Engineering topics
Thomale, Ronny
Publications and source records attributed to Thomale, Ronny.
Sublattice modulated superconductivity in the kagome Hubbard model
Here we identify a superconducting order featuring spatial pair modulations on the kagome lattice subject to onsite Hubbard U and nearest neighbor V interactions. Within our functional renormalization group analysis, this state appears with a concomitant d-wave superconducting (SC) instability at zero lattice momentum, where it distinguishes itself through intra-unit cell modulations of the pairing function thus breaking the discrete space group symmetry. The relative weight of the sublattice modulated superconductor (SMS) and d-wave SC is influenced by the absolute interaction strength and coupling ratio V/U. Parametrically adjacent to this domain at weak coupling, we find an intra-unit cell modulated vestigial charge density wave and an s-wave SC instability. Our study provides a microscopic setting and thorough description of this novel SMS arising within a translation symmetry broken background.
Dynamics and resilience of the unconventional charge density wave in ScV 6 Sn 6 bilayer kagome metal
Long-range electronic ordering descending from a metallic parent state constitutes a rich playground to study the interplay of structural and electronic degrees of freedom. In this framework, kagome metals are in the most interesting regime where both phonon and electronically mediated couplings are significant. Several of these systems undergo a charge density wave transition. However, to date, the origin and the main driving force behind this charge order is elusive. Here, we use the kagome metal ScV 6 Sn 6 as a platform to investigate this problem, since it features both a kagome-derived nested Fermi surface and van-Hove singularities near the Fermi level, and a charge-ordered phase that strongly affects its physical properties. By combining time-resolved reflectivity, first principles calculations and photo-emission experiments, we identify the structural degrees of freedom to play a fundamental role in the stabilization of charge order, indicating that ScV 6 Sn 6 features an instance of charge order predominantly originating from phonons.
High Resolution Polar Kerr Effect Studies of CsV 3 Sb 5 : Tests for Time-Reversal Symmetry Breaking below the Charge-Order Transition
We report high resolution polar Kerr effect measurements on CsV 3 Sb 5 single crystals in search for signatures of spontaneous time reversal symmetry breaking below the charge order transition at T * = 94 K. Utilizing two different versions of zero-area loop Sagnac interferometers operating at 1550 nm wavelength, each with the fundamental attribute that without a time reversal symmetry breaking sample at its path, the interferometer is perfectly reciprocal, we find no observable Kerr effect to within the noise floor limit of the apparatus at 30 nanoradians. Simultaneous coherent reflection ratio measurements confirm the sharpness of the charge order transition in the same optical volume as the Kerr measurements. At finite magnetic field we observe a sharp onset of a diamagnetic shift in the Kerr signal at T *, which persists down to the lowest temperature without change in trend. Since 1550 nm is an energy that was shown to capture all features of the optical properties of the material that interact with the charge order transition, we are led to conclude that it is highly unlikely that time reversal symmetry is broken in the charge ordered state in CsV 3 Sb 5 .
Hybrid s -wave superconductivity in CrB 2
In a metal with multiple Fermi pockets, the formation of s-wave superconductivity can be conventional due to electron-phonon coupling or unconventional due to spin fluctuations. Here, we analyze the hexagonal diboride CrB 2 , which is an itinerant antiferromagnet at ambient conditions and turns superconducting upon increasing pressure. While the high-pressure behavior of T c suggests conventional s-wave pairing, we find that spin fluctuations promoting unconventional s-wave pairing become important in the vicinity of the antiferromagnetic dome. As the symmetry class of the s-wave state is independent of its underlying mechanism, we argue that CrB 2 is a realization of a hybrid s-wave superconductor where unconventional and conventional s-wave mechanisms team up to form a joint superconducting dome.
Flat band separation and robust spin Berry curvature in bilayer kagome metals
Kagome materials have emerged as a setting for emergent electronic phenomena that encompass different aspects of symmetry and topology. It is debated whether the XV 6 Sn 6 kagome family (where X is a rare-earth element), a recently discovered family of bilayer kagome metals, hosts a topologically non-trivial ground state resulting from the opening of spin–orbit coupling gaps. These states would carry a finite spin Berry curvature, and topological surface states. Here we investigate the spin and electronic structure of the XV 6 Sn 6 kagome family. We obtain evidence for a finite spin Berry curvature contribution at the centre of the Brillouin zone, where the nearly flat band detaches from the dispersing Dirac band because of spin–orbit coupling. In addition, the spin Berry curvature is further investigated in the charge density wave regime of ScV 6 Sn 6 and it is found to be robust against the onset of the temperature-driven ordered phase. Utilizing the sensitivity of angle-resolved photoemission spectroscopy to the spin and orbital angular momentum, our work unveils the spin Berry curvature of topological kagome metals and helps to define its spectroscopic fingerprint.
Theory of glide symmetry protected helical edge states in a WTe 2 monolayer
Helical edge states in quantum spin Hall (QSH) materials are central building blocks of topological matter design and engineering. Despite their principal topological protection against elastic backscattering, the level of operational stability depends on manifold parameters such as the band gap of the given semiconductor system in the “inverted” regime, temperature, disorder, and crystal orientation. Here, we theoretically investigate electronic and transport properties of QSH edge states in large gap 1-T' WTe 2 monolayers. We explore the impact of edge termination, disorder, temperature, and interactions on experimentally addressable edge state observables, such as local density of states and conductance. We show that conductance quantization can remain surprisingly robust even for heavily disordered samples because of an anomalously small edge state decay length and additional protection related to the large direct gap allowed by glide symmetry. From the simulation of temperature-dependent resistance, we find that moderate disorder enhances the stability of conductance by localizing bulk states. We evaluate the edge state velocity and Luttinger liquid parameter as functions of the chemical potential, finding prospects for physics beyond linear helical Luttinger liquids in samples with ultraclean and well-defined edges.
Crystallography of hyperbolic lattices
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. Here we show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices, from exact diagonalization on the graph to solving a finite set of equations in terms of irreducible representations. The significance of this achievement needs to be compared to the all-important role played by conventional Euclidean crystallography in the study of solids. We exemplify the high potential of this approach by constructing and diagonalizing finite-dimensional Bloch wave Hamiltonians.
Time-reversal symmetry-breaking charge order in a kagome superconductor
The kagome lattice 1 , which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders 2,3,4,5,6,7,8 and, most rarely, to unconventional superconductivity 6,9 . Recently, charge sensitive probes have indicated that the kagome superconductors AV 3 Sb 5 (A = K, Rb, Cs) 9,10,11 exhibit unconventional chiral charge order 12,13,14,15,16,17,18,19, which is analogous to the long-sought-after quantum order in the Haldane model 20 or Varma model 21 . However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV 3 Sb 5 . We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV 3 Sb 5 and that the T c /λ$^{-2}_{ab}$ ratio (where T c is the superconducting transition temperature and λ ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.
Unconventional chiral charge order in kagome superconductor KV 3 Sb 5
Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV 3 Sb 5 , with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Therefore theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.
Topological Defect Engineering and $\mathcal{PT}$ Symmetry in Non-Hermitian Electrical Circuits
In this work, we employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $\mathcal{PT}$ and chiral symmetry anti-$\mathcal{PT (APT)}$. The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $\mathcal{PT}$-symmetric gain and loss on localized edge and defect states in a non-Hermitian Su-Schrieffer-Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the $\mathcal{APT}$-symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel $\mathcal{PT}$-symmetric $\mathbb{Z}_2$ invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not $\mathcal{PT}$ symmetric, the topological defect state disappears and only reemerges when $\mathcal{APT}$ symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.
A proposal for reconciling diverse experiments on the superconducting state in Sr 2 RuO 4
A variety of precise experiments have been carried out to establish the character of the superconducting state in Sr 2 RuO 4 . Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here we propose that these results can be reconciled if we assume that there is a near-degeneracy between a \({d}_{{x}^{2}-{y}^{2}}\) (B 1g in group theory nomenclature) and a \({g}_{xy({x}^{2}-{y}^{2})}\) (A 2g ) superconducting state. From a weak-coupling perspective, such an accidental degeneracy can occur at a point at which a balance between the on-site and nearest-neighbor repulsions triggers a d-wave to g-wave transition.
Robust d x 2 - y 2 -wave superconductivity of infinite-layer nickelates
Motivated by the recent observation of superconductivity in strontium-doped NdNiO 2 , we study the superconducting instabilities in this system from various vantage points. Starting with first-principles calculations, we construct two distinct tight-binding models, a simpler single-orbital as well as a three-orbital model, both of which capture the key low-energy degrees of freedom to varying degrees of accuracy. We study superconductivity in both models using the random phase approximation. We then analyze the problem at stronger coupling, and study the dominant pairing instability in the associated t-J model limit. Finally, in all instances, the dominant pairing tendency is in the d x 2 -y 2 channel, analogous to the cuprate superconductors.