arXiv subjects

Mathias S. Scheurer

Publications and source records attributed to Mathias S. Scheurer.

At least 37 records · Page 2Linked to original sources

arXiv2025

Quantum geometry and impurity sensitivity of superconductors without time-reversal symmetry: application to rhombohedral graphene and altermagnets

Analyzing the consequences of the quantum geometry induced by the momentum dependence of Bloch states has emerged as a very rich and active field in condensed matter physics. For instance, for the superfluid stiffness or the pairing mechanism, these geometric aspects can play an important role. We here demonstrate that quantum geometry can also be essential for the disorder sensitivity of a superconductor, in particular when time-reversal symmetry is broken in the normal-state Bloch Hamiltonian. We derive a general expression for the behavior of the critical temperature $T_c$ involving weighted (anti-)commutators of the superconducting order parameter and impurity matrix elements, which includes both wave-function effects and kinetic pair breaking due to broken time-reversal symmetry in the dispersion. We analyze how the former effects lead to "quantum geometric pair breaking", where any superconductor becomes susceptible to microscopically non-magnetic impurities, and formally relate it to the maximum possible localization of two-particle Wannier states. Further, in the presence of kinetic pair breaking, impurities can also enhance pairing, leading to an overall more complex, non-monotonic behavior of $T_c$ with impurity concentration. We also analyze the fate of finite-momentum pairing. Our results are directly relevant to rhombohedral graphene, twisted MoTe$_2$, and superconducting altermagnets.

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arXiv2025

Superconductivity of Incoherent Electrons near the Relativistic Mott Transition in Twisted Dirac Materials

We demonstrate that superconductivity driven by strong quantum-critical fluctuations can emerge near relativistic Mott transitions in twisted two-dimensional materials, taking on a remarkably rich character. In twisted double-bilayer WSe$_2$, all time-reversal-even, gap-opening collective modes promote pairing, whereas time-reversal-odd modes do not. In a Dirac model of twisted bilayer graphene, the Gross-Neveu transition into inter-valley-coherent insulators gives rise to a spectrum of degenerate and nearly degenerate superconducting states. More generally, we show that the richer the Dirac structure, the more readily pairs can form. A crucial ingredient of the theory is that critical fluctuations render the electronic states strongly incoherent, allowing attractive pairing channels to overcome the bare Dirac semi-metal behavior. Finally, we demonstrate a direct relation between boson-mediated pairing and the formation of charge-carrying skyrmionic excitations in the proximate insulating state.

cond-mat.str-el↗

arXiv2025

Vestigial pairing from fluctuating magnetism and triplet superconductivity

We study the finite-temperature vestigial superconducting phases of a two-dimensional system of fluctuating spin-triplet pairing and spin magnetism. Denoting the respective primary order parameters by $\mathbf{d}$ and $\mathbf{N}$, which are not long-range ordered at finite temperature, the composite fields $ϕ_{dd} = \mathbf{d}\cdot\mathbf{d}$ and $ϕ_{dN} = \mathbf{d}\cdot\mathbf{N}$ are spin-rotation invariant and can condense at finite temperature. Using a large-$N$ approach that respects the Mermin-Wagner theorem, we here derive the phase diagram which features two vestigial superconductors: $(A)$ a charge-$4e$ superconductor with $ϕ_{dd}\neq 0$ and $ϕ_{dN} =0$ and $(B)$ a charge-$2e$ state with $ϕ_{dN} ,ϕ_{dd}\neq 0$. We analyze the temperature and coupling-constant dependent properties of these two superconductors using a perturbative approach and a variational Hartree-Fock study. This reveals non-trivial spectra in the superconductors, which result from the fundamental building blocks being distinct from the usual Cooper pairs--in phase $(A)$, the elementary bosons are bound states of four electrons and, in phase $(B)$, of three electrons and a hole. This work complements the previous study [Nat. Commun. 15, 1713 (2024), arXiv:2301.01344], which focused on the properties of phase $(B)$.

cond-mat.supr-con↗

arXiv2025

Probing Vortex Dynamics in 2D Superconductors with Scanning Quantum Microscope

The visualization of the magnetic responses of a two-dimensional (2D) superconducting material on the nanoscale is a powerful approach to unravel the underlying supercurrent behavior and to investigate critical phenomena in reduced dimensions. In this study, scanning quantum microscopy is utilized to explore the local magnetic response of the 2D superconductor 2H-NbSe2. Our technique enables both static and dynamic sensing of superconducting vortices with high sensitivity and a spatial resolution down to 30 nm, unveiling unexpected phenomena linked to the intrinsic 2D nature of the superconductor, which are challenging to detect with more conventional local probes. Vortices do not arrange in a hexagonal lattice, but form a distorted vortex glass with expanding vortex size. A vortex can exhibit strong local dynamics due to thermal excitation. As the critical temperature is approached, a clear melting of the vortex glass is identified, leading to distinct configurations under different cooling conditions. Vortex fluctuations can also be probed through spin Hahn-echo measurements, which reveal the spin decoherence even well below the critical temperature -- and, intriguingly, enhanced decoherence at lower temperatures. Spatiotemporal microscopy of the magnetic dynamics associated with vortex excitations and fluctuations provides direct evidence of 2D superconducting phenomena at the nanoscale.

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arXiv2025

Spin-orbit crossover and the origin of magnetic torque in kagome metals

Recent experiments on the kagome metal CsV$_3$Sb$_5$ reveal a curious phase transition-like feature: a nematic magnetic torque response that abruptly sets in at $T_τ\approx 130$K, above the known charge density wave transition at $T_\text{CDW} \approx 100$K. Counterintuitively, elastoresistance measurements--a standard probe of nematicity--show no corresponding signal, ruling out a nematic phase transition and placing strong constraints on possible explanations. Beyond nematicity, the torque is paramagnetic for in-plane magnetic field, while above a critical out-of-plane field, an in-plane magnetisation appears, accompanied by hysteresis. We show that this combination of features cannot be accounted for by charge density waves or intraband magnetic order. Instead, we propose that interband ordering--via a symmetry-allowed interband spin-orbit coupling and a time-reversal and spatial symmetry-breaking interband order parameter--together with a background strain field, consistent with typical experimental conditions, provides a natural explanation; in our picture, the behaviour at $T_τ$ is understood as a crossover in the symmetry-allowed interband spin-orbit coupling strength. Our theory accounts for the nematic magnetic torque, hysteresis, and the transition-like onset at $T_τ$, while also making testable predictions, including strain-induced magnetisation. In doing so, it challenges the prevailing view of the normal state.

cond-mat.str-el↗

arXiv2025

Ising superconductivity in bulk layered non-centrosymmetric 4H-NbSe2

Transition metal dichalcogenides exhibit multiple polymorphs that enable the exploration of diverse quantum states, including valley-selective spin polarization, the valley Hall effect, Ising superconductivity, and nontrivial topology. Monolayer 2$H$-NbSe$_2$ is a promising candidate for realizing Ising superconductivity due to its spin-split, out-of-plane spin-polarized states arising from inversion symmetry breaking and strong spin-orbit coupling. In contrast, bulk 2$H$-NbSe$_2$ retains inversion symmetry and lacks spin splitting, limiting its suitability for hosting Ising superconductivity. Here, we report the growth of high-quality single crystals of the acentric bulk superconducting polymorph, 4$H$-NbSe$_2$, which intrinsically breaks the inversion symmetry and supports valley-selective spin-polarized states. Magnetization and resistivity measurements reveal anisotropic superconductivity, with the in-plane upper critical field exceeding the Pauli limit, while out-of-plane fields suppress superconductivity more rapidly, before reaching the Pauli limit, which strongly suggests the presence of Ising pairing. First-principles calculations and symmetry analysis confirm significant valley-selective spin splitting with out-of-plane spin polarization, further supporting the emergence of Ising superconductivity in 4$H$-NbSe$_2$. These results establish 4$H$-NbSe$_2$ as a robust bulk platform to investigate Ising superconductivity and valley-selective phenomena in transition-metal dichalcogenides.

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arXiv2025

Intrinsic superconducting diode effect and nonreciprocal superconductivity in rhombohedral graphene multilayers

Recent experiments have revealed that superconductivity in rhombohedral tetralayer graphene can emerge from a valley-polarized and, hence, chiral normal state. The interplay of pairing and the reduced normal-state symmetries sparked widespread interest. In this work, we demonstrate within a microscopic theoretical formalism that this stabilizes a non-reciprocal superconducting state. Our results are based on a fully self-consistent framework for determining the superconducting order parameter from a Kohn-Luttinger mechanism. We show that the system displays a sizeable intrinsic superconducting diode effect, i.e., without the need for applying external magnetic fields, which is also highly tunable by an external displacement field. Moreover, we find that the angular dependence of the critical current is highly sensitive to the Fermi surfaces of the normal state. Hence, our results suggest that the critical current could provide insights into the type of Fermi surface topology from which superconductivity arises.

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arXiv2025

Fractionalized Altermagnets: from neighboring and altermagnetic spin-liquids to spin-symmetric band splitting

We study quantum-fluctuation-driven fractionalized phases in the vicinity of altermagnetic order. First, the long-range magnetic orders in the vicinity of collinear altermagnetism are identified; these feature a non-coplanar "orbital altermagnet" which has altermagnetic symmetries in spin-rotation invariant observables. We then describe neighboring fractionalized phases with topological order reached when quantum fluctuations destroy long-range spin order, within Schwinger-boson theory and an SU(2) gauge theory of fluctuating magnetism. Discrete symmetries remain broken in some of the fractionalized phases, with the orbital altermagnet becoming an "altermagnetic spin liquid". We compute the electronic spectral function in the doped system, which is characterized by split Fermi surfaces with preserved spin-rotation symmetry.

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arXiv2025

Probing superconductivity with tunneling spectroscopy in rhombohedral graphene

Motivated by experiments on rhombohedral tetralayer graphene showing signs of superconductivity emerging from a valley-polarized normal state, we here analyze theoretically how scanning tunneling spectroscopy can be used to probe the superconducting order parameter of the system. To describe different pairing scenarios on equal footing, we develop a microscopic tunneling approach that can capture arbitrary, including finite-momentum, superconducting order parameters and low-symmetry normal-state Hamiltonians. Our analysis shows that the broken time-reversal symmetry in a single valley leads to unique features in the weak-tunneling regime that are different for commensurate and incommensurate Cooper pair momenta. We further uncover an unconventional spatial dependence of the Andreev conductance, allowing to distinguish between three topologically distinct classes of single-$\mathbf{q}$ pairing states in the system, and compute the signatures of a competing translational-symmetry breaking three-$\mathbf{q}$ ''moiré superconductor''.

cond-mat.supr-con↗

arXiv2025

Moiré $M$-valley bilayers: quasi-one-dimensional physics, unconventional spin textures and twisted van Hove singularities

Motivated by the discovery of quasi-two-dimensional kagome metals AV$_3$Sb$_5$, we consider the theory of twisted bilayers in which the Fermi surface is near the $M$-point. Surprisingly, unlike twisted bilayers of graphene or transition metal dichalcogenides, the moiré potential is quasi-one-dimensional: at each $M$-valley, the potential flattens the dispersion strongly along one direction, and weakly along the perpendicular direction. The combination of spin-orbit coupling and twist-induced broken inversion symmetry results in a similarly anisotropic `$\textit{moiré-Rashba}$' potential, which spin-splits the dispersion into coexisting two-dimensional and quasi-one-dimensional bands. We discuss novel aspects of the interplay between mixed dimensionality and spin textures in this platform. First, an applied electric field produces spin polarisation which can be tuned by doping, suggesting potential spintronics applications. Secondly, an in-plane magnetic field momentum- and spin-polarises the Fermi surfaces, producing unconventional spin density waves. Thirdly, in the small-twist-angle limit, the large density of states due to a twisted van Hove singularity near $M$ results in a dense energy spectrum. Our results demonstrate a new variation of moiré bandstructure engineering, instigating the study of spin-textured one-dimensional physics in moiré materials.

cond-mat.str-el↗

arXiv2025

Eliashberg Theory and Superfluid Stiffness of Band-Off-Diagonal Pairing in Twisted Graphene

Recently, band-off-diagonal superconductivity has been proposed [Nat. Commun. 14, 7134 (2023)] as a candidate pairing state for twisted graphene systems. Based on mean-field theory, it was shown that it not only naturally emerges from both intervalley electron-phonon coupling and fluctuations of the nearby correlated insulator, but also exhibits nodal and gapped regimes as indicated by scanning tunneling microscopy experiments. Here we study band-off-diagonal pairing within Eliashberg theory. We show that despite the additional frequency dependence, the leading-order description of both intervalley coherent fluctuations or intervalley phonons exhibits a symmetry prohibiting admixture of an intraband component to the interband pairing state. It is found that even- and odd-frequency pairing mix, which originates from the reduced number of flavor degrees of freedom in the normal state. From analytic continuation, we obtain the electronic spectral function showing that, also within Eliashberg theory, the interband nature leads to an enhanced spectral weight below the order-parameter energy compared to band-diagonal pairing. Finally, we also study the superfluid stiffness of band-off-diagonal pairing, taking into account multi-band and quantum geometry effects. It is shown that for $s$-wave and chiral momentum dependencies, conventionally leading to fully gapped phases, an interband structure reduces the temperature scale below which the stiffness saturates. Depending on parameters, for the chiral state, this scale can even be suppressed all the way to zero temperature leading to a complex competition of multiple dispersive and geometrical contributions. Our results show that interband pairing might also be able to explain more recent stiffness measurements in the superconducting state of twisted multilayer graphene.

cond-mat.supr-con↗

arXiv2025

Dissipation-enhanced non-reciprocal superconductivity: application to multi-valley superconductors

We here propose and study theoretically a non-equilibrium mechanism for the superconducting diode effect, which applies specifically to the case where time-reversal-symmetry -- a prerequisite for the diode effect -- is spontaneously broken by the superconducting electrons themselves. We employ a generalized time-dependent Ginzburg-Landau formalism to capture dissipation effects in the non-equilibrium current-carrying state via phase slips and show that the coupling of the resistive current to the symmetry-breaking order is enough to induce a diode effect. Depending on parameters, the critical current asymmetry can be sizeable, asymptotically reaching a perfect diode efficiency; the competition of symmetry-breaking order, superconducting and resistive currents gives rise to rich physics, such as current-stabilized, non-equilibrium superconducting correlations. Although our mechanism is more general, the findings are particularly relevant to twisted trilayer and rhombohedral tetralayer graphene, where the symmetry-breaking order parameter refers to the imbalance of the two valleys of the systems.

cond-mat.supr-con↗

arXiv2024

Physics-informed Transformers for Electronic Quantum States

Neural-network-based variational quantum states in general, and more recently autoregressive models in particular, have proven to be powerful tools to describe complex many-body wave functions. However, their performance crucially depends on the computational basis chosen and they often lack physical interpretability. To mitigate these issues, we here propose a modified variational Monte-Carlo framework which leverages prior physical information to construct a computational second-quantized basis containing a reference state that serves as a rough approximation to the true ground state. In this basis, a Transformer is used to parametrize and autoregressively sample the corrections to the reference state, giving rise to a more interpretable and computationally efficient representation of the ground state. We demonstrate this approach using a non-sparse fermionic model featuring a metal-insulator transition and employing Hartree-Fock and a strong-coupling limit to define physics-informed bases. We also show that the Transformer's hidden representation captures the natural energetic order of the different basis states. This work paves the way for more efficient and interpretable neural quantum-state representations.

cond-mat.str-el↗

arXiv2024

Adatom engineering magnetic order in superconductors: Applications to altermagnetic superconductivity

We study theoretically how superlattices based on adatoms on surfaces of unconventional superconductors can be used to engineer novel pairing states that break time-reversal symmetry and exhibit non-trivial magnetic point symmetries. We illustrate this using a square-lattice Hubbard model with $d$-wave superconductivity and a subleading $s$-wave state as an example. An adatom superlattice with square-lattice symmetries is shown to stabilize an "orbital-altermagnetic superconductor'', a state that exhibits loop current patterns and associated orbital magnetic moments, which preserve superlattice translations but are odd under four-fold rotations. This state is further characterized by a non-zero Berry curvature quadrupole moment and, upon including spin-orbit coupling, by an altermagnetic spin splitting of the bands and non-trivial spin textures in the superlattice unit cell, with zero net spin moment.

cond-mat.supr-con↗

arXiv2024

A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order

Motivated by recent experiments on correlated van der Waals materials, including twisted and rhombohedral graphene and twisted WSe$_2$, we perform an analytical and numerical study of the effects of strong on-site and short-range interactions in fractionally filled ideal Chern bands. We uncover an extensive non-trivial ground state manifold within the band filling range $0 < ν< 1$ and introduce a general principle, the ''three-rule'', for combining flatband wave functions, which governs their zero-energy property on the torus geometry. Based on the structure of these wave functions, we develop a variational approach that reveals distinct phases under different perturbations: metallic behavior emerges from a finite dispersion, and superconductivity is induced by attractive Cooper channel interactions. Our approach, not reliant on the commonly applied mean-field approximations, provides an analytical expression for the macroscopic wave function of the off-diagonal long-range order correlator, attributing pairing susceptibility to the set of non-trivial zero-energy ground state wave functions. Extending to finite screening lengths and beyond the ideal limit using exact diagonalization simulations, we demonstrate the peculiar structure in the many-body wave function's coefficients to be imprinted in the low-energy spectrum of the topologically ordered Halperin spin-singlet state. Our findings also make connections to frustration-free models of non-commuting projector Hamiltonians, potentially aiding the future construction of exact ground states for various fractional fillings.

cond-mat.str-el↗

arXiv2024

Altermagnetic superconducting diode effect

Non-reciprocal superconductivity, also known as the superconducting diode effect, has been extensively studied in the presence of a magnetic field or some form of ferromagnetic order breaking time-reversal symmetry. We here show that another class of magnetic order known as altermagnetism, which also breaks time-reversal symmetry but does not exhibit a finite net magnetic moment, can also give rise to a superconducting diode effect. Whether this is the case depends on the combination of the system's point group and altermagnetic order parameter which we explore systematically for two-dimensional crystalline systems. If the superconducting electrons are in a centrosymmetric crystalline environment, an electric field $E_z$ (or other sources of inversion symmetry breaking) can be used to turn on and tune the non-reciprocity, yielding an electric-field tunable diode effect; there are also non-centrosymmetric point groups, which are not reached by applying $E_z \neq 0$ in a centrosymmetric crystal, but still allow for an altermagnetic order parameter with non-reciprocal superconductivity. Depending on the residual magnetic point group, the zeros of the critical current asymmetry, $J_c(\hat{n}) - J_c(-\hat{n})$, are pinned along high-symmetry crystalline directions $\hat{n}=\hat{e}_j$ or are free to rotate in the plane of the system. In some cases, the zeros can be rotated by tuning the electric field $E_z$. We discuss all of these phenomena both on the general level using exact symmetry arguments and more explicitly by constructing and solving minimal lattice models. We provide experimental setups to realize the altermagnetic superconducting diode effect.

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arXiv2024

Approximate symmetries, insulators, and superconductivity in continuum-model description of twisted WSe$_2$

Motivated by the recent discovery of superconductivity in twisted bilayer WSe$_2$, we analyze the correlated physics in this system in the framework of a continuum model for the moiré superlattice. Using the symmetries in a fine-tuned limit of the system, we identify the strong-coupling ground states and their fate when the perturbations caused by finite bandwidth, displacement field, and the phase of the intralayer potential are taken into account. We classify the superconducting instabilities and, employing a spin-fermion-like model, study the superconducting instabilities in proximity to these insulating particle-hole orders. This reveals that only a neighboring intervalley coherent phase (with zero or finite wave vector) is naturally consistent with the observed superconducting state. Depending on details, the superconductor will be nodal or a chiral gapped state while further including electron-phonon coupling leads to a fully gapped, time-reversal symmetric pairing state.

cond-mat.supr-con↗

arXiv2024

Band theory for heterostructures with interface superlattices

Motivated by recent experiments demonstrating the creation of atomically sharp interfaces between hexagonal sapphire and cubic SrTiO$_3$ with finite twist, we here develop and study a general electronic band theory for this novel class of moiré heterostructures. We take into account the three-dimensional nature of the two crystals, allow for arbitrary combinations of Bravais lattices, finite twist angles, and different locations in momentum space of the low-energy electronic bands of the constituent materials. We analyze the general condition for a well-defined crystalline limit in the interface electron system and classify the associated "crystalline reference points". We discuss this in detail for the example of the two-dimensional lattice planes being square and triangular lattices on the two sides of the interface; this reveals non-trivial reference points at finite twist angle and lattice mismatch, leading to a novel form of magic angles, which we refer to as "geometric magic angles". We further show that band structures of mixed dimensionality naturally emerge, where quasi-one- and two-dimensional pockets coexist. Explicit computations for different bulk Bloch Hamiltonians yield a collection of interesting features, such as isolated bands localized at interfaces of non-topological insulators, Dirac cones, van Hove singularities, a non-trivial evolution of the band structures with Zeeman-field, and topological interface bands. Our work illustrates the potential of these heterostructures and is anticipated to provide the foundation for moiré interface design and for the analysis of correlated physics in these systems.

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