arXiv subjects

Thomas Scaffidi

Publications and source records attributed to Thomas Scaffidi.

At least 37 records · Page 2Linked to original sources

arXiv2023

Hydrodynamic electronic transport

The ``flow'' of electric currents and heat in standard metals is diffusive with electronic motion randomized by impurities. However, for ultraclean metals, electrons can flow like water with their flow being described by the equations of hydrodynamics. While theoretically postulated, this situation was highly elusive for decades. In the last decade, several experimental groups have found strong indications for this type of flow, especially in graphene-based devices. In this review, we give an overview of some of the recent key developments, both on the theoretical and experimental side.

cond-mat.str-el↗

arXiv2023

Degeneracy between even- and odd-parity superconductivity in the quasi-1D Hubbard model and implications for Sr2RuO4

Based on a weak coupling calculation, we show that an accidental degeneracy appears between even- and odd-parity superconductivity in the quasi-1D limit of the repulsive Hubbard model on the square lattice. We propose that this effect could be at play on the quasi-1D orbitals Ru $d_{zx}$ and $d_{zy}$ of Sr2RuO4, leading to a gap of the form $Δ_\text{even} + i Δ_\text{odd}$ which could help reconcile several experimental results.

cond-mat.supr-con↗

arXiv2022

Spread and erase -- How electron hydrodynamics can eliminate the Landauer-Sharvin resistance

It has long been realized that even a perfectly clean electronic system harbors a Landauer-Sharvin resistance, inversely proportional to the number of its conduction channels. This resistance is usually associated with voltage drops on the system's contacts to an external circuit. Recent theories have shown that hydrodynamic effects can reduce this resistance, raising the question of the lower bound of resistance of hydrodynamic electrons. Here we show that by a proper choice of device geometry, it is possible to spread the Landauer-Sharvin resistance throughout the bulk of the system, allowing its complete elimination by electron hydrodynamics. We trace the effect to the dynamics of electrons flowing in channels that terminate within the sample. For ballistic systems this termination leads to back-reflection of the electrons and creates resistance. Hydrodynamically, the scattering of these electrons off other electrons allows them to transfer to transmitted channels and avoid the resistance. Counter-intuitively, we find that in contrast to the ohmic regime, for hydrodynamic electrons the resistance of a device with a given width can decrease with its length, suggesting that a long enough device may have an arbitrarily small total resistance.

cond-mat.mes-hall↗

arXiv2022

Terahertz Radiation from the Dyakonov-Shur Instability of Hydrodynamic Electrons in a Corbino Geometry

Hydrodynamic electrons flowing through a two-dimensional channel are predicted to undergo a plasma instability above a critical drift velocity. This Dyakonov-Shur (DS) instability terminates as a coherent nonlinear oscillator which shows promise as a source of radiation that could fill the so-called TeraHertz gap. In this work, we study radial flow in a Corbino disk, and demonstrate how the DS instability is substantially enhanced in this geometry, both in terms of a lower critical drift velocity and a higher generated power. Interestingly, hydrodynamic electron flows were recently reported in a graphene sample of this geometry, and our results are therefore directly relevant to current efforts to detect this experimentally elusive phenomenon. The analysis is based on a hydrodynamic approach and features both linearized calculations as well as full numerical simulations of the Navier-Stokes equation.

cond-mat.mes-hall↗

arXiv2022

The Superconductivity of Sr$_2$RuO$_4$ Under $c$-Axis Uniaxial Stress

Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr$_2$RuO$_4$ can be tuned through a single Van Hove singularity which results in a strong enhancement of both $T_\text{c}$ and $H_\text{c2}$. Out-of-plane ($c$ axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, causing it to approach two Van Hove singularities simultaneously. Here we achieve a record value of $3.2$ GPa compression along the $c$ axis of Sr$_2$RuO$_4$. Although the rise in $H_\text{c2}$ shows that we are indeed approaching the van Hove points, $T_\text{c}$ is suppressed, a result that contradicts expectations based on simple two-dimensional models. As a first attempt to take the third dimension into account, we present three-dimensional calculations in the weak interaction limit, and discuss the extent to which they are consistent with observation. Our experimental results highlight the importance of out-of-plane effects in low-dimensional systems in general and provide new constraints on theories of the pairing interaction in Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2021

Imaging Hydrodynamic Electrons Flowing Without Landauer-Sharvin Resistance

Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conductance limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-electron transistor imaging of electronic flow in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer-Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance - as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron-phonon scattering, we reveal the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landuer-Sharvin resistance. Finally, by imaging spiraling magneto-hydrodynamic Corbino flows, we reveal the key emergent length scale predicted by hydrodynamic theories - the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies

cond-mat.mes-hall↗

arXiv2021

From trivial to topological paramagnets: The case of $\mathbb{Z}_2$ and $\mathbb{Z}_2^3$ symmetries in two dimensions

Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and non-trivial bosonic symmetry-protected topological phases, protected by $\mathbb{Z}_2$ and $\mathbb{Z}_2^3$ symmetries, in two dimensions. In all cases, we find that the trivial and the topological phases are separated by an intermediate phase in which the protecting symmetry is spontaneously broken. Depending on the model, we identify a variety of magnetic orders on the triangular lattice, including ferromagnetism, $\sqrt{3}\times\sqrt{3}$ order, and stripe orders (both commensurate and incommensurate). Critical properties are determined through a finite-size scaling analysis. Possible scenarios regarding the nature of the phase transitions are discussed.

cond-mat.str-el↗

arXiv2021

Variational wavefunctions for Sachdev-Ye-Kitaev models

Given a class of $q$-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, like for the Sachdev-Ye-Kitaev (SYK) models. This prompts us to propose a new class of wavefunctions for SYK models inspired by the variational coupled cluster algorithm. We introduce a static ("0+0D") large-$N$ field theory to study the energy, two-point correlators, and entanglement properties of these states. Most importantly, we demonstrate a finite disorder-averaged approximation ratio of $r \approx 0.62$ between the variational and ground state energy of SYK for $q=4$. Moreover, the variational states provide an exact description of spontaneous symmetry breaking in a related two-flavor SYK model.

cond-mat.str-el↗

arXiv2021

Directional ballistic transport in the two-dimensional metal PdCoO2

In an idealized infinite crystal, the material properties are constrained by the symmetries of its unit cell. Naturally, the point-group symmetry is broken by the sample shape of any finite crystal, yet this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from anisotropic Fermi surfaces are needed. Here we show how strongly facetted Fermi surfaces and long quasiparticle mean free paths present in microstructures of PdCoO2 yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. Bar shaped transport devices narrower than the mean free path are carved from single crystals using focused ion beam (FIB) milling, such that the ballistic charge carriers at low temperatures frequently collide with both sidewalls defining a channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and transverse voltages appear in zero magnetic field. We robustly identify the channel direction as the source of symmetry breaking via ballistic Monte- Carlo simulations and numerical solution of the Boltzmann equation.

cond-mat.mes-hall↗

arXiv2021

Origin and Limit of the Recovery of Damaged Information by Time Reversal

Recently it was found that scrambled information can be partially recovered by a time-reversed evolution, even after being damaged by an intruder. We reconsider the origin of the information recovery, and argue that the presence of classical chaos does not preclude it and only leads to a quantitative reduction of the recovery ratio. We also show how decoherence (i.e. entanglement with the intruder) limits the recovery, by proving an upper bound on the recovery ratio in terms of the entangling power of the intruder's action.

quant-ph↗

arXiv2020

Does scrambling equal chaos?

Focusing on semiclassical systems, we show that the parametrically long exponential growth of out-of-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model. We derive a lower bound on the OTOC Lyapunov exponent which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e. for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.

cond-mat.stat-mech↗

arXiv2020

Ballistic and hydrodynamic magnetotransport in narrow channels

An increasing number of low carrier density materials exhibit a surprisingly large transport mean free path due to inefficient momentum relaxation. Consequently, charge transport in these systems is markedly non-ohmic but rather ballistic or hydrodynamic, features which can be explored by driving current through narrow channels. Using a kinetic equation approach we theoretically investigate how a non-quantizing magnetic field discerns ballistic and hydrodynamic transport, in particular in the spatial dependence of the transverse electric field, $E_y$: We find that $E_y$ is locally enhanced when the flow exhibits a sharp directional anisotropy in the non-equilibrium density. As a consequence, at weak magnetic fields, the curvature of $E_y$ has opposite signs in the ballistic and hydrodynamic regimes. Moreover, we find a robust signature of the onset of non-local correlations in the form of distinctive peaks of the transverse field, which are accessible by local measurements. Our results demonstrate that a purely hydrodynamic approach is insufficient in the Gurzhi regime once a magnetic field is introduced.

cond-mat.mes-hall↗

arXiv2019

Energy drag in particle-hole symmetric systems as a quantum quench

Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry -- for instance, the half-filled Hubbard model or graphene near the Dirac point -- the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analogue, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantum quench, we show that thermal drag, unlike charge drag, displays a non-Fermi's Golden Rule growth at short times due to a logarithmic scattering singularity generic to one dimension. Exploiting the integrability of the Hubbard model, we obtain the long-time limit of the quench for weak interactions. Finally, we comment on thermal drag effects in higher dimensional systems.

cond-mat.str-el↗

arXiv2019

Superconducting order of $\mathrm{Sr}_2\mathrm{RuO}_4$ from a three-dimensional microscopic model

We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate ($\mathrm{Sr}_2\mathrm{RuO}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. Nature 574, 72 (2019)]. The chiral $p$-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.

cond-mat.supr-con↗

arXiv2019

A Universal Operator Growth Hypothesis

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate $α$ in generic systems, with an extra logarithmic correction in 1d. The rate $α$ --- an experimental observable --- governs the exponential growth of operator complexity in a sense we make precise. This exponential growth even prevails beyond semiclassical or large-$N$ limits. Moreover, $α$ upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents $λ_L \leq 2 α$, which complements and improves the known universal low-temperature bound $λ_L \leq 2 πT$. We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.

cond-mat.stat-mech↗

arXiv2019

Chaos in a classical limit of the Sachdev-Ye-Kitaev model

We study chaos in a classical limit of the Sachdev-Ye-Kitaev (SYK) model obtained in a suitably defined large-S limit. The low-temperature Lyapunov exponent is found to depend linearly on temperature, with a slope that is parametrically different than in the quantum case: it is proportional to N/S. The classical dynamics can be understood as the rotation of an N-dimensional body with a random inertia tensor, corresponding to the random couplings of the SYK Hamiltonian. This allows us to find an extensive number of fixed points, corresponding to the body's principal axes of rotation. The thermodynamics is mapped to the p-spin model with p=2, which exhibits a spin glass phase at low temperature whose presence does not preclude the existence of chaos.

cond-mat.stat-mech↗

arXiv2019

Integrable and chaotic dynamics of spins coupled to an optical cavity

We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand, and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational-Gaudin type integrability and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop `dressing tails' of higher-body terms, reminiscent of the dressed local integrals of motion found in Many-Body Localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-$S$ limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in light of the limitations set by cavity dissipation.

cond-mat.stat-mech↗

arXiv2019

Visualizing Poiseuille flow of hydrodynamic electrons

Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work, we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, we image the Hall voltage of electronic flow through channels of high-mobility graphene. We find that the profile of the Hall field across the channel is a key physical quantity for distinguishing ballistic from hydrodynamic flow. We image the transition from flat, ballistic field profiles at low temperature into parabolic field profiles at elevated temperatures, which is the hallmark of Poiseuille flow. The curvature of the imaged profiles is qualitatively reproduced by Boltzmann calculations, which allow us to create a 'phase diagram' that characterizes the electron flow regimes. Our results provide long-sought, direct confirmation of Poiseuille flow in the solid state, and enable a new approach for exploring the rich physics of interacting electrons in real space.

cond-mat.mes-hall↗