arXiv subjects

Felix Flicker

Publications and source records attributed to Felix Flicker.

At least 19 recordsLinked to original sources

arXiv2026

Theory of the Spinon-Mediated Witness Spin Glass in Herbertsmithite

Herbertsmithite is a prototypical candidate quantum spin liquid (QSL), believed to feature a long-range entangled ground state and deconfined fractionalised spinon excitations. Confirmation of these properties has been hindered by the presence of magnetic impurities (spin-1/2 Cu2+ spins substituted onto non-magnetic Zn2+ sites). Recently these impurities were reconceptualised as 'witnesses' of the QSL, inheriting long-range interactions and entanglement mediated by the QSL spinons, leading to spin glass formation amongst witnesses below 260 mK. Here we present a full theoretical account of this idea. Despite having only one free parameter (the witness-kagome spin coupling), our model captures the full range of experimental data, including: the formation of a spin glass amongst witnesses; the frequency and temperature dependence of the magnetic noise; a sharp peak in the DC magnetic susceptibility as a function of temperature; and the static neutron scattering structure factor at 2 K. Both candidate QSLs (Z2 and U(1)) give similar agreement with all data; however, our model predicts a qualitative difference between the Z2 and U(1) neutron scattering intensities below 260 mK, providing a long-sought definitive test to distinguish the two cases. We also predict phase diagrams as a function of temperature and witness concentration, finding a phase transition to different long-range ordered witness states for Z2 and U(1) at high concentration.

cond-mat.other↗

arXiv2026

Electronic Sound and Diffusion in Disordered Multiband Metals

Multiband metals can host acoustic plasmons: gapless collective charge excitations involving out-of-phase motion of electrons in different bands, sometimes referred to as 'demons'. Using a hydrodynamic description valid at high temperatures, and a microscopic description with vertex corrections valid at low temperatures, we show, upon including disorder inevitably present in real materials, that the mode frequency becomes purely imaginary, resulting in diffusive behaviour over a finite range of small wave vectors $q\le q_c$. This framework provides a natural, parameter-free explanation for the anomalous nonlinear dispersion recently reported for the demon in Sr$_2$RuO$_4$, which deviates from the gapless behaviour predicted by the random phase approximation. Our results establish demons as fundamentally distinct from previously known acoustic excitations, such as phonons and photons, which exhibit inertial dynamics protected by symmetries or gauge redundancies.

cond-mat.str-el↗

arXiv2026

Fractal Topology of Majorana Bound States in Superconducting Quasicrystals

Quasicrystalline order induces a fractal energy spectrum, yet its impact on topological protection remains an open fundamental question. Here, we demonstrate that the topological phase transitions characterised by the appearance of Majorana Bound States themselves have a fractal character. By extending this analysis to the full family of Sturmian words, we uncover Kitaev's Butterfly $-$ a spectral fractal analogous to Hofstadter's butterfly, but fundamentally distinguished by a central superconducting gap. Within this framework, we identify Majorana's Butterfly as a fractal topological phase diagram governed by the competition between quasicrystallinity and superconducting pairing. We show that this competition dictates a hierarchy of Majorana stability, where the survival of the topological phase against fractal fragmentation is determined by the relative strength of these competing energy scales.

cond-mat.mes-hall↗

arXiv2025

Spinon mediation of witness spin dynamics in herbertsmithite

The kagome lattice of spin-1/2 copper atoms in herbertsmithite is conjectured to sustain a quantum spin liquid state with spinon quasiparticles. Ideally, the kagome crystal planes are each separated by a plane of spinless zinc atoms. However, in real crystals some spin-1/2 copper atoms substitute randomly onto these inter-kagome zinc sites. Here we reconceptualize such 'impurity' atoms as quantum witness spins whose dynamics is designed to probe the spin liquid state. We then introduce spin noise spectroscopy to measure the frequency and temperature dependence of witness spin dynamics, demonstrating that their phenomenology is consistent with extensive interactions between witness spins mediated by propagation of spinons through a quantum spin liquid. Ultimately, a sharp transition occurs at around 260 mK, below which the properties of both spin noise and magnetic susceptibility suggest that the witness spins form a spin glass phase. Among theoretical models considered, we demonstrate that our observations are only consistent with spinon-mediated interactions between witness spins by either a Z2 or U(1) quantum spin liquid, with the former model more closely matching the data. Our work demonstrates that quantum mechanical witness spins may now conceivably be used as a widely applicable probe of quantum spin liquid physics.

cond-mat.str-el↗

arXiv2025

In-plane anisotropy of charge density wave fluctuations in 1$T$-TiSe$_2$

We report measurements of anisotropic triple-$q$ charge density wave (CDW) fluctuations in the transition metal dichalcogenide 1$T$-TiSe$_2$ over a large volume of reciprocal space with X-ray diffuse scattering. Above the transition temperature, $T_{\text{CDW}}$, the out-of-plane diffuse scattering is characterized by rod-like structures which indicate that the CDW fluctuations in neighboring layers are largely decoupled. In addition, the in-plane diffuse scattering is marked by ellipses which reveal that the in-plane fluctuations are anisotropic. Our analysis of the diffuse scattering line shapes and orientations suggests that the three charge density wave components contain independent phase fluctuations. At $T_{\text{CDW}}$, long range coherence is established in both the in-plane and out-of-plane directions, consistent with the large observed value of the CDW gap compared to $T_{\text{CDW}}$, and the predicted presence of a hierarchy of energy scales.

cond-mat.str-el↗

arXiv2023

Exact Solution to the Quantum and Classical Dimer Models on the Spectre Aperiodic Monotiling

The decades-long search for a shape that tiles the plane only aperiodically under translations and rotations recently ended with the discovery of the `spectre' aperiodic monotile. In this setting we study the dimer model, in which dimers are placed along tile edges such that each vertex meets precisely one dimer. The complexity of the tiling combines with the dimer constraint to allow an exact solution to the model. The partition function is $\mathcal{Z}=2^{N_{\textrm{Mystic}}+1}$ where $N_{\textrm{Mystic}}$ is the number of `Mystic' tiles. We exactly solve the quantum dimer (Rokhsar Kivelson) model in the same setting by identifying an eigenbasis at all interaction strengths $V/t$. We find that test monomers, once created, can be infinitely separated at zero energy cost for all $V/t$, constituting a deconfined phase in a 2+1D bipartite quantum dimer model.

cond-mat.str-el↗

arXiv2023

Lifshitz transition enabling superconducting dome around the quantum critical point in TiSe$_2$

Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature. So far, this has been mostly studied in magnetically ordered materials. By contrast, the interplay between charge order and superconductivity at a QCP is not fully understood. Here, we present resistance measurements proving that a dome of superconductivity surrounds the charge-density-wave (CDW) QCP in pristine samples of 1$T$-TiSe$_2$ tuned with hydrostatic pressure. Furthermore, we use quantum oscillation measurements to show that the superconductivity sets in at a Lifshitz transition in the electronic band structure. We use density functional theory to identify the Fermi pockets enabling superconductivity: large electron and hole pockets connected by the CDW wave vector $\vec{Q}$ which emerge upon partial suppression of the zero-pressure CDW gap. Hence, we conclude that superconductivity is of interband type enabled by the presence of hole and electron bands connected by the CDW $\vec{Q}$ vector. Earlier calculations show that interband interactions are repulsive, which suggests that unconventional s$_{\pm}$ superconductivity is realised in TiSe$_2$ - similar to the iron pnictides. These results highlight the importance of Lifshitz transitions in realising unconventional superconductivity and help understand its interaction with CDW order in numerous materials.

cond-mat.supr-con↗

arXiv2023

Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including six-fold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette ($\phi$) is half of the flux quantum, zero-modes are found localized around the reflected `anti-hats'; and (v) its Hofstadter spectrum is periodic in $\phi$, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest.

cond-mat.mes-hall↗

arXiv2023

Hamiltonian Cycles on Ammann-Beenker Tilings

We provide a simple algorithm for constructing Hamiltonian graph cycles (visiting every vertex exactly once) on a set of arbitrarily large finite subgraphs of aperiodic two-dimensional Ammann-Beenker (AB) tilings. Using this result, and the discrete scale symmetry of AB tilings, we find exact solutions to a range of other problems which lie in the complexity class NP-complete for general graphs. These include the equal-weight traveling salesperson problem, providing, for example, the most efficient route a scanning tunneling microscope tip could take to image the atoms of physical quasicrystals with AB symmetries; the longest path problem, whose solution demonstrates that collections of flexible molecules of any length can adsorb onto AB quasicrystal surfaces at density one, with possible applications to catalysis; and the three-coloring problem, giving ground states for the $q$-state Potts model ($q \ge 3$) of magnetic interactions defined on the planar dual to AB, which may provide useful models for protein folding.

cond-mat.stat-mech↗

arXiv2023

Compression theory for inhomogeneous systems

The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on inhomogeneous graphs. However, the lack of translational invariance presents a fundamental challenge to theoretical tools, such as the renormalization group, which were so successful in characterizing the universal physical behaviour in critical phenomena. Here we show that compression theory allows the extraction of relevant degrees of freedom in arbitrary geometries, and the development of efficient numerical tools to build an effective theory from data. We demonstrate our method by applying it to a strongly correlated system on an Ammann-Beenker quasicrystal, where it discovers an exotic critical point with broken conformal symmetry. We also apply it to an antiferromagnetic system on non-bipartite random graphs, where any periodicity is absent.

cond-mat.stat-mech↗

arXiv2021

Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators

We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional tenfold way and crystalline-symmetry-based classifications of topological insulators. Its topology is protected by a \emph{linking number} invariant, which necessitates long-range spin-orbit coupled hoppings for its realization. While these ingredients have so far precluded its realization in solid state systems and other quantum simulation architectures, in a companion manuscript [1901.08597] we predict that Hopf insulators can in fact arise naturally in dipolar interacting systems. Here, we investigate a specific such architecture in lattices of polar molecules, where the effective `spin' is formed from sublattice degrees of freedom. We introduce two techniques that allow one to optimize dipolar Hopf insulators with large band gaps, and which should also be readily applicable to the simulation of other exotic bandstructures. First, we describe the use of Floquet engineering to control the range and functional form of dipolar hoppings and second, we demonstrate that molecular AC polarizabilities (under circularly polarized light) can be used to precisely tune the resonance condition between different rotational states. To verify that this latter technique is amenable to current generation experiments, we calculate from first principles the AC polarizability for $\sigma^+$ light for ${}^{40}$K$^{87}$Rb. Finally, we show that experiments are capable of detecting the unconventional topology of the Hopf insulator by varying the termination of the lattice at its edges, which gives rise to three distinct classes of edge mode spectra.

cond-mat.quant-gas↗

arXiv2021

Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings

We study classical dimers on two-dimensional quasiperiodic Ammann-Beenker (AB) tilings. Despite the lack of periodicity we prove that each infinite tiling admits 'perfect matchings' in which every vertex is touched by one dimer. We introduce an auxiliary 'AB$^*$' tiling obtained from the AB tiling by deleting all 8-fold coordinated vertices. The AB$^*$ tiling is again two-dimensional, infinite, and quasiperiodic. The AB$^*$ tiling has a single connected component, which admits perfect matchings. We find that in all perfect matchings, dimers on the AB$^*$ tiling lie along disjoint one-dimensional loops and ladders, separated by 'membranes', sets of edges where dimers are absent. As a result, the dimer partition function of the AB$^*$ tiling factorizes into the product of dimer partition functions along these structures. We compute the partition function and free energy per edge on the AB$^*$ tiling using an analytic transfer matrix approach. Returning to the AB tiling, we find that membranes in the AB$^*$ tiling become 'pseudomembranes', sets of edges which collectively host at most one dimer. This leads to a remarkable discrete scale-invariance in the matching problem. The structure suggests that the AB tiling should exhibit highly inhomogenous and slowly decaying connected dimer correlations. Using Monte Carlo simulations, we find evidence supporting this supposition in the form of connected dimer correlations consistent with power law behaviour. Within the set of perfect matchings we find quasiperiodic analogues to the staggered and columnar phases observed in periodic systems.

cond-mat.stat-mech↗

arXiv2021

Multiband charge density wave exposed in a transition metal dichalcogenide

In the presence of multiple bands, well-known electronic instabilities may acquire new complexity. While multiband superconductivity is the subject of extensive studies, the possibility of multiband charge density waves (CDWs) has been largely ignored so far. Here, combining energy dependent scanning tunnelling microscopy (STM) topography with a simple model of the charge modulations and a self-consistent calculation of the CDW gap, we find evidence for a multiband CDW in 2H-NbSe$_2$. This CDW not only involves the opening of a gap on the inner band around the K-point, but also on the outer band. This leads to spatially out-of-phase charge modulations from electrons on these two bands, which we detect through a characteristic energy dependence of the CDW contrast in STM images.

cond-mat.str-el↗

arXiv2020

A microscopic Ginzburg--Landau theory and singlet ordering in Sr$_2$RuO$_4$

The long-standing quest to determine the superconducting order of Sr$_2$RuO$_4$ (SRO) has received renewed attention after recent nuclear magnetic resonance (NMR) Knight shift experiments have cast doubt on the possibility of spin-triplet pairing in the superconducting state. As a putative solution, encompassing a body of experiments conducted over the years, a $d+ig$-wave order parameter caused by an accidental near-degeneracy has been suggested [S. A. Kivelson et al., npj Quantum Materials $\bf{5}$, 43 (2020)]. Here we develop a general Ginzburg--Landau theory for multiband superconductors. We apply the theory to SRO and predict the relative size of the order parameter components. The heat capacity jump expected at the onset of the second order parameter component is found to be above the current threshold deduced by the experimental absence of a second jump. Our results tightly restrict theories of $d+ig$ order, and other candidates caused by a near-degeneracy, in SRO. We discuss possible solutions to the problem.

cond-mat.supr-con↗

arXiv2020

Absence of superconducting dome at the charge-density-wave quantum phase transition in 2H-NbSe2

Superconductivity is often found in a dome around quantum critical points, i.e. 2nd-order quantum phase transitions. Here, we show that an enhancement of superconductivity is avoided at the critical pressure of the charge-density-wave (CDW) state in NbSe$_2$. We present comprehensive high-pressure Hall effect and magnetic susceptibility measurements of the CDW and superconducting state in NbSe$_2$. Initially, the 2nd-order CDW transition is suppressed smoothly but it drops to zero abruptly at PCDW = 4.4 GPa thus indicating a change to 1st order whilstthe superconducting transition temperature Tc rises continuously up to PCDW but is constant above. The putative 1st-order nature of the CDW transition is suggested as the cause for the absence of a superconducting dome at PCDW. Indeed, we show that the suppression of the superconducting state at low pressures is due to the loss of density of states inside the CDW phase whilst the initial suppression of the CDW state is accounted for by the stiffening of the underlying bare phonon mode.

cond-mat.supr-con↗

arXiv2019

Charge order from structured coupling in VSe$_2$

Charge order--ubiquitous among correlated materials--is customarily described purely as an instability of the electronic structure. However, the resulting theoretical predictions often do not match high-resolution experimental data. A pertinent case is $1T$-VSe$_2$, whose single-band Fermi surface and weak-coupling nature make it qualitatively similar to the Peierls model underlying the traditional approach. Despite this, its Fermi surface is poorly nested, the thermal evolution of its charge density wave (CDW) ordering vectors displays an unexpected jump, and the CDW gap itself evades detection in direct probes of the electronic structure. We demonstrate that the thermal variation of the CDW vectors is naturally reproduced by the electronic susceptibility when incorporating a structured, momentum-dependent electron-phonon coupling, while the evasive CDW gap presents itself as a localized suppression of spectral weight centered above the Fermi level. Our results showcase the general utility of incorporating a structured coupling in the description of charge ordered materials, including those that appear unconventional.

cond-mat.str-el↗

arXiv2019

Superconducting order of $\mathrm{Sr}_2\mathrm{RuO}_4$ from a three-dimensional microscopic model

We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate ($\mathrm{Sr}_2\mathrm{RuO}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. Nature 574, 72 (2019)]. The chiral $p$-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.

cond-mat.supr-con↗

arXiv2019

Uniaxial Strain Tuning of Superconductivity in 2$H$-NbSe$_{2}$

We explore the effect of lattice anisotropy on the charge-ordered superconductor 2H-NbSe$_{2}$. Using a novel strain apparatus, we measure the superconducting transition temperature $T_{sc}$ as a function of uniaxial strain. It is found that $T_{sc}$ is independent of tensile(compressive) strain below a threshold of 0.2\% (0.1\%), but decreases strongly with larger strains with an average rate of $1.3\,$K/\% ($2.5\,$K/\%). Transport signatures of charge order are largely unaffected as a function of strain. Theoretical considerations show that the change in the behavior of $T_{sc}$ with strain coincides with a phase transition from 3Q to 1Q charge order in the material. The spectral weight on one of the Fermi surface bands is found to change strongly as a consequence of this phase transition, providing a pathway to tune superconducting order.

cond-mat.supr-con↗