arXiv subjects

Tobias Holder

Publications and source records attributed to Tobias Holder.

At least 19 recordsLinked to original sources

arXiv2026

Theory of two-dimensional Wigner crystals with defects: Interactions, melting transitions and collective modes

The physics of Wigner solids is characterized by an interplay of elasticity and long-range electrostatics, endowing crystal defects with properties distinct from those in charge-neutral crystals. Recent experiments observing lattice melting and Wigner-crystal-adjacent phases in two dimensions necessitate an examination of how defects affect the long-wavelength properties of such solids. Here, we use duality techniques to construct a comprehensive framework for studying the contribution of vacancies and interstitials, dislocations, and disclinations to the effective action of two-dimensional charged crystals. This allows for a systematic investigation of the interaction energies for the different combinations of defect pairs. We further study melting transitions due to defect proliferation, assessing and justifying some of the assumptions present in the literature. In the metallic Wigner crystal phase, characterized by a finite ground state density of vacancies, we find phonons with a dispersion relation that varies in an unusual way with the vacancy density. Consequently, we discuss how thermodynamic properties of such a vacancy Fermi liquid can be probed in measurements of the melting temperature and speed of sound. The field theory developed here can serve as a starting point in the study of anomalous Hall crystals and charge density waves with defects.

cond-mat.str-el↗

arXiv2026

Quantum Critical Dynamics Induced by Topological Zero Modes

We investigate the low-frequency ac transport in the Su-Schrieffer-Heeger (SSH) chain with chiral disorder near the topological delocalization transition. Our key finding is that the formation of hybridized pairs of topological domain wall zero modes leads to the anomalous logarithmic scaling of the ac conductivity $σ(ω) \sim \log ω$ at criticality, and $σ(ω) \sim ω^{2 δ} \log ^2 ω$ away from it. Using the combination of real-space renormalization group analysis and qualitative hybridization arguments, we demonstrate that the form of the scaling of ac conductivity at criticality stems directly from the stretched-exponential ($ψ(x) \sim e^{-s \sqrt{x}}~\,$) spatial decay of zero-mode wavefunctions at the critical point.

cond-mat.mes-hall↗

arXiv2026

Quantum Geometry and the Hidden Scales in Materials

Electronic properties of quantum materials solids are often well understood via the low energy dispersion of Bloch bands, motivating single band approximations in many metals and semiconductors. However, a closer look reveals length and time scales introduced by quantum dipole fluctuations due to interband mixing, which are reflected in the momentum space textures of the electronic wavefunctions. This structure is usually referred to as quantum geometry. These new scales not only qualitatively modify the linear and nonlinear responses of a material but can also have a vital role in determining the many-body ground state at low temperatures. In this Perspective, we explore how quantum geometry impacts properties of materials and outline recent experimental advances that have begun to explore quantum geometric effects in various condensed matter platforms. We discuss the separation of scales that can allow us to estimate the significance of quantum geometry in various response functions.

cond-mat.mtrl-sci↗

arXiv2026

Miniband Generation by Surface Acoustic Waves

We introduce a new class of tunable periodic structures, formed by launching two obliquely propagating surface acoustic waves on a piezoelectric substrate that supports a two-dimensional quantum material. The resulting acoustoelectric superlattice exhibits two salient features. First, its periodicity is widely tunable, spanning a length scale intermediate between moiré superlattices and optical lattices, enabling the formation of narrow, topologically nontrivial energy bands. Second, unlike moiré systems, where the superlattice amplitude is set by intrinsic interlayer tunneling and lattice relaxation, the amplitude of the acoustoelectric potential is externally tunable via the surface acoustic wave power. Using massive monolayer graphene as an example, we demonstrate that varying the frequencies and power of the surface acoustic waves enables in-situ control over the band structure of the 2D material, generating flat bands and nontrivial valley Chern numbers, featuring a highly localized Berry curvature.

cond-mat.mes-hall↗

arXiv2025

Functional approach to superfluid stiffness: Role of quantum geometry in unconventional superconductivity

Nontrivial quantum geometry of electronic bands has been argued to facilitate superconductivity even for the case of flat dispersions where the conventional contribution to the superfluid weight is suppressed by the large effective mass. However, most previous work focused on the case of conventional superconductivity while many contemporary superconducting quantum materials are expected to host unconventional pairing. Here, we derive a generalized expression for the superfluid weight employing mean-field BCS theory for systems with time-reversal symmetry in the normal state and arbitrary unconventional superconducting order with zero-momentum intraband pairing. Our derivation reveals the necessity of incorporating functional derivatives of the grand potential with respect to the superconducting gap function. Through perturbative analysis in the isolated narrow-bands limit, we demonstrate that this contribution arises from quantum geometrical effects, specifically due to a nontrivial Wilczek-Zee connection. Utilizing the newly obtained expressions for the superfluid weight, we apply our framework to an extended Kane-Mele model, contrasting conventional $s$-wave superconductivity with chiral $d$-wave superconductivity.

cond-mat.supr-con↗

arXiv2025

Superdielectrics: Disorder-induced perfect screening in insulators

We study the relationship between the quantities that encode the insulating properties of matter: the ground-state quantum metric, the average localization length, and the electric susceptibility. By examining the one-dimensional Anderson insulator model and the Su-Schrieffer-Heeger chain with chiral disorder, we demonstrate that the former two measures are proportional in one-dimensional systems near criticality, and both are determined by the properties of the hybridized localized states around the Fermi energy. We employ these insights to demonstrate that the behavior of the electric susceptibility is drastically different in the bond-disordered SSH chain, with the possibility that it may diverge even when the localization length and the quantum metric remain finite. This divergence, caused by the proliferation of impurity resonances at a particular energy, leads to a novel regime that exhibits mixed characteristics of metals and insulators. We term this regime superdielectric: an insulating state characterized by a finite quantum metric and divergent static electric susceptibility, which implies perfect screening in the absence of the dc conductivity. We demonstrate that the superdielectric phase also emerges in higher-dimensional materials, such as graphene with vacancies and Kekulé bond distortion.

cond-mat.mes-hall↗

arXiv2025

Visualizing isospin magnetic texture and intervalley exchange interaction in rhombohedral tetralayer graphene

The tunable band structure and nontrivial topology of multilayer rhombohedral graphene lead to a variety of correlated electronic states with isospin orders-meaning ordered states in the combined spin and valley degrees of freedom-dictated by the interplay of spin-orbit coupling and Hunds exchange interactions. However, methods for mapping local isospin textures and determining the exchange energies are currently lacking. Here, we image the magnetization textures in tetralayer rhombohedral graphene using a nanoscale superconducting quantum interference device. We observe sharp magnetic phase transitions that indicate spontaneous time-reversal symmetry breaking. In the quarter-metal phase, the spin and orbital moments align closely, providing a bound on the spin-orbit coupling energy. We also show that the half-metal phase has a very small magnetic anisotropy, which provides an experimental lower bound on the intervalley Hunds exchange interaction energy. This is found to be close to its theoretical upper bound. The ability to resolve the local isospin texture and the different interaction energies will allow a better understanding of the phase transition hierarchy and the numerous correlated electronic states arising from spontaneous and induced isospin symmetry breaking in graphene heterostructures.

cond-mat.mes-hall↗

arXiv2025

Revealing Quantum Geometry in Nonlinear Quantum Materials

Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the relatively few effects which have been documented for them. This review gives a modern perspective how quantum geometric quantities naturally enter the nonlinear responses of quantum materials and demonstrate their deep connection with excitation energy, lifetimes, symmetry, and corresponding physical processes. The multitude of nonlinear responses can be subdivided into nonlinear optical effects, subgap responses, and nonlinear transport phenomena. Such a distinction by energy scales facilitates an intuitive understanding of the underlying electronic transitions, giving rise to a unified picture of the electron motion beyond linear order. The well-known injection and shift currents constitute the main resonances in the optical regime. Exploiting their respective lifetime and symmetry dependencies, this review elucidates how these resonances can be distinguished by a corresponding quantum geometric quantity that shares the same symmetry. This is followed by a brief exposition of the role of quasiparticle lifetimes for nonlinear subgap responses, which presents a window into the microscopic short-term dynamics as well as the ground state correlation and localization. We conclude with an account of the anomalous motion due to the Berry curvature dipole and quantum metric dipole in nonlinear transport, clarifying the correspondence between physical observables and the underlying mechanisms. This review highlights the close relationship between quantum geometry and nonlinear response, showing the way towards promising probes of quantum geometry and enabling novel avenues to characterize complex materials.

cond-mat.mes-hall↗

arXiv2025

Transverse voltage in anisotropic hydrodynamic conductors

Weak momentum dissipation in ultra-clean metals gives rise to novel non-Ohmic current flow, including ballistic and hydrodynamic regimes. Recently, hydrodynamic flow has attracted intense interest because it presents a valuable window into the electronic correlations and the longest lived collective modes of quantum materials. However, diagnosing viscous flow is difficult as the macroscopic observables of ballistic and hydrodynamic transport such as the average current distribution can be deceptively similar, even if their respective microscopics deviate notably. Based on kinetic Boltzmann theory, here we propose to address this issue via the transverse channel voltage at zero magnetic field, which can efficiently detect hydrodynamic flow in a number of materials. To this end, we show that the transverse voltage is sensitive to the interplay between anisotropic fermiology and boundary scattering, resulting in a non-trivial behavior in narrow channels along crystalline low-symmetry directions. We discuss several materials where the channel-size dependent stress of the quantum fluid leads to a characteristic sign change of the transverse voltage as a new hallmark of the cross-over from the ballistic to the hydrodynamic regime.

cond-mat.mes-hall↗

arXiv2025

Drude weight of an interacting flat-band metal

Flatband systems form a new class of materials that challenge the conventional wisdom of transport. The intrinsically strong electronic correlations combined with the vanishing kinetic energy scale suggest a sensitive dependence of transport properties on the flat band states and make interacting flat bands promising candidates for exotic quantum transport. Utilizing the Drude weight, we investigate the low-frequency spectral properties of the electrical conductivity within a controlled analytic treatment of the many-body response at temperatures above the bandwidth and the interaction strength and below the bandgap. Focusing on this new transport regime, we demonstrate the potential of a quantum geometric approach for interacting systems and intermediate temperatures. The derived spectral weight yields unexplored four-point geometric contributions unrelated to the quantum metric, which questions the previously proposed projection methods. For long-ranged interactions, we show that the low-frequency spectral weight reduces to the variance of the Berry curvature.

cond-mat.str-el↗

arXiv2024

Competing Orbital Magnetism and Superconductivity in electrostatically defined Josephson Junctions of Alternating Twisted Trilayer Graphene

The coexistence of superconductivity and magnetism within a single material system represents a long-standing goal in condensed matter physics. Van der Waals-based moiré superlattices provide an exceptional platform for exploring competing and coexisting broken symmetry states. Alternating twisted trilayer graphene (TTG) exhibits robust superconductivity at the magic angle of 1.57° and 1.3°, with suppression at intermediate twist angles. In this study, we investigate the intermediate regime and uncover evidence of orbital magnetism. As previously reported, superconductivity is suppressed near the charge neutrality point (CNP) and emerges at larger moiré fillings. Conversely, we find orbital magnetism most substantial near the CNP, diminishing as superconductivity develops. This complementary behavior is similarly observed in the displacement field phase space, highlighting a competitive interplay between the two phases. Utilizing gate-defined Josephson junctions, we probe orbital magnetism by electrostatically tuning the weak links into the magnetic phase, revealing an asymmetric Fraunhofer interference pattern. The estimated orbital ferromagnetic ordering temperature is approximately half the superconducting critical temperature, coinciding with the onset of Fraunhofer asymmetry. Our findings suggest that the observed orbital magnetism is driven by valley polarization and is distinct from the anomalous Hall effect reported at integer fillings in twisted graphene systems. These results offer insights into the interplay between superconductivity and magnetism in moiré superlattices.

cond-mat.str-el↗

arXiv2024

Pressure tuning of intrinsic and extrinsic sources to the anomalous Hall effect in CrGeTe$_3$

The integrated Berry curvature is a geometric property that has dramatic implications for material properties. This study investigates the integrated Berry curvature and other contributions to the anomalous Hall effect in CrGeTe$_3$ as a function of pressure. The anomalous Hall effect is absent in the insulating phase of CrGeTe$_3$ and evolves with pressure in a dome-like fashion as pressure is applied. The dome's edges are characterized by Fermi surface deformations, manifested as mixed electron and hole transport. We corroborate the presence of bipolar transport by ab-initio calculations which also predict a nonmonotonic behavior of the Berry curvature as a function of pressure. Quantitative discrepancies between our calculations and experimental results indicate that additional scattering mechanisms, which are also strongly tuned by pressure, contribute to the anomalous Hall effect in CrGeTe$_3$.

cond-mat.str-el↗

arXiv2024

Shift and Polarization of Excitons from Quantum Geometry

Despite a long history, certain aspects of excitons - the bound inter-band states which form when a valence band hole and a conduction band electron pair - have remained relatively unexplored. This holds particularly true for the wavefunction of an exciton, for which few properties have been explored theoretically in various limiting cases. An intuitive language robustly characterizing the topology of bound electron-hole states is lacking, but needed in order to address the global features of the charge distribution of the excitonic state, to properly understand their transport theory, and to supplement the numerical investigation of excitons in ab-initio approaches. Here, we address these gaps by developing a comprehensive framework for the quantum geometry and topology of two-dimensional exciton states in terms of the exact connections which describe the interaction-renormalized exciton bundle in a periodic lattice. Based on this description, we derive two gauge-invariant quantities, which we identify as the exciton shift vector and the exciton dipole vector. Using the shift vector, we elucidate the topology of exciton bands compared to the topology of the parent electronic band structure, pinpointing precisely how interactions can introduce nontrivial topology to the exciton bands beyond the topology which is contained in the single-particle bands. We further elucidate how shift and polarizations enter into the semiclassical equations of motion for the exciton center of mass coordinates.

cond-mat.mes-hall↗

arXiv2024

Incommensurate inter-valley coherent states in ABC graphene: collective modes and superconductivity

Recent experiments in ABC trilayer graphene detected superconductivity on the border of a phase transition to a symmetry-broken phase. In this work, we use unrestricted Hartree-Fock to study the nature of this phase. We find a close competition between two incommensurate inter-valley coherent (IVC) phases: an IVC crystal where the ordering occurs at multiple wavevectors, and an IVC spiral with a single ordering wavevector. Focusing on one of the regimes where superconductivity is observed experimentally, we find a continuous (or very weakly first order) transition between a half metallic phase to an IVC crystal, followed by a first-order transition into an IVC spiral. Using time-dependent Hartree-Fock, we study the collective mode spectrum in the half-metalic phase. We find a soft inter-valley mode that can mediate superconductivity in a narrow sliver of density near the continuous transition, with a Tc that can reach a few hundreds of mK and a sign-changing s-wave order parameter. The spin stiffness in the half metal phase is found to be surprisingly low, of the order of a few degrees Kelvin.

cond-mat.str-el↗

arXiv2024

The quantum geometric origin of capacitance in insulators

In band insulators, where the Fermi surface is absent, adiabatic transport is allowed only due to the geometry of the Hilbert space. By driving the system at a small but finite frequency $ω$, transport is still expected to depend sensitively on the quantum geometry. Here we show that this expectation is correct and can be made precise by expressing the Kubo formula for conductivity as the variation of the \emph{time-dependent polarization} with respect to the applied field. In particular, a little appreciated effect is that at linear order in frequency, the longitudinal conductivity results from an intrinsic capacitance, determined by the ratio of the quantum metric and the spectral gap. We demonstrate that this intrinsic capacitance has a measurable effect in a wide range of insulators with non-negligible metric, including the electron gas in a quantizing magnetic field, the gapped bands of hBN-aligned twisted bilayer graphene, and obstructed atomic insulators such as diamond whose large refractive index has a topological origin. We also discuss the influence of quantum geometry on the dielectric constant.

cond-mat.mes-hall↗

arXiv2024

Connecting cooperative transport by ants with the physics of self-propelled particles

Paratrechina longicornis ants are known for their ability to cooperatively transport large food items. Previous studies have focused on the behavioral rules of individual ants and explained the efficient coordination using the coupled-carrier model. In contrast to this microscopic description, we instead treat the transported object as a single self-propelled particle characterized by its velocity magnitude and angle. We experimentally observe P. longicornis ants cooperatively transporting loads of varying radii. By analyzing the statistical features of the load's movement, we show that its salient properties are well captured by a set of Langevin equations describing a self-propelled particle. We relate the parameters of our macroscopic model to microscopic properties of the system. While the autocorrelation time of the velocity direction increases with group size, the autocorrelation time of the speed has a maximum at an intermediate group size. This corresponds to the critical slowdown close to the phase transition identified in the coupled-carrier model. Our findings illustrate that a self-propelled particle model can effectively characterize a system of interacting individuals.

physics.bio-ph↗

arXiv2023

Intervalley coherence and intrinsic spin-orbit coupling in rhombohedral trilayer graphene

Rhombohedral graphene multilayers provide a clean and highly reproducible platform to explore the emergence of superconductivity and magnetism in a strongly interacting electron system. Here, we use electronic compressibility and local magnetometry to explore the phase diagram of this material class in unprecedented detail. We focus on rhombohedral trilayer in the quarter metal regime, where the electronic ground state is characterized by the occupation of a single spin and valley isospin flavor. Our measurements reveal a subtle competition between valley imbalanced (VI) orbital ferromagnets and intervalley coherent (IVC) states in which electron wave functions in the two momentum space valleys develop a macroscopically coherent relative phase. Contrasting the in-plane spin susceptibility of the IVC and VI phases reveals the influence of graphene's intrinsic spin-orbit coupling, which drives the emergence of a distinct correlated phase with hybrid VI and IVC character. Spin-orbit also suppresses the in-plane magnetic susceptibility of the VI phase, which allows us to extract the spin-orbit coupling strength of $λ\approx 50μ$eV for our hexagonal boron nitride-encapsulated graphene system. We discuss the implications of finite spin-orbit coupling on the spin-triplet superconductors observed in both rhombohedral and twisted graphene multilayers.

cond-mat.mes-hall↗

arXiv2023

Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall effect (NLAHE) and nonreciprocal magnetoresistance (NMR, longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a NLAHE and NMR in films of the doped antiferromagentic topological insulator MnBi$_2$Te$_4$. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.

cond-mat.mes-hall↗