arXiv subjects
Publications and source records attributed to Matteo Dürrnagel.
We develop a class of microscopic lattice models in which pair density wave order emerges in the asymptotically exact weak coupling limit. The underlying mechanism is due to non-symmorphic momentum symmetry implied by the models' projective space group representation of electrons. Our mechanism suggests moiré systems and extended s-wave altermagnets as potential hosts for pair density wave order.
We study an interacting kagome-lattice realization of a quadratic band-touching semimetal at 2/3 filling with onsite and nearest-neighbor repulsive interactions. Combining functional renormalization group and slave-boson approaches, we map its phase diagram from intermediate to strong coupling and uncover a hierarchy of unconventional electronic orders. The leading instabilities comprise loop-current order, spontaneous altermagnetism arising from a spin-Pomeranchuk instability, and spin-loop-current order with distinctive and largely unexplored properties. We demonstrate how the interplay of band kinematics, electronic interactions, and quantum geometry governs the selection of these phases. Our findings establish quadratic band-touching semimetals as a promising platform for unconventional symmetry breaking and suggest analogous phenomena in other parabolic semimetals.
RuO$_2$ has emerged as a prototypical candidate for altermagnetism. In the face of daunting evidence for magnetic order in the bulk, the focus naturally shifted to surfaces and ultrathin films, where Coulomb interactions are dimensionally quenched and electron correlations strongly enhanced. Here, we examine atomically ordered, ultrathin RuO$_2$(110) grown on Ru(0001) using a combination of scanning tunneling microscopy (STM), density functional theory, and density matrix renormalization group methods. We observe a nonmagnetic charge order that is imprinted by the incommensurate moiré stacking with the substrate and enhanced by the electronic Fermi surface scattering within the flat-band surface state. We further identify a nonmagnetic, metastable $c(2 \times 2)$ surface reconstruction that arises from surface phonon softening and can be toggled reversibly via STM tip manipulation. Spin-polarized STM measurements, however, reveal no evidence of magnetic order on the RuO$_2$(110) surface. Our findings of a nonmagnetic charge-modulation position ultrathin RuO$_2$(110) as an intriguing platform for exploring moiré-assisted electronic orders.
We formulate a functional renormalization group (FRG) ansatz for correlated electron models that incorporates electronic interactions as well as electron-phonon coupling (EPC) stemming from dispersive phonon bands. Particularizing to the RG flow of the electron-electron interaction vertex, we treat phonon- and electron-mediated Fermi liquid instabilities on equal footing as we analyze tentative electronic order parameters related to charge, spin, nematicity, and superconducting pairing. We illustrate the approach at the example of Peierls-type transitions we find for the Hubbard model on the square lattice coupled to acoustic phonon bands. Our method allows to incorporate full electronic and phononic ab initio input, and thus lends itself to the analysis of electronic order from intertwined electronic interactions and EPC at a microscopically most substantiated level.
Pair density wave (PDW) exhibits periodic amplitude and sign modulations of the superconducting order parameter. Such a pairing state has long been proposed to be highly sensitive to nonmagnetic scattering, but its experimental realization remains elusive. Here we discover a nonmagnetic PDW-breaking effect in a kagome superconductor, using designer atomic nonmagnetic impurities and high-precision scanning tunneling microscopy (STM) at a base temperature of 30mK. We detect 2x2 pair density modulations by Josephson STM with a superconducting tip and 2x2 pairing gap modulations by normal STM. We find that the pairing modulations in both cases are substantially suppressed upon doping the kagome lattice with dilute isovalent nonmagnetic impurities, whereas the charge order and uniform superconductivity remain robust. We further identify the correlation between atomic dopants and the local suppression of PDW. We attribute these findings to a nonmagnetic pair-breaking effect, arising from the phase modulation of PDW in the kagome d-orbital. Taken together with its signatures in other state-of-the-art spectroscopy and transport measurements linked by theory, our findings support the ground state of the kagome superconductor as a correlated topological phase with superconducting loop currents.
We propose extended s-wave altermagnets (sAMs) as a class of magnetic states which are fully gapped, spin-compensated, and feature spin-polarized bands. sAMs are formed through valley-exchange symmetries, which act as momentum-space translations beyond standard crystallographic spin-group classifications. Using an effective two-valley model, we demonstrate that sAMs exhibit isotropic spin splitting, enable spin-selective transport in tailored heterostructures, and give rise to descendant pair density wave order. From a microscopic sAM minimal model, we develop the guiding principles to identify sAMs in quantum magnets.
By means of slave-boson theory for the Hubbard model on the checkerboard lattice, we calculate dynamical altermagnetic spin susceptibilities from the metallic to the Mott-insulating regime. We track magnon dispersion and lifetime renormalization, allowing us to uncover a crossover from a chirality-selective dissipation of magnon modes to coherent yet strongly deformed chiral magnon branches across the metal insulator transition. Our formalism lends itself to a quantitative description of collective spin dynamics in correlated altermagnets.
Recent experiments have identified fascinating electronic orders in kagome materials, including intriguing superconductivity, charge density wave (CDW) and nematicity. In particular, some experimental evidence for AV$_3$Sb$_5$ (A = K,Rb,Cs) and related kagome metals hints at the formation of orbital currents in the charge density wave ordered regime, providing a mechanism for spontaneous time-reversal symmetry breaking in the absence of local moments. In this work, we comprehensively explore the competitive charge instabilities of the spinless kagome lattice with inter-site Coulomb interactions at the pure-sublattice van Hove filling. From the analysis of the charge susceptibility, we find that, at the nesting vectors, while the onsite charge order is dramatically suppressed, the bond charge orders are substantially enhanced owing to the sublattice texture on the hexagonal Fermi surface. Furthermore, we demonstrate that nearest-neighbor and next nearest-neighbor bonds are characterized by significant intrinsic real and imaginary bond fluctuations, respectively. The 2$\times$2 loop current order is thus favored by the next nearest-neighbor Coulomb repulsion. Interestingly, increasing interactions further leads to a nematic state with intra-cell sublattice density modulation that breaks the $C_6$ rotational symmetry. We further explore superconducting orders descending from onsite and bond charge fluctuations, and discuss our model's implications on the experimental status quo.
Recent discoveries in kagome materials have unveiled their capacity to harbor exotic quantum states, including intriguing charge density wave (CDW) and superconductivity. Notably, accumulating experimental evidence suggests time-reversal symmetry breaking within the CDW, hinting at the long-pursued loop current order (LCO). Despite extensive research efforts, achieving its model realization and understanding the mechanism through unbiased many-body simulations have remained both elusive and challenging. In this Letter, we develop a microscopic model for LCO on the spinless kagome lattice with nonlocal interactions, utilizing unbiased functional renormalization group calculations to explore ordering tendencies across all two-particle scattering channels. At the Van Hove filling, we identify sublattice interference to suppress onsite CDW order, leaving LCO, charge bond order, and nematic CDW state as the main competitors. Remarkably, a $2\times2$ LCO emerges as the many-body ground state over a significant parameter space with strong second nearest-neighbor repulsion, stemming from the unique interplay between sublattice characters and lattice geometry. The resulting electronic model with LCO bears similarities to the Haldane model and culminates in a quantum anomalous Hall state. We also discuss potential experimental implications for kagome metals.
We analyze the phase transition between a symmetric metallic parent state and itinerant altermagnetic order. The underlying mechanism we reveal in our microscopic model of electrons on a Lieb lattice does not involve orbital ordering, but derives from sublattice interference.
Translation symmetry-breaking order is assumed to be suppressed by the lack of Fermi surface nesting near certain higher-order Van Hove singularities (HOVHS). We show the anisotropic band-flattening inherent to such HOVHS, combined with broadening of the Fermi surface due to elevated critical temperatures, results in the Fermi surface becoming approximately nested at a wavevector unrelated to the precise shape of the Fermi surface - leading to a $\sqrt{3}\times\sqrt{3}$ Kekulé density wave formation. The effect is demonstrated using unbiased renormalization group calculations for a model of the breathing kagome lattice. Our mechanism - termed diffuse nesting - represents an entirely new notion in the study of Fermi surface instabilities.
Quantum geometry strongly impacts physical properties in flat-band systems. We consider its role in bosonic condensation and superfluidity on flat bands, and show that the superfluid weight has an important contribution proportional to the condensate quantum metric. Based on this result, we uncover conditions under which flat-band superfluidity is unlikely. For instance, we find that stable flat-band superfluidity in a two-dimensional system requires at least three bands within Bogoliubov theory. Because the quantum geometry at the condensation momentum plays a disproportionately large role, a large integrated quantum metric is not sufficient for flat-band superfluidity, but how the quantum metric is distributed in the Brillouin zone is crucial.
Kagome metals have established a new arena for correlated electron physics. To date, the predominant experimental evidence centers around unconventional charge order, nematicity, and superconductivity, while magnetic fluctuations due to electronic interactions, i.e., beyond local atomic magnetism, have largely been elusive. We find the challenge of locating the appropriate parameter regime for such exotic order to center around two aspects. First, the correlations implied by low-energy orbitals have to be sufficiently large to yield a dominance of magnetic fluctuations and weak to retain an itinerant parent state. Second, the kinematic kagome profile at the Fermi level demands an efficient mitigation of sublattice interference causing the suppression of magnetic fluctuations descending from electronic on-site repulsion. We elucidate our methodology by analyzing the potential copper-based kagome compound CsCu$_3$Cl$_5$: From ab initio design and many-body analysis, we develop a model framework of realistic Cu-based kagome materials the simulations of which reveal unconventional magnetic order in a kagome metal.
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.
Van-Hove (vH) singularities in the vicinity of the Fermi level facilitate the emergence of electronically mediated Fermi surface instabilities. This is because they provide a momentum-localized enhancement of density of states promoting selective electronic scattering channels. High-temperature topological superconductivity has been argued for in graphene at vH filling which, however, has so far proven inaccessible due to the demanded large doping from pristine half filling. We propose compensated metallicity as a path to unlock vH-driven pairing close to half filling in an electronic honeycomb lattice model. Enabled by an emergent multi-pocket fermiology, charge compensation is realized by strong breaking of chiral symmetry from intra-sublattice hybridization, while retaining vH dominated physics at the Fermi level. We conclude by proposing tangible realizations through quantum material design.
Among many-body instabilities in correlated quantum systems, electronic nematicity, defined by the spontaneous breaking of rotational symmetry, has emerged as a critical phenomenon, particularly within high-temperature superconductors. Recently, this behavior has been identified in CsTi$_3$Bi$_5$, a member of the AV$_3$Sb$_5$ (A = K, Rb, Cs) kagome family, recognized for its intricate and unconventional quantum phases. Despite accumulating indirect evidence, the fundamental mechanisms driving nematicity in CsTi$_3$Bi$_5$ remain inadequately understood, sparking ongoing debates. In this study, we employ polarization-dependent angle-resolved photoemission spectroscopy to reveal definitive signatures of an orbital-selective nematic deformation in the electronic structure of CsTi$_3$Bi$_5$. This direct experimental evidence underscores the pivotal role of orbital degrees of freedom in symmetry breaking, providing new insights into the complex electronic environment. By applying the functional renormalization group technique to a fully interacting ab initio model, we demonstrate the emergence of a finite angular momentum ($d$-wave) Pomeranchuk instability in CsTi$_3$Bi$_5$, driven by the concomitant action of electronic correlations within specific orbital channels and chemical potential detuning away from Van Hove singularities. By elucidating the connection between orbital correlations and symmetry-breaking instabilities, this work lays a crucial foundation for future investigations into the broader role of orbital selectivity in quantum materials, with far-reaching implications for the design and manipulation of novel electronic phases.
Understanding of unconventional superconductivity is crucial for engineering materials with specific order parameters or elevated superconducting transition temperatures. However, for many materials, the pairing mechanism and symmetry of the order parameter remain unclear: reliable and efficient methods of predicting the order parameter and its response to tuning parameters are lacking. Here, we investigate the response of superconductivity in Sr$_2$RuO$_4$ to structural distortions via the random phase approximation (RPA) and functional renormalization group (FRG), starting from realistic models of the electronic structure. Our results suggest that RPA misses the interplay of competing fluctuation channels. FRG reproduces key experimental findings. We predict a magic octahedral rotation angle, maximizing the superconducting $T_c$ and a dominant $d_{x^2-y^2}$ pairing symmetry. To enable experimental verification, we provide calculations of the phase-referenced Bogoliubov Quasiparticle Interference imaging. Our work demonstrates a designer approach to tuning unconventional superconductivity with relevance and applicability for a wide range of quantum materials.
The recent discovery of a variety of intricate electronic order in kagome metals has sprouted significant theoretical and experimental interest. From an electronic perspective on the potential microscopic origin of these phases, the most basic model is given by a Hubbard model on the kagome lattice. We employ functional renormalization group (FRG) to analyze the kagome Hubbard model. Through our methodological refinement of FRG both within its N-patch and truncated unity formulation, we resolve previous discrepancies of different FRG approaches (Wang et al., 2013 vs. Kiesel et al., 2013), and analyze both the pure ($p$-type) and mixed ($m$-type) van Hove fillings of the kagome lattice. We further study the RG flow into symmetry broken phases to identify the energetically preferred linear combination of the respective order parameter without any need for additional mean field analysis. Our findings suggest some consistency with recent experiments, and underline the richness of electronic phases already found in the kagome Hubbard model. We also provide a no-go theorem for a complex charge bond ordered phase in the single orbital kagome Hubbard model, suggesting that this model cannot capture aspects of orbital current phases.