arXiv subjects

Kryštof Kolář

Publications and source records attributed to Kryštof Kolář.

12 recordsLinked to original sources

arXiv2026

Robustness of real-space topology in moiré systems

The appearance of fractional Chern insulators in moiré systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a systematic study of real-space topology and the associated fictitious magnetic fields in moiré systems. We first show that at the level of individual Bloch wavefunctions, the real-space Chern number, akin to a Pontryagin index, is a fragile marker. It generically vanishes except for specific limits where the Bloch functions exhibit fine-tuned zeroes within the unit cell, such as the chiral limit of twisted bilayer graphene (TBG) or the adiabatic regime of twisted homobilayer transition metal dichalcogenides (TMD). We then show that these limitations do not apply to textures associated with ensembles of Bloch wavefunctions, such as entire bands or the ensemble of states at a given energy. The Chern number of these textures defines a robust topological index protected by a spectral gap. We find that symmetries constrain it to be nonzero for both twisted TMDs and TBG across all twist angles and levels of corrugation, implying experimental signatures in scanning tunneling microscopy measurements. By projection to the band ensemble texture, a single-component Hamiltonian under fictitious magnetic field emerges in a broad regime, enabling a direct comparison of multicomponent bands to Landau-level wavefunctions. We also study real-space topology within the topological heavy fermion model of TBG, finding that the real-space topological features are supported only by the light c-electrons.

cond-mat.mes-hall↗

arXiv2026

Superfluid weight in disordered flat-band superconductors as a competition between localization functionals

According to Anderson's theorem, the gap of a time-reversal symmetric weak-coupling superconductor is unaffected by non-magnetic disorder. However, the superfluid weight (stiffness) is reduced in the disordered limit by a factor of $Δτ$, a product of the scattering time $τ$ and the superconducting order parameter $Δ$. Here we show that the opposite holds true in flat-band superconductors. While non-magnetic disorder does reduce the order parameter, we find that its direct effect on superfluid weight is mostly negligible. We show analytically that the effect of disorder is to lowest order given in terms of the difference between the intraband and interband parts of the localization functional of impurity wavefunctions, finding it to be typically vanishing.

cond-mat.supr-con↗

arXiv2026

Surface-Selective Probe of Spin-Triplet Superconductivity in Rhombohedral Graphene

Superconductivity in rhombohedral graphene has been observed across many layer numbers, with mounting evidence pointing toward spin-triplet pairing, yet complementary probes of the superconducting spin structure remain needed. Here we use one-sided WS$_2$ proximity in rhombohedral pentalayer graphene (R5G) as a surface-selective spin-orbit probe. The induced Ising spin-orbit coupling is strongest for carriers localized near the WS$_2$ interface, allowing the displacement field to tune the overlap between superconducting carriers and the spin-orbit perturbation. We observe a strongly asymmetric superconducting landscape: two robust pockets, SC1 and SC2, survive only on mutually opposite signs of displacement field, while a third pocket, SC3, is substantially weaker. Gate-tracking features, quantum oscillations, and self-consistent band-structure calculations identify the layer polarization and Fermi-surface character of the relevant carriers. The robust superconducting states are absent or strongly weakened when the active high-DOS carriers are polarized toward the WS$_2$ interface. Since Ising spin-orbit coupling is compatible with time-reversed spin-singlet pairing but competes with same-spin intervalley triplet pairing by canting or pinning the parent spin texture, this surface-selective suppression provides additional evidence for spin-triplet superconductivity involving both hole-like and electron-like carriers. Our results establish one-sided TMD proximity as a displacement-field-tunable probe of superconducting spin structure in rhombohedral graphene.

cond-mat.mes-hall↗

arXiv2026

Electrostatically stabilized surface flat bands in rhombohedral graphite at zero displacement field

Rhombohedral (ABC-stacked) multilayer graphene hosts interaction-driven phases enabled by surface flat bands at large displacement fields. In thick flakes, however, strong screening suppresses internal electric fields, raising the question of whether a flat-band regime is accessible within the same experimental paradigm. Here, we show that self-consistent, nonlinear electrostatics provides a robust alternative mechanism: even in the absence of a displacement field, a nonuniform near-surface potential flattens the surface-band dispersion and enhances the density of states. In the strong-coupling limit, electrostatics drives the system toward uniform half-filling at each momentum, yielding an asymptotically flat surface band without any gating. At realistic interaction strengths, surface-band flatness is tuned by the proximal gate, with maximal flatness achieved at hole doping when the band is empty. Combining analytic arguments with fully self-consistent calculations in a realistic model, we map the resulting low-field regime and connect to finite $N\!\sim\! 6-15$ layered samples, providing a framework for analyzing the symmetry-broken phases observed in these systems. Our results motivate future experiments in large-$N$ devices and establish a low-field regime for exploring electrostatically induced flat-band physics.

cond-mat.mes-hall↗

arXiv2026

Tunneling signatures of interband coherence in dilute exciton condensates

We theoretically investigate signatures of exciton condensation and the underlying interband coherence in scanning tunneling microscopy. We consider both monolayer and bilayer condensates in the regime of a dilute condensate of tightly bound excitons. For monolayer condensates, interband coherence is directly encoded in spatially oscillating contributions to the tunneling conductance, which break the underlying lattice symmetry. We show how scanning tunneling microscopy allows one to extract the exciton wavefunction. For bilayer condensates, we show that the formation of the exciton insulator is signaled by the emergence of a characteristic peak in the tunneling conductance, which can be used to extract the (local) exciton density. Our results are based on analytical considerations using a systematic solution of the mean-field equations in powers of the exciton density as well as numerical calculations.

cond-mat.mes-hall↗

arXiv2025

Flat band surface state superconductivity in thick rhombohedral graphene

Rhombohedral multilayer graphene has recently emerged as a rich platform for studying correlation driven magnetic, topological and superconducting states. While most experimental efforts have focused on devices with N$\leq 9$ layers, the electronic structure of thick rhombohedral graphene features flat-band surface states even in the infinite layer limit. Here, we use layer resolved capacitance measurements to directly detect these surface states for $N\approx 13$ layer rhombohedral graphene devices. Using electronic transport and local magnetometry, we find that the surface states host a variety of ferromagnetic phases, including both valley imbalanced quarter metals and broad regimes of density in which the system spontaneously spin polarizes. We observe several superconducting states localized to a single surface state. These superconductors appear on the unpolarized side of the density-tuned spin transitions, and show strong violations of the Pauli limit consistent with a dominant attractive interaction in the spin-triplet, valley-singlet pairing channel. In contrast to previous studies of rhombohedral multilayers, however, we find that superconductivity can persist to zero displacement field where the system is inversion symmetric. Energetic considerations suggest that superconductivity in this regime is described by the existence of two independent surface superconductors coupled via tunneling through the insulating single crystal graphite bulk.

cond-mat.supr-con↗

arXiv2025

Strong Correlations and Superconductivity in the Supermoiré Lattice

The supermoiré lattice, arising from the interference of multiple moiré patterns, dramatically reshapes the electronic band structure by introducing new minibands and modifying band dispersion. Concurrently, strong electronic interactions within moiré flat bands lead to the emergence of various correlated states. However, the impact of the supermoiré lattice on the flat band systems with strong interactions remains largely unexplored. Here, we report the existence of the supermoiré lattice in the mirror-symmetry-broken twisted trilayer graphene, elucidating its role in generating mini-flat bands and mini-Dirac bands. Furthermore, we demonstrate interaction-induced symmetry-broken phases in the supermoiré mini-flat bands alongside the cascade of superconductor-insulator transitions enabled by the supermoiré lattice. Our work shows that robust superconductivity can exist in the mirror-symmetry-broken TTG and underscores the significance of the supermoiré lattice as an additional degree of freedom for tuning the electronic properties in twisted multilayer systems, sheds light on the correlated quantum phases such as superconductivity in the original moiré flat bands, and highlights the potential of using the supermoiré lattice to design and simulate novel quantum phases.

cond-mat.str-el↗

arXiv2025

Single-gate tracking behavior in flat-band multilayer graphene devices

A central feature of many van der Waals (vdW) materials is the ability to precisely control their charge doping, $n$, and electric displacement field, $D$, using top and bottom gates. For devices composed of only a few layers, it is commonly assumed that $D$ causes the layer-by-layer potential to drop linearly across the structure. Here, we show that this assumption fails for a broad class of crystalline and moiré vdW structures based on Bernal- or rhombohedral-stacked multilayer graphene. We find that the electronic properties at the Fermi level are largely dictated by special layer-polarized states arising at Bernal-stacked crystal faces, which typically coexist in the same band with layer-delocalized states. We uncover a novel mechanism by which the layer-delocalized states completely screen the layer-polarized states from the bias applied to the remote gate. This screening mechanism leads to an unusual scenario where voltages on either gate dope the band as expected, yet the band dispersion and associated electronic properties remain primarily (and sometimes exclusively) governed by the gate closer to the layer-polarized states. Our results reveal a novel electronic mechanism underlying the atypical single-gate-controlled transport characteristics observed across many flat-band graphitic structures, and provide key theoretical insights essential for accurately modeling these systems.

cond-mat.mes-hall↗

arXiv2024

Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides

We study the topological bands in twisted bilayer transition metal dichalcogenides in an external magnetic field. We first focus on a paradigmatic model of WSe$_2$, which can be described in an adiabatic approximation as particles moving in a periodic potential and an emergent periodic magnetic field with nonzero average. We understand the magnetic-field dependent spectra of WSe$_2$ based on the point net zero flux, at which the external field cancels the average emergent field. At this point, the band structure interpolates between the tightly-bound and nearly-free (weak periodic potential) paradigms as the twist angle increases. For small twist angles, the energy levels in a magnetic field mirror the Hofstadter butterfly of the Haldane model. For larger twist angles, the isolated Chern band at zero flux evolves from nearly-free bands at the point of net zero flux. We also apply our framework to a realistic model of twisted bilayer MoTe$_2$, which has recently been suggested to feature higher Landau level analogs. We show that at negative unit flux per unit cell, the bands exhibit remarkable similarity to a backfolded parabolic dispersion, even though the adiabatic approximation is inapplicable. This backfolded parabolic dispersion naturally explains the similarity of the Chern bands at zero applied flux to the two lowest Landau levels, offering a simple picture supporting the emergence of non-Abelian states in twisted bilayer MoTe$_2$. We propose the study of magnetic field dependent band structures as a versatile method to investigate the nature of topological bands and identify Landau level analogs.

cond-mat.mes-hall↗

arXiv2023

The electrostatic fate of $N$-layer moiré graphene

Twisted $N$-layer graphene (TNG) moiré structures have recently been shown to exhibit robust superconductivity similar to twisted bilayer graphene (TBG). In particular for $N=4$ and $N=5$, the phase diagram features a superconducting pocket that extends beyond the nominal full filling of the flat band. These observations are seemingly at odds with the canonical understanding of the low-energy theory of TNG, wherein the TNG Hamiltonian consists of one flat-band sector and accompanying dispersive bands. Using a self-consistent Hartee-Fock treatment, we explain how the phenomenology of TNG can be understood through an interplay of in-plane Hartree and inhomogeneous layer potentials, which cause a reshuffling of electronic bands. We extend our understanding beyond the case of N = 5 realized in experiment so far. We decribe how the Hartree and layer potentials control the phase diagram for devices with N $>$ 5 and tend to preclude exchange-driven correlated phenomena in this limit. To circumvent these electrostatic constraints, we propose a new flat-band paradigm that could be realized in large-N devices by taking advantage of two nearly flat sectors acting together to enhance the importance of exchange effects.

cond-mat.mes-hall↗

arXiv2023

Strain Disorder and Gapless Intervalley Coherent Phase in Twisted Bilayer Graphene

Correlated insulators are frequently observed in magic angle twisted bilayer graphene at even fillings of electrons or holes per moiré unit-cell. Whereas theory predicts these insulators to be intervalley coherent excitonic phases, the measured gaps are routinely much smaller than theoretical estimates. We explore the effects of random strain variations on the intervalley coherent phase, which have a pair-breaking effect analogous to magnetic disorder in superconductors. We find that the spectral gap may be strongly suppressed by strain disorder, or vanish altogether, even as intervalley coherence is maintained. We discuss predicted features of the tunneling density of states, show that the activation gap measured in transport experiments corresponds to the diminished gap, and thus offer a solution for the apparent discrepancy between the theoretical and experimental gaps.

cond-mat.mes-hall↗

arXiv2022

Anderson's theorem for correlated insulating states in twisted bilayer graphene

The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under $\mathcal{PT}$, where $\mathcal{P}$ and $\mathcal{T}$ denote particle-hole conjugation and time reversal, respectively. In contrast, $\mathcal{PT}$-even perturbations will in general induce subgap states and reduce or even eliminate the gap. We use this result to classify the stability of the K-IVC state against various experimentally relevant perturbations. The existence of an Anderson theorem singles out the K-IVC state from other possible insulating ground states.

cond-mat.mes-hall↗