arXiv subjects

Tobias Holder

Publications and source records attributed to Tobias Holder.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantum metric-induced nonlinear transport in a topological antiferromagnet

The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor which characterizes the topology of quantum states. The former is known to generate a zoo of important discoveries such as quantum Hall effect and anomalous Hall effect (AHE), while the consequences of the quantum metric have rarely been probed by transport. In this work, we observed quantum metric induced nonlinear transport, including both nonlinear AHE and diode-like nonreciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi$_2$Te$_4$. Our observation reveals that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature, and are insensitive to disorder scattering, thus verifying their origin in the band structure topology. They also flip signs between electron and hole-doped regions, in agreement with theoretical calculations. Our work provides a pathway to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.

cond-mat.mes-hall↗

arXiv2023

Para-hydrodynamics from weak surface scattering in ultraclean thin flakes

Electron hydrodynamics typically emerges in electron fluids with a high electron-electron collision rate. However, new experiments with thin flakes of WTe$_2$ have revealed that other momentum-conserving scattering processes can replace the role of the electron-electron interaction, thereby leading to a novel, so-called para-hydrodynamic regime. Here, we develop the kinetic theory for para-hydrodynamic transport. To this end, we consider a ballistic electron gas in a thin 3-dimensional sheet where the momentum-relaxing ($\ell_{mr}$) and momentum-conserving ($\ell_{mc}$) mean free paths are decreased due to boundary scattering from a rough surface. The resulting effective mean free path of the electronic flow is then expressed in terms of microscopic parameters of the sheet boundaries, predicting that a para-hydrodynamic regime with $\ell_{mr}\gg \ell_{mc}$ emerges generically in ultraclean three-dimensional materials. Using our approach, we recover the transport properties of WTe$_2$ in the para-hydrodynamic regime in good agreement with existing experiments.

cond-mat.mes-hall↗

arXiv2023

Direct Observation of Collective Modes of the Charge Density Wave in the Kagome Metal CsV$_3$Sb$_5$

A new group of kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this parent charge order phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations - the collective modes - have not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV$_3$Sb$_5$ and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab-initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for better understanding of the unconventional phases hosted on the kagome lattice.

cond-mat.str-el↗

arXiv2022

Unifying semiclassics and quantum perturbation theory at nonlinear order

Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo's formula for resonances at finite frequency. However, a precise connection between both approaches has not been established. Focusing on the second order nonlinear response, here we show how the semiclassical limit can be recovered from perturbation theory in the velocity gauge, provided that finite quasiparticle lifetimes are taken into account. We find that matrix elements related to the band geometry combine in this limit to produce the semiclassical nonlinear conductivity. We demonstrate the power of the new formalism by deriving a quantum contribution to the nonlinear conductivity which is of order $τ^{-1}$ in the relaxation time $τ$, which is principally inaccessible within the Boltzmann approach. We outline which steps can be generalized to higher orders in the applied perturbation, and comment about potential experimental signatures of our results.

cond-mat.mes-hall↗

arXiv2022

Multilayer graphenes as a platform for interaction-driven physics and topological superconductivity

Motivated by the recent discoveries of superconductivity in bilayer and trilayer graphene, we theoretically investigate superconductivity and other interaction-driven phases in multilayer graphene stacks. To this end, we study the density of states of multilayer graphene with up to four layers at the single-particle band structure level in the presence of a transverse electric field. Among the considered structures, tetralayer graphene with rhombohedral (ABCA) stacking reaches the highest density of states. We study the phases that can arise in ABCA graphene by tuning the carrier density and transverse electric field. For a broad region of the tuning parameters, the presence of strong Coulomb repulsion leads to a spontaneous spin and valley symmetry breaking via Stoner transitions. Using a model that incorporates the spontaneous spin and valley polarization, we explore the Kohn-Luttinger mechanism for superconductivity driven by repulsive Coulomb interactions. We find that the strongest superconducting instability is in the $p-$wave channel, and occurs in proximity to the onset of Stoner transitions. Interestingly, we find a range of densities and transverse electric fields where superconductivity develops out of a strongly corrugated, singly-connected Fermi surface in each valley, leading to a topologically non-trivial chiral $p+ip$ superconducting state with an even number of co-propagating chiral Majorana edge modes. Our work establishes ABCA stacked tetralayer graphene as a promising platform for observing strongly correlated physics and topological superconductivity.

cond-mat.supr-con↗

arXiv2022

General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity and other insulators (with zero Chern number) present zero Hall conductance in the linear response regime. Here, we find that a general magnetic insulator possesses a nonlinear Hall conductivity quadratic to the electric field if the system breaks inversion symmetry. This conductivity originates from an induced orbital magnetization due to virtual interband transitions. We identify three contributions to the wavepacket motion, a velocity shift, a positional shift, and a Berry curvature renormalization. In contrast to the crystalline solid, we find that this nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas, indicating a fundamental difference between the QAHE and the Integer quantum Hall effect.

cond-mat.mes-hall↗

arXiv2022

Twisted photovoltaics at terahertz frequencies from momentum shift current

The bulk photovoltaic effect (BPVE) converts light into a coherent dc current at zero bias, through what is commonly known as the shift current. This current has previously been attributed to the displacement of the electronic wave function center in real space, when the sample is excited by light. We reveal that materials like twisted bilayer graphene (TBG) with a flatband dispersion are uniquely suited to maximize the BPVE because they lead to an enhanced shift in the momentum space, unlike any previously known shift current mechanism. We identify properties of quantum geometry, which go beyond the quantum geometric tensor, and are unrelated to Berry charges, as the physical origin of the large BPVE we observe in TBG. Our calculations show that TBG with a band gap of several meV exhibits a giant BPVE in a range of 0.2-1 THz, which represents the strongest BPVE reported so far at this frequency in a two-dimensional material and partially persists even a room temperature. Our paper provides a design principle for shift current generation, which applies to a broad range of twisted heterostructures with the potential to overcome the so-called "terahertz gap" in THz sensing.

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arXiv2022

Bound on resistivity in flat-band materials due to the quantum metric

The quantum metric is a central quantity of band theory but has so far not been related to many response coefficients due to its nonclassical origin. However, within a newly developed Kubo formalism for fast relaxation, the decomposition of the dc electrical conductivity into both classical (intraband) and quantum (interband) contributions recently revealed that the interband part is proportional to the quantum metric. Here, we show that interband effects due to the quantum metric can be significantly enhanced and even dominate the conductivity for semimetals at charge neutrality and for systems with highly quenched bandwidth. This is true in particular for topological flat-band materials of nonzero Chern number, where for intermediate relaxation rates an upper bound exists for the resistivity due to the common geometrical origin of quantum metric and Berry curvature. We suggest to search for these effects in highly tunable rhombohedral trilayer graphene flakes.

cond-mat.mes-hall↗

arXiv2022

Proposal for realizing anomalous Floquet insulators via Chern band annihilation

Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI). The AFAI features a quasi-energy spectrum with chiral edge modes and a fully localized bulk, leading to non-adiabatic but quantized charge pumping. Here, we show how such a Floquet phase can be realized in a driven, disordered Quantum Anomalous Hall insulator, which is assumed to have two critical energies where the localization length diverges, carrying states with opposite Chern numbers. Driving the system at a frequency close to resonance between these two energies localizes the critical states and annihilates the Chern bands, giving rise to an AFAI phase. We exemplify this principle by studying a model for a driven, magnetically doped topological insulator film, where the annihilation of the Chern bands and the formation of the AFAI phase is demonstrated using the rotating wave approximation. This is complemented by a scaling analysis of the localization length for two copies of a quantum Hall network model with a tunable coupling between them. We find that by tuning the frequency of the driving close to resonance, the driving strength required to stabilize the AFAI phase can be made arbitrarily small.

cond-mat.str-el↗

arXiv2022

Direct observation of vortices in an electron fluid

Vortices are the hallmarks of hydrodynamic flow. Recent studies indicate that strongly-interacting electrons in ultrapure conductors can display signatures of hydrodynamic behavior including negative nonlocal resistance, Poiseuille flow in narrow channels, and a violation of the Wiedemann-Franz law. Here we provide the first visualization of whirlpools in an electron fluid. By utilizing a nanoscale scanning superconducting quantum interference device on a tip (SQUID-on-tip) we image the current distribution in a circular chamber connected through a small aperture to an adjacent narrow current carrying strip in high-purity type-II Weyl semimetal WTe2. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that the vortices are present only for small apertures, whereas the flow is laminar (non-vortical) for larger apertures, consistent with the theoretical analysis of the hydrodynamic regime and in contrast to the expectations of ballistic transport in WTe2 at low temperatures. Moreover, near the vortical-to-laminar transition, we observe a single vortex in the chamber splitting into two vortices, a behavior that can occur only in the hydrodynamic regime and cannot be sustained by ballistic transport. These findings suggest a novel mechanism of hydrodynamic flow: instead of the commonly considered electron-electron scattering at the bulk, which becomes extremely weak at low temperatures, the spatial diffusion of charge carriers' momenta is enabled by small-angle scattering at the planar surfaces of thin pure crystals. This surface-induced para-hydrodynamics opens new avenues for exploring and utilizing electron fluidics in high-mobility electron systems.

cond-mat.mes-hall↗

arXiv2021

Truly local topological dynamics of driven defects in Chern insulator

Robust zero modes supported by defects is one of the key features of topological matter. Its presence renders a system topologically inhomegeneuous, thus having no well-defined global topological invariant. The quantities labeling different areas of the sample according to their topological state were dubbed local topological markers. Here we study their dynamics and the possibility to control their distribution over the sample. We suggest a new perspective on the evolution of local markers. It gives a clear physical description of the markers evolution in terms of response functions and the ease of measurement. Furthermore, new markers' equations of motion are truly local, being ensured that the current of the marker exists and obeys the lattice continuity equation. The formalism presented does not rely on the single-particle quantities therefore might be extended to interacting systems.

cond-mat.stat-mech↗

arXiv2021

Unconventional superconductivity in systems with annular Fermi surfaces: Application to rhombohedral trilayer graphene

We show that in a two-dimensional electron gas with an annular Fermi surface, long-range Coulomb interactions can lead to unconventional superconductivity by the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the inner and outer Fermi surfaces are close to each other. The most prevalent state has chiral $p$-wave symmetry, but $d$-wave and extended $s$-wave pairing are also possible. We discuss these results in the context of rhombohedral trilayer graphene, where superconductivity was recently discovered in regimes where the normal state has an annular Fermi surface. Using realistic parameters, our mechanism can account for the order of magnitude of $T_c$, as well as its trends as a function of electron density and perpendicular displacement field. Moreover, it naturally explains some of the outstanding puzzles in this material, that include the weak temperature dependence of the resistivity above $T_c$, and the proximity of spin singlet superconductivity to the ferromagnetic phase.

cond-mat.supr-con↗

arXiv2021

Mixed axial-gravitational anomaly from emergent curved spacetime in nonlinear charge transport

In 3+1 dimensional spacetime, two vector gauge anomalies are known: The chiral anomaly and the mixed axial-gravitational anomaly. While the former is well documented and tied to the presence of a magnetic field, the latter instead requires a nonzero spacetime curvature, which has made it rather difficult to study. In this work, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that can be either longitudinal or transverse to electric field. Consequently, the continuity equation for the chiral current is not conserved at order $τ^{-1}$, where $τ$ is the quasiparticle relaxation time. We can identify the anomaly as a mixed axial-gravitational one, and predict a material in which the anomaly-induced current can be isolated in a purely electrical measurement. Our findings indicate that charge transport generically derives from quasiparticle motion in an emergent curved spacetime, with potentially far-reaching consequences for all types of response functions.

cond-mat.mes-hall↗

arXiv2021

Electrons flow like falling cats: Deformations and emergent gravity in quantum transport

The effective low-energy excitations in a metallic or semimetallic crystalline system (i.e. electronic quasiparticles) always have a finite spatial extent. It is self-evident but virtually unexplored how the associated internal degrees of freedom manifest themselves in the quasiparticle response. Here, we investigate this question by illuminating an intimate connection between the theory of nonlinear response and the equations of motion of classical deformable bodies. This connection establishes that nth-order response in an external perturbation corresponds to nth-order derivatives of the quasiparticle motion, where the resulting motion is anomalous at every order due to the internal degrees of freedom. This new point of view predicts that quasiparticles necessarily move in an emergent curved spacetime, even in a homogeneous and defectless lattice. We underscore these concepts using recent results on the second order electrical conductivity, elucidating the associated anomalous acceleration that the quasiparticle exhibits. Based on our observations, we predict the existence of an infinite series of anomalous components of the quasiparticle motion, and propose a new mapping between response theory in flat space and a gravitational theory for the center-of-mass coordinate.

cond-mat.mes-hall↗

arXiv2021

Specific Heat of a Quantum Critical Metal

We investigate the specific heat, $c$, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where $c/T$ is close to the value expected from the non-interacting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of $c/T$, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of $c/T$ onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.

cond-mat.str-el↗

arXiv2021

Half and quarter metals in rhombohedral trilayer graphene

Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moiré heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions marked by negative electronic compressibility. The transitions define the boundaries between phases where quantum oscillations have either four-fold, two-fold, or one-fold degeneracy, associated with a spin and valley degenerate normal metal, spin-polarized `half-metal', and spin and valley polarized `quarter metal', respectively. For electron doping, the salient features are well captured by a phenomenological Stoner model with a valley-anisotropic Hund's coupling, likely arising from interactions at the lattice scale. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, by rotational alignment of a hexagonal boron nitride substrate to induce a moiré superlattice, we find that the superlattice perturbs the preexisting isospin order only weakly, leaving the basic phase diagram intact while catalyzing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter metal states occur at half- or quarter superlattice band filling. Our results show that rhombohedral trilayer graphene is an ideal platform for well-controlled tests of many-body theory and reveal magnetism in moiré materials to be fundamentally itinerant in nature.

cond-mat.mes-hall↗

arXiv2021

Chirality induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of the current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle and reaches about 20\% for an angle of 1.5$^\circ$ in a 10 T in-plane magnetic field. We propose the band structure topology (asymmetry), which leads to a direction-sensitive mean free path, as a useful way to anticipate the UMR effect. The UMR provides a probe for chirality and band flatness in the twisted bilayers.

cond-mat.mes-hall↗

arXiv2020

Long-range nontopological edge currents in charge-neutral graphene

Van der Waals heterostructures display a rich variety of unique electronic properties. To identify novel transport mechanisms, nonlocal measurements have been widely used, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers. This approach was employed in search of dissipationless spin and valley transport, topological charge-neutral currents, hydrodynamic flows and helical edge modes. Monolayer, bilayer, and few-layer graphene, transition-metal dichalcogenides, and moire superlattices were found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated. Graphene, in particular, exhibits giant nonlocality at charge neutrality, a prominent behavior that attracted competing explanations. Utilizing superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging, we demonstrate that the commonly-occurring charge accumulation at graphene edges leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, while the edge conductance has little impact on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality both at charge neutrality and away from it produces exotic flow patterns in which charges can flow against the global electric field. We have visualized surprisingly intricate patterns of nonlocal currents, which are sensitive to edge disorder. The observed one-dimensional edge transport, being generic and nontopological, is expected to support nonlocal transport in many electronic systems, offering insight into numerous controversies in the literature and linking them to long-range guided electronic states at system edges.

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