilayer hexagonal boron nitride that our expressions for local polarization give the correct result at the unit cell level, which is a first approximation to the local polarization in a moiré superlattice. We also illustrate using an effective model that the local polarization can be directly calculated in real space. Finally, we discuss the relation between polarization and band topology, for which it is essential to have a correct definition of polarization textures.

cond-mat.mtrl-sci↗

arXiv2023

Pairing of Composite-Electrons and Composite-Holes in $ν_T=1$ Quantum Hall Bilayers

Motivated by recent experimental indications of preformed electron-hole pairs in $ν_T=1$ quantum Hall bilayers at relatively large separation, we formulate a Chern-Simons (CS) theory of the coupled composite electron liquid (CEL) and composite hole liquid (CHL). We show that the effective action of the CS gauge field fluctuations around the saddle-point leads to stable pairing between CEL and CHL. We find that the CEL-CHL pairing theory leads to a dominant $s$-wave channel in contrast to the dominant $p$-wave channel found in the CEL-CEL pairing theory. Moreover, the CEL-CHL pairing is generally stronger than the CEL-CEL pairing across the whole frequency spectrum. Finally, we discuss possible differences between the two pairing mechanisms that may be probed in experiments.

cond-mat.str-el↗

arXiv2023

Polar meron-antimeron networks in strained and twisted bilayers

Out-of-plane polar domain structures have recently been discovered in strained and twisted bilayers of inversion symmetry broken systems such as hexagonal boron nitride. Here we show that this symmetry breaking also gives rise to an in-plane component of polarization, and the form of the total polarization is determined purely from symmetry considerations. The in-plane component of the polarization makes the polar domains in strained and twisted bilayers topologically non-trivial, forming a network of merons and antimerons (half-skyrmions and half-antiskyrmions). For twisted systems, the merons are of Bloch type whereas for strained systems they are of Néel type. We propose that the polar domains in strained or twisted bilayers may serve as a platform for exploring topological physics in layered materials and discuss how control over topological phases and phase transitions may be achieved in such systems.

cond-mat.mtrl-sci↗

arXiv2023

Quantum geometry beyond projective single bands

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many geometrical concepts for single bands, the exploration of these concepts to a multi-band paradigm still promises a new field of interest. Formally, multi-band systems, featuring in particular degeneracies, have been related to projective spaces, explaining also the success of relating quantum geometrical aspects of flat band systems, albeit usually in the single band picture. Here, we propose a different route involving Plücker embeddings to represent arbitrary classifying spaces, being the essential objects that encode $all$ the relevant topology.This paradigm allows for the quantification of geometrical quantities directly in readily manageable vector spaces that a priori do not involve projectors or the need of flat band conditions. As a result, our findings are shown to pave the way for identifying new geometrical objects and defining metrics in arbitrary multi-band systems, especially beyond the single flatband limit, promising a versatile tool that can be applied in contexts that range from response theories to finding quantum volumes and bounds on superfluid densities as well as possible quantum computations.

cond-mat.mes-hall↗

arXiv2023

Helicity-dependent Ultrafast Photocurrents in Weyl Magnet Mn$_3$Sn

We present an optical pump-THz emission study on non-collinear antiferromagnet Mn$_3$Sn. We show that Mn$_3$Sn acts as a source of THz radiation when irradiated by femtosecond laser pulses. The polarity and amplitude of the emitted THz fields can be fully controlled by the polarisation of optical excitation. We explain the THz emission with the photocurrents generated via the photon drag effect by combining various experimental measurements as a function of pump polarisation, magnetic field, and sample orientation with thorough symmetry analysis of response tensors.

cond-mat.mes-hall↗

arXiv2023

Andreev reflection in Euler materials

Many previous studies of Andreev reflection have demonstrated that unusual effects can occur in media which have a nontrivial bulk topology. Following this line of investigation, we study Andreev reflection in topological Euler materials by analysing a simple model of a bulk node with a generic winding number $n\geq 0$. We find that the magnitudes of the resultant reflection coefficients depend strongly on whether the winding is even or odd. Moreover this parity dependence is reflected in the differential conductance curves, which are highly suppressed for $n$ even but not $n$ odd. This gives a possible route through which the recently discovered Euler topology could be probed experimentally.

cond-mat.mes-hall↗

arXiv2023

Second Euler number in four dimensional synthetic matter

Two-dimensional Euler insulators are novel kind of systems that host multi-gap topological phases, quantified by a quantised first Euler number in their bulk. Recently, these phases have been experimentally realised in suitable two-dimensional synthetic matter setups. Here we introduce the second Euler invariant, a familiar invariant in both differential topology (Chern-Gauss-Bonnet theorem) and in four-dimensional Euclidean gravity, whose existence has not been explored in condensed matter systems. Specifically, we firstly define two specific novel models in four dimensions that support a non-zero second Euler number in the bulk together with peculiar gapless boundary states. Secondly, we discuss its robustness in general spacetime-inversion invariant phases and its role in the classification of topological degenerate real bands through real Grassmannians. In particular, we derive from homotopy arguments the minimal Bloch Hamiltonian form from which the tight-binding models of any second Euler phase can be generated. Considering more concretely the gapped Euler phase associated with the tangent bundle of the four-sphere, we show that the bulk band structure of the nontrivial 4D Euler phase necessarily exhibits triplets of linked nodal surfaces (where the three types of nodal surfaces are formed by the crossing of the three successive pairs of bands within one four-band subspace). Finally, we show how to engineer these new topological phases in a four-dimensional ultracold atom setup. Our results naturally generalize the second Chern and spin Chern numbers to the case of four-dimensional phases that are characterised by real Hamiltonians and open doors for implementing such unexplored higher-dimensional phases in artificial engineered systems, ranging from ultracold atoms to photonics and electric circuits.

cond-mat.mes-hall↗

arXiv2022

Projected spin texture as a bulk indicator of fragile topology

We study the relationship between projected momentum-space spin textures and Wilson loop winding, proving a map between band topology of and spin topology in certain restricted symmetry settings, relevant to fragile topology. Our results suggest that the spin gap may act as a smoking gun bulk indicator for fragile topology within specific scenarios.

cond-mat.mes-hall↗