arXiv subjects

Mathias S. Scheurer

Publications and source records attributed to Mathias S. Scheurer.

At least 55 records · Page 3Linked to original sources

arXiv2024

AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning

Deep generative models complement Markov-chain-Monte-Carlo methods for efficiently sampling from high-dimensional distributions. Among these methods, explicit generators, such as Normalising Flows (NFs), in combination with the Metropolis Hastings algorithm have been extensively applied to get unbiased samples from target distributions. We systematically study central problems in conditional NFs, such as high variance, mode collapse and data efficiency. We propose adversarial training for NFs to ameliorate these problems. Experiments are conducted with low-dimensional synthetic datasets and XY spin models in two spatial dimensions.

cs.LG↗

arXiv2024

An exactly solvable dissipative spin liquid

Exactly solvable Hamiltonians with spin liquid ground states have proven to be extremely useful, not only because they unambiguously demonstrate that these phases can arise in systems of interacting spins but also as a pedagogical illustration of the concept and as a controlled starting point for further theoretical analysis. However, adding dissipative couplings to the environment - an important aspect for the realization of these phases - generically spoils the exact solvability. We here present and study a Lindbladian, describing a square-lattice spin-liquid with dissipative coupling to the environment, that admits an exact solution in terms of Majorana fermions coupled to static $\mathbb{Z}_2$ gauge fields. This solution allows us to characterize the steady-state solutions as well as ``quasiparticle'' excitations within the Lindbladian spectrum. This emergence of distinct types of quasiparticle excitations of the Lindbladian leads to a separation of timescales that govern the equilibration time of the expectation values of different classes of observables, some of which we identify as fractionalized string-like operators. This exactly solvable Lindbladian is expected to provide a starting point for a better understanding of the behavior of fractionalized systems under dissipative time evolution.

cond-mat.str-el↗

arXiv2023

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. For instance, recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of unusual consequences: most notably, the pairing invariant under all symmetries can have protected nodal lines or be fully gapped, depending on parameters, and the band-off-diagonal chiral d-wave state exhibits transitions between gapped and nodal regions upon varying the chemical potential. We demonstrate that nodal band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley-coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

cond-mat.supr-con↗

arXiv2023

Displacement-field-tunable superconductivity in an inversion-symmetric twisted van der Waals heterostructure

We investigate the superconducting properties of inversion-symmetric twisted trilayer graphene by considering different parent states, including spin-singlet, triplet, and SO(4) degenerate states, with or without nodal points. By placing transition metal dichalcogenide layers above and below twisted trilayer graphene, spin-orbit coupling is induced in TTLG and, due to inversion symmetry, the spin-orbit coupling does not spin-split the bands. The application of a displacement field ($D_0$) breaks the inversion symmetry and creates spin-splitting. We analyze the evolution of the superconducting order parameters in response to the combined spin-orbit coupling and $D_0$-induced spin-splitting. Utilizing symmetry analysis combined with both a direct numerical evaluation and a complementary analytical study of the gap equation, we provide a comprehensive understanding of the influence of spin-orbit coupling and $D_0$ on superconductivity. These results contribute to a better understanding of the superconducting order in twisted trilayer graphene.

cond-mat.mes-hall↗

arXiv2023

Quadratic Dirac fermions and the competition of ordered states in twisted bilayer graphene

Magic-angle twisted bilayer graphene (TBG) exhibits a captivating phase diagram as a function of doping, featuring superconductivity and a variety of insulating and magnetic states. The bands host Dirac fermions with a reduced Fermi velocity; experiments have shown that the Dirac dispersion reappears near integer fillings of the moiré unit cell -- referred to as the $\textit{Dirac revival}$ phenomenon. The reduced velocity of these Dirac states leads us to propose a scenario in which the Dirac fermions possess an approximately quadratic dispersion. The quadratic momentum dependence and particle-hole degeneracy at the Dirac point results in a logarithmic enhancement of interaction effects, which does not appear for a linear dispersion. The resulting non-trivial renormalisation group (RG) flow naturally produces the qualitative phase diagram as a function of doping -- with nematic and insulating states near integer fillings, which give way to superconducting states past a critical relative doping. The RG method further produces different results to strong-coupling Hartree-Fock treatments: producing T-IVC insulating states for repulsive interactions, explaining the results of very recent STM experiments, alongside nodal $A_2$ superconductivity near half-filling, whose properties explain puzzles in tunnelling studies of the superconducting state. The model explains a diverse range of additional experimental observations, unifying many aspects of the phase diagram of TBG.

cond-mat.str-el↗

arXiv2023

Anisotropic multiband superconductivity in 2M-WS$_{2}$ probed by controlled disorder

The intrinsically superconducting Dirac semimetal 2M-WS$_{2}$ is a promising candidate to realize proximity-induced topological superconductivity in its protected surface states. A precise characterization of the bulk superconducting state is essential for understanding the nature of surface superconductivity in the system. Here, we perform a detailed experimental study of the temperature and nonmagnetic disorder dependence of the London penetration depth $λ$, the upper critical field $H_{c2}$, and the superconducting transition temperature $T_c$ in 2M-WS$_{2}$. We observe a power-law dependence $λ(T) - λ(0) \propto T^{3}$ at temperatures below $0.35~T_c$, which is remarkably different from the expected exponential attenuation of a fully gapped isotropic $s$-wave superconductor. We then probe the effect of controlled nonmagnetic disorder induced by 2.5 MeV electron irradiation at various doses and find a significant $T_c$ suppression rate. Together with the observed increase of the slope $dH_{c2}/dT|_{T=T_c}$ with irradiation, our results reveal a strongly anisotropic $s^{++}$ multiband superconducting state that takes the same sign on different Fermi sheets. Our results have direct consequences for the expected proximity-induced superconductivity of the topological surface states.

cond-mat.supr-con↗

arXiv2023

Enhanced Superconducting Diode Effect due to coexisting Phases

The superconducting diode effect refers to an asymmetry in the critical supercurrent $J_c(\hat{n})$ along opposite directions, $J_c(\hat{n})\neq J_c(-\hat{n})$. While the basic symmetry requirements for this effect are known, it is, for junction-free systems, difficult to capture within current theoretical models the large current asymmetries $J_c(\hat{n})/J_c(-\hat{n})$ recently observed in experiment. We here propose and develop a theory for an enhancement mechanism of the diode effect arising from spontaneous symmetry breaking. We show - both within a phenomenological and a microscopic theory - that there is a coupling of the supercurrent and the underlying symmetry-breaking order parameter. This coupling can enhance the current asymmetry significantly. Our work might not only provide a possible explanation for recent experiments on trilayer graphene but also pave the way for future realizations of the superconducting diode effect with large current asymmetries.

cond-mat.supr-con↗

arXiv2023

Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands

Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, "rotating" the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number $|C|=1$, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

cond-mat.str-el↗

arXiv2023

Machine Learning Microscopic Form of Nematic Order in twisted double-bilayer graphene

Modern scanning probe techniques, like scanning tunneling microscopy (STM), provide access to a large amount of data encoding the underlying physics of quantum matter. In this work, we analyze how convolutional neural networks (CNN) can be employed to learn effective theoretical models from STM data on correlated moiré superlattices. These engineered systems are particularly well suited for this task as their enhanced lattice constant provides unprecedented access to intra-unit-cell physics and their tunability allows for high-dimensional data sets within a single sample. Using electronic nematic order in twisted double-bilayer graphene (TDBG) as an example, we show that including correlations between the local density of states (LDOS) at different energies allows CNNs not only to learn the microscopic nematic order parameter, but also to distinguish it from heterostrain. These results demonstrate that neural networks constitute a powerful methodology for investigating the microscopic details of correlated phenomena in moiré systems and beyond.

cond-mat.str-el↗

arXiv2023

Classifying topological neural network quantum states via diffusion maps

We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. Using a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum, we sample wave functions with probability decaying exponentially with their variational energy; this defines our training dataset that we use as input to a diffusion map scheme. The diffusion map provides a low-dimensional embedding of the wave functions, revealing the presence or absence of superselection sectors and, thus, topological order. We show that for the diffusion map, the required similarity measure of quantum states can be defined in terms of the network parameters, allowing for an efficient evaluation within polynomial time. However, possible ''gauge redundancies'' have to be carefully taken into account. As an explicit example, we apply the method to the toric code.

quant-ph↗

arXiv2023

Vestigial singlet pairing in a fluctuating magnetic triplet superconductor: Applications to graphene moiré systems

Motivated by the phenomenology of graphene moiré superlattices, we study a 2D model with strong tendencies towards both magnetism and triplet superconductivity. Individually, their respective order parameters, $\vec{N}$ and $\vec{d}$, cannot order at finite temperature. Nonetheless, the model exhibits a variety of vestigial phases, including charge-$4e$ superconductivity and broken time-reversal symmetry. Our main focus is on a phase characterized by finite $\vec{d} \cdot \vec{N}$, which has the same symmetries as the BCS state, a Meissner effect, and metastable supercurrents, yet rather different spectral properties: most notably, the suppression of the electronic density of states at the Fermi can resemble that of either a fully gapped or nodal superconductor, depending on parameters. This could provide a possible explanation for recent tunneling experiments in graphene moiré systems.

cond-mat.supr-con↗

arXiv2022

Moiré phonons and impact of electronic symmetry breaking in twisted trilayer graphene

Twisted trilayer graphene is a particularly promising moiré superlattice system, due to its tunability, strong superconductivity, and complex electronic symmetry breaking. Motivated by these properties, we study lattice relaxation and the long-wavelength phonon modes of this system. We show that mirror-symmetric trilayer graphene hosts, aside from the conventional acoustic phonon modes, two classes of shear modes, which are even and odd under mirror reflection. The mirror-even modes are found to be gapless and equivalent to the "phason" modes of twisted bilayer graphene, with appropriately rescaled parameters. The modes odd under mirror symmetry have no analogue in twisted bilayer graphene and exhibit a finite gap, which we show is directly proportional to the degree of lattice relaxation. We also discuss the impact of mirror-symmetry breaking, which can be tuned by a displacement field or result from a stacking shift, and of rotational- as well as time-reversal-symmetry breaking, resulting from spontaneous electronic order. We demonstrate that this can induce finite angular momentum to the phonon branches. Our findings are important to the interpretation of recent experiments, concerning the origin of superconductivity and of linear-in-$T$ resistivity.

cond-mat.mes-hall↗

arXiv2022

Tunable superconductivity and Möbius Fermi surfaces in an inversion-symmetric twisted van der Waals heterostructure

We study theoretically a moiré superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows to switch on/off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field $D_0$, and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with $D_0$; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase transitions between competing superconducting phases. Second, we reveal that, with application of $D_0$, the spin-orbit-induced spin textures exhibit vortices which lead to "Möbius fermi surfaces'' in the interior of the Brillouin zone: diabatic electron trajectories, which are predicted to dominate quantum oscillation experiments, require encircling the $Γ$ point twice, making their Möbius nature directly observable. We further show that the superconducting order parameter inherits the unconventional, Möbius spin textures. Our findings suggest that this system provides a promising experimental avenue for studying systematically the impact of spin-orbit coupling on the multitude of topological and correlated phases in near-magic-angle twisted trilayer graphene.

cond-mat.mes-hall↗

arXiv2022

Theory of zero-field superconducting diode effect in twisted trilayer graphene

In a recent experiment [Lin et al., arXiv:2112.07841], the superconducting phase hosted by a heterostructure of mirror-symmetric twisted trilayer graphene and WSe$_2$ was shown to exhibit significantly different critical currents in opposite directions in the absence of external magnetic fields. We here develop a microscopic theory and analyze necessary conditions for this zero-field superconducting diode effect. Taking into account the spin-orbit coupling induced in trilayer graphene via the proximity effect, we classify the pairing instabilities and normal-state orders and derive which combinations are consistent with the observed diode effect, in particular, its field trainability. We perform explicit calculations of the diode effect in several different models, including the full continuum model for the system, and illuminate the relation between the diode effect and finite-momentum pairing. Our theory also provides a natural explanation of the observed sign change of the current asymmetry with doping, which can be related to an approximate chiral symmetry of the system, and of the enhanced transverse resistance above the superconducting transition. Our findings not only elucidate the rich physics of trilayer graphene on WSe$_2$, but also establish a means to distinguish between various candidate interaction-induced orders in spin-orbit-coupled graphene moiré systems, and could therefore serve as a guide for future experiments as well.

cond-mat.mes-hall↗

arXiv2022

Electron spin resonance and collective excitations in magic-angle twisted bilayer graphene

In a strongly correlated system, collective excitations contain key information regarding the electronic order of the underlying ground state. An abundance of collective modes in the spin and valley isospin channels of magic-angle graphene moiré bands has been alluded to by a series of recent experiments. However, direct observation of collective excitations has remained elusive due to the lack of a spin probe. In this work, we use a resistively-detected electron spin resonance technique to look for low-energy collective excitations in magic-angle twisted bilayer graphene. We report direct observation of collective modes in the form of microwave-induced resonance near half filling of the moiré flatbands. The frequency-magnetic field dependence of these resonance modes sheds light onto the nature of intervalley spin coupling, allowing us to extract parameters such as intervalley exchange interaction and spin stiffness. Two independent observations testify that the generation and detection of the microwave resonance relies on the strong correlation within the flat moiré energy band. First, the onset of robust resonance response coincides with the spontaneous flavor polarization at half moiré filling, and remains absent in the density range where the underlying Fermi surface is isospin unpolarized. Second, we performed the same resonance measurement on graphene monolayer and bilayer samples, including twisted bilayer with a large twist angle, where flatband physics is absent. We observe no indication of resonance response in these samples across a large range of carrier density, microwave frequency and power. A natural explanation is that the resonance response near the magic angle originates from "Dirac revivals" and the resulting isospin order.

cond-mat.mes-hall↗

arXiv2022

A new flavor of correlation and superconductivity in small twist-angle trilayer graphene

When layers of graphene are rotationally misaligned by the magic angle, the moiré superlattice features extremely flat bands. Due to the enhanced density of states, the Coulomb interaction induces a variety of instabilities. The most prominent occur at integer filling and are therefore commonly attributed to spontaneous polarization of the moiré unit cell's `flavor' degrees of freedom -- spin, valley, and the flat-band degeneracy. As the dominant member of the hierarchy, these correlated states are thought to crucially determine further instabilities at lower energy scales, such as superconductivity and weaker incompressible states at fractional filling. In this work, we examine the behavior of twisted trilayer graphene in a window of twist angle around $1.3^{\circ}$, well below the expected magic angle of $1.55^{\circ}$. In this small twist angle regime, we find surprisingly narrow bands, which are populated with both an abundance of correlation-driven states at fractional filling as well as robust superconductivity. The absence of linear-in-$T$ resistivity without significant reduction of the superconducting transition temperature, provides insights into the origin of both phenomena. Most remarkably, the hierarchy between integer and fractional filling is absent, indicating that flavor polarization does not play a governing role. The prominence of fractional filling in the small twist angle regime also points towards a longer-range effective Coulomb interaction. Combined, our results shed new light on outstanding questions in the field, while establishing the small twist angle regime as a new paradigm for exploring novel flavors of moiré physics.

cond-mat.mes-hall↗

arXiv2022

Zero-field superconducting diode effect in small-twist-angle trilayer graphene

The critical current of a superconductor can be different for opposite directions of current flow when both time-reversal and inversion symmetry are broken. %When time-reversal and inversion symmetry are simultaneously broken, the critical current of a 2D superconductor is expected to depend on the directions of current flow. Such nonreciprocal behavior in superconducting transport, which creates a superconducting diode, has recently been demonstrated experimentally by breaking these symmetries with an applied magnetic field \cite{Ando2020diodes} or by construction of a magnetic tunnel junction \cite{Diez2021magnetic}. Here we report an intrinsic superconducting diode effect which is present at zero external magnetic field in mirror symmetric twisted trilayer graphene (tTLG). Such nonreciprocal behavior, with sign that can be reversed through training with an out-of-plane magnetic field, provides direct evidence of the microscopic coexistence between superconductivity and time-reversal symmetry breaking. In addition to the magnetic-field trainability, we show that the zero-field diode effect can be controlled by varying carrier density or twist angle. In accordance with these experimental controls, a natural interpretation for the origin of the intrinsic diode effect is an imbalance in valley occupation of the underlying Fermi surface, which likely leads to finite-momentum Cooper pairing and nematicity in the superconducting phase.

cond-mat.mes-hall↗

arXiv2021

Twistons in a Sea of Magic

Magic angle twisted trilayer graphene (TTG) has recently emerged as a new platform to engineer strongly correlated flat bands. Here, we reveal the structural and electronic properties of TTG using low temperature scanning tunneling microscopy at twist angles for which superconductivity has been observed. Real trilayer samples deviate from their idealized structure due to a strong reconstruction of the moiré lattice, which locks layers into near-magic angle, mirror symmetric domains comparable in size to the superconducting coherence length. The price for this magic relaxation is the introduction of an array of localized twist angle faults, termed twistons. These novel, gate-tunable moiré defects offer a natural explanation for the superconducting dome observed in transport and provide an avenue to probe superconducting pairing mechanisms through disorder tuning.

cond-mat.str-el↗