arXiv subjects

Thilo Kopp

Publications and source records attributed to Thilo Kopp.

At least 19 recordsLinked to original sources

arXiv2026

Many-body Euler topology

Integer and fractional Chern insulators exhibit a nonzero quantized anomalous Hall conductivity due to a spontaneous breaking of time reversal symmetry. To identify nontrivial topology in their time-reversal symmetric many-body spectra, we introduce many-body Euler numbers as a counterpart to many-body Chern numbers. Exemplarily, we perform calculations in a topological Hubbard model that can realize Chern and fractional Chern insulating phases. Furthermore, we lay out a classification scheme to realize different topological phases in interacting systems using symmetry indicators in analogy to topological band theory.

cond-mat.str-el↗

arXiv2025

Band representations in Strongly Correlated Settings: The Kitaev Honeycomb Model

In the study of quantum spin liquids, the Kitaev model plays a pivotal role due to the fact that its ground state is exactly known as well as the fact that it may be realized in strongly frustrated materials such as ${\alpha}$-RuCl${}_3$. While topological insulators and superconductors can be investigated by means of topological band theory -- in particular the topological quantum chemistry (TQC) formalism -- the Kitaev model evades such a treatment, as it is not possible to set up a proper single-particle Green's function for it. We instead associate spin operators with ``orbitals'' that give rise to a band structure. It is thereby possible to analyze the corresponding excitation spectrum engendered by these localized excitations by means of TQC. Special attention is given to the low-energy topological edge mode spectrum. Our work sheds light on the question how the TQC formalism may be generalized to strongly correlated and topologically ordered systems like the Kitaev model.

cond-mat.str-el↗

arXiv2024

Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux

Motivated by recently reported magnetic-field induced topological phases in ultracold atoms and correlated Moir\'e materials, we investigate topological phase transitions in a minimal model consisting of interacting spinless fermions described by the Hofstadter model on a square lattice. For interacting lattice Hamiltonians in the presence of a commensurate magnetic flux it has been demonstrated that the quantized Hall conductivity is constrained by a Lieb-Schultz-Mattis (LSM)-type theorem due to magnetic translation symmetry. In this work, we revisit the validity of the theorem for such models and establish that a topological phase transition from a topological to a trivial insulating phase can be realized but must be accompanied by spontaneous magnetic translation symmetry breaking caused by charge ordering of the spinless fermions. To support our findings, the topological phase diagram for varying interaction strength is mapped out numerically with exact diagonalization for different flux quantum ratios and band fillings using symmetry indicators. We discuss our results in the context of the LSM-type theorem.

cond-mat.mes-hall↗

arXiv2022

Winding vectors of topological defects: Multiband Chern numbers

Chern numbers can be calculated within a frame of vortex fields related to phase conventions of a wave function. In a band protected by gaps the Chern number is equivalent to the total number of flux carrying vortices. In the presence of topological defects like Dirac cones this method becomes problematic, in particular if they lack a well-defined winding number. We develop a scheme to include topological defects into the vortex field frame. A winding number is determined by the behavior of the phase in reciprocal space when encircling the defect's contact point. To address the possible lack of a winding number we utilize a more general concept of winding vectors. We demonstrate the usefulness of this ansatz on Dirac cones generated from bands of the Hofstadter model.

cond-mat.mes-hall↗

arXiv2022

Bad metal and negative compressibility transitions in a two-band Hubbard model

We analyze the paramagnetic state of a two-band Hubbard model with finite Hund's coupling close to integer filling at $n=2$ in two spacial dimensions. Previously, a Mott metal-insulator transition was established at $n=2$ with a coexistence region of a metallic and a bad metal state in the vicinity of that integer filling. The coexistence region ends at a critical point beyond which a charge instability persists. Here we investigate the transition into negative electronic compressibility states for an extended filling range close to $n=2$ within a slave boson setup. We analyze the separate contributions from the (fermionic) quasiparticles and the (bosonic) multiparticle incoherent background and find that the total compressibility depends on a subtle interplay between the quasiparticle excitations and collective fields. Implementing a Blume-Emery-Griffiths model approach for the slave bosons, which mimics the bosonic fields by Ising-like pseudospins, we suggest a feedback mechanism between these fields and the fermionic degrees of freedom. We argue that the negative compressibility can be sustained for heterostructures of such strongly correlated planes and results in a large capacitance of these structures. The strong density dependence of these capacitances allows to tune them through small electronic density variations. Moreover, by resistive switching from a Mott insulating state to a metallic state through short electric pulses, transitions between fairly different capacitances are within reach.

cond-mat.str-el↗

arXiv2021

Signatures of topological phase transitions in the s-wave superconductor at finite temperature

In two dimensions, an s-wave superconductor in the presence of Rashba spin-orbit coupling possesses distinct topologically non-trivial ground state phases controlled by Zeeman splitting and band filling. These phases can be characterized in terms of spin textures in momentum space. Although the spin texture becomes topologically trivial at finite temperatures, we identify thermodynamic signatures that are directly related to the topological phase transitions of the ground state. In particular, relative maxima in the entropy as a function of the magnetic field in the vicinity of topological phase transitions emerge and are attributed to a sign change in the derivative of the magnetization with respect to temperature.

cond-mat.supr-con↗

arXiv2021

Magnetotransport of Functional Oxide Heterostructures Affected by Spin-Orbit Coupling: A Tale of Two-Dimensional Systems

Oxide heterostructures allow for detailed studies of 2D electronic transport phenomena. Herein, different facets of magnetotransport in selected spin-orbit-coupled systems are analyzed and characterized by their single-band and multiband behavior, respectively. Experimentally, temperature- and magnetic field-dependent measurements in the single-band system BaPbO$_3$/SrTiO$_3$ reveal strong interplay of weak antilocalization (WAL) and electron-electron interaction (EEI). Within a scheme which treats both, WAL and EEI, on an equal footing a strong contribution of EEI at low temperatures is found which suggests the emergence of a strongly correlated ground state. Furthermore, now considering multiband effects as they appear, e.g., in the model system LaAlO$_3$/SrTiO$_3$, theoretical investigations predict a huge impact of filling on the topological Hall effect in systems with intermingled bands. Already weak band coupling produces striking deviations from the well-known Hall conductivity that are explainable in a fully quantum mechanical treatment which builds upon the hybridization of intersecting Hofstadter bands.

cond-mat.mes-hall↗

arXiv2020

Optical conductivity and resistivity in a four-band model for ZrTe$_5$ from ab-initio calculations

ZrTe$_5$ is considered a potential candidate for either a Dirac semimetal or a topological insulator in close proximity to a topological phase transition. Recent optical conductivity results motivated a two-band model with a conical dispersion in 2D, in contrast to density functional theory calculations. Here, we reconcile the two by deriving a four-band model for ZrTe$_5$ using $\textbf{k} \cdot \textbf{p}$ theory, and fitting its parameters to the ab-initio band structure. The optical conductivity with an adjusted electronic structure matches the key features of experimental data. The chemical potential varies strongly with temperature, to the point that it may cross the gap entirely between zero and room temperature. The temperature-dependent resistivity displays a broad peak, and confirms theoretically the conclusions of recent experiments attributing the origin of the resistivity peak to the large shift of the chemical potential with temperature.

cond-mat.mes-hall↗

arXiv2019

Non-unique connection between bulk topological invariants and surface physics

At the heart of the study of topological insulators lies a fundamental dichotomy: topological invariants are defined in infinite systems, but surface states as their main footprint only exist in finite systems. In the slab geometry, namely infinite in two planar directions and finite in the perpendicular direction, the 2D topological invariant was shown to display three different types of behaviour. The perpendicular Dirac velocity turns out to be a critical control parameter discerning between different qualitative situations. When it is zero, the three types of behaviour extrapolate to the three 3D topologically distinct phases: trivial, weak and strong topological insulators. We show analytically that the boundaries between types of behaviour are topological phase transitions of particular significance since they allow to predict the 3D topological invariants from finite-thickness transitions. When the perpendicular Dirac velocity is not zero, we identify a new phase with surface states but no band inversion at any finite thickness, disentangling these two concepts which are closely linked in 3D. We also show that at zero perpendicular Dirac velocity the system is gapless in the 3D bulk and therefore not a topological insulating state, even though the slab geometry extrapolates to the 3D topological phases. Finally, in a parameter regime with strong dispersion perpendicular to the surface of the slab, we encounter the unusual case that the slab physics displays non-trivial phases with surface states but nevertheless extrapolates to a 3D trivial state.

cond-mat.mes-hall↗

arXiv2019

Electronic transport in thin films of BaPbO$_3$: Unraveling two-dimensional quantum effects

Recently, perovskite related BaPbO$_3$ has attracted attention due to its hidden topological properties and, moreover, has been used as a thin layer in heterostructures to induce two-dimensional superconductivity. Here we investigate the normal state electronic transport properties of thin films of BaPbO$_3$. Temperature and magnetic field dependent sheet resistances are strongly affected by two-dimensional quantum effects. Our analysis decodes the interplay of spin--orbit coupling, disorder, and electron--electron interaction in this compound. Similar to recently discussed topological materials, we find that weak antilocalization is the dominant protagonist in magnetotransport, whereas electron--electron interactions play a pronounced role in the temperature dependence. A systematic understanding of these quantum effects is essential to allow for an accurate control of properties not only of thin films of BaPbO$_3$, but also of topological heterostructures.

cond-mat.mes-hall↗

arXiv2019

Anti-Localization in Oxides: Effective Spin-3/2 Model

Weak anti-localization offers an experimental tool to address spin--orbit coupling of two-dimensional oxide surfaces and interfaces via magneto-transport. To overcome the shortcomings of the formulation for single-band spin-1/2 electrons, we consider an effective three-band model that allows a decomposition into a pseudo-spin representation 1/2+3/2. Whereas the well-established spin-1/2 transport signature results from the singlet and triplet sectors in the Cooperon equation, a new structure originates from the quintet and septet sectors generated by the spin 3/2x3/2 representation.

cond-mat.mes-hall↗

arXiv2017

Supercurrent as a Probe for Topological Superconductivity in Magnetic Adatom Chains

A magnetic adatom chain, proximity coupled to a conventional superconductor with spin-orbit coupling, exhibits locally an odd-parity, spin-triplet pairing amplitude. We show that the singlet-triplet junction, thus formed, leads to a net spin accumulation in the near vicinity of the chain. The accumulated spins are polarized along the direction of the local $\mathbf{d}$-vector for triplet pairing and generate an enhanced persistent current flowing around the chain. The spin polarization and the "supercurrent" reverse their directions beyond a critical exchange coupling strength at which the singlet superconducting order changes its sign on the chain. The current is strongly enhanced in the topological superconducting regime where Majorana bound states appear at the chain ends. The current and the spin profile offer alternative routes to characterize the topological superconducting state in adatom chains and islands.

cond-mat.supr-con↗

arXiv2017

In-gap features in superconducting LaAlO$_3$-SrTiO$_3$ interfaces observed by tunneling spectroscopy

We identified quasiparticle states at well-defined energies inside the superconducting gap of the electron system at the LaAlO$_3$-SrTiO$_3$ interface using tunneling spectroscopy. The states are found only in a number of samples and depend upon the thermal-cycling history of the samples. The states consist of a peak at zero energy and other peaks at finite energies, symmetrically placed around zero energy. These peaks disappear, together with the superconducting gap, with increasing temperature and magnetic field. We discuss the likelihood of various physical mechanisms that are known to cause in-gap states in superconductors and conclude that none of these mechanisms can easily explain the results. The conceivable scenarios are the formation of Majorana bound states, Andreev bound states, or the presence of an odd-frequency spin triplet component in the superconducting order parameter.

cond-mat.supr-con↗

arXiv2017

Interface-Driven Two-Dimensional Superconductivity in Bilayers of BaBiO$_3$ and BaPbO$_3$

Besides the cuprate superconductors lead-doped barium bismuthate still attracts intense interest concerning its relatively high critical temperature and the nature of its superconductivity in vicinity to a charge density wave ordered topological insulator. Here we present bilayers of barium bismuthate and barium leadate and find two-dimensional superconductivity at their interfaces well described by current-voltage characteristics compatible with a Berezinskii-Kosterlitz-Thouless transition. Magneto-transport studies independently prove the two-dimensional character of the superconducting properties in these bilayers. The particular dependence of the superconducting transition temperature on the thickness of the barium leadate top layer suggests the formation of the superconducting state to be strain-induced through the interface.

cond-mat.supr-con↗

arXiv2017

Capacitance and compressibility of heterostructures with strong electronic correlations

Strong electronic correlations related to a repulsive local interaction suppress the electronic compressibility in a single-band model, and the capacitance of a corresponding metallic film is directly related to its electronic compressibility. Both statements may be altered significantly when two extensions to the system are implemented which we investigate here: (i) we introduce an attractive nearest-neighbor interaction $V$ as antagonist to the repulsive on-site repulsion $U$, and (ii) we consider nano-structured multilayers (heterostructures) assembled from two-dimensional layers of these systems. We determine the respective total compressibility $κ$ and capacitance $C$ of the heterostructures within a strong coupling evaluation, which builds on a Kotliar-Ruckenstein slave-boson technique. Whereas the capacitance $C(n)$ for electronic densities $n$ close to half-filling is suppressed---illustrated by a correlation induced dip in $C(n)$---it may be appreciably enhanced close to a van Hove singularity. Moreover, we show that the capacitance may be a non-monotonic function of $U$ close to half-filling for both attractive and repulsive $V$. The compressibility $κ$ can differ from $C$ substantially, as $κ$ is very sensitive to internal electrostatic energies which in turn depend on the specific set-up of the heterostructure. In particular, we show that a capacitor with a polar dielectric has a smaller electronic compressibility and is more stable against phase separation than a standard non-polar capacitor with the same capacitance.

cond-mat.str-el↗

arXiv2017

Momentum-Space Spin Texture in a Topological Superconductor

A conventional superconductor with spin-orbit coupling turns into a topological superconductor beyond a critical strength of the Zeeman energy. The spin-expectation values $\mathbf{S}(\mathbf{k})$ in momentum space trace this transition via a characteristic change in the topological character of the spin texture within the Brillouin zone. At the transition the skyrmion counting number switches from 0 to 1/2 identifying the topological superconductor via its meron-like spin texture. The change in the skyrmion counting number is crucially controlled by singular points of the map $\mathbf{S}(\mathbf{k})/|\mathbf{S}(\mathbf{k})|$ from the Brillouin zone, i.e. a torus, to the unit sphere. The complexity of this spin-map is discussed at zero temperature as well as for the extension to finite temperatures.

cond-mat.supr-con↗

arXiv2016

Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like "spin" texture in momentum space. Here, we apply the previously formulated low-energy model for Bi$_2$Se$_3$, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transition between two topologically distinct phases. The topological phase transition takes place without energy gap closing at the Fermi level and leaves the transverse Hall conductance unchanged and quantized to $e^2/2h$. The momentum-space skyrmion texture persists in a finite field range. It may find its realization in hybrid heterostructures with an interface between a three-dimensional topological insulator and a ferromagnetic insulator.

cond-mat.mes-hall↗

arXiv2016

The mechanism of spin-orbit coupling in a 2D oxide interface

The presence of spin-orbit coupling drives the anomalous magnetotransport at oxide interfaces and forms the basis for numerous intriguing properties of these 2D electron systems, such as topologically protected phases or anti-localization. For many of those systems, the identification of the underlying coupling mechanism is obfuscated by multi-band effects. We therefore analyze the transport of LaAlO$_3$/SrTiO$_3$ interfaces under high pressures, a technique to single out the multi-band contributions. We argue that the observed magnetoresistance is due to quantum interference and not related to Coulomb interaction. Therefore, this system is an excellent candidate to generate a metal-insulator transition of the long-sought symplectic 2D universality class. It is shown that the spin-orbit coupling can be linked unambiguously to the band structure with a cubic (Dresselhaus-like) rather than a linear (Rashba-like) spin-orbit band splitting.

cond-mat.str-el↗