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Andrew P. Mackenzie

Publications and source records attributed to Andrew P. Mackenzie.

At least 37 records · Page 2Linked to original sources
arXiv2023

Superconducting Penetration Depth Through a Van Hove Singularity: Sr$_2$RuO$_4$ Under Uniaxial Stress

In the unconventional superconductor Sr$_2$RuO$_4$, uniaxial stress along the $[100]$ direction tunes the Fermi level through a Van Hove singularity (VHS) in the density of states, causing a strong enhancement of the superconducting critical temperature $T_\textrm{c}$. Here, we report measurements of the London penetration depth $λ$ as this tuning is performed. We find that the zero-temperature superfluid density, here defined as $λ(0)^{-2}$, increases by $\sim$15%, with a peak that coincides with the peak in $T_\textrm{c}$. We also find that the low temperature form of $λ(T)$ is quadratic over the entire strain range. Using scanning tunneling microscopy, we find that the gap increases from $Δ_0 \approx 350~μ$eV in unstressed Sr$_2$RuO$_4$ to $Δ_0 \approx 600~μ$eV in a sample strained to near the peak in $T_c$. With a nodal order parameter, an increase in the superconducting gap could bring about an increase in the superfluid density through reduced sensitivity to defects and through reduced non-local effects in the Meissner screening. Our data indicate that tuning to the VHS increases the gap throughout the Brillouin zone, and that non-local effects are likely more important than reduced scattering.

cond-mat.supr-con↗
arXiv2023

On non-local electrical transport in anisotropic metals

We discuss various aspects of non-local electrical transport in anisotropic metals. For a metal with circular Fermi surface, the scattering rates entering the local conductivity and viscosity tensors are well-defined, corresponding to eigenfrequencies of the linearized collision operator. For anisotropic metals, we provide generalized formulas for these scattering rates and use a variational approximation to show how they relate to microscopic transition probabilities. We develop a simple model of a collision operator for a metal of arbitrary Fermi surface with finite number of quasi-conserved quantities, and derive expressions for the wavevector-dependent conductivity $σ(q)$ and the spatially-varying conductivity $σ(x)$ for a long, narrow channel. We apply this to the case of different rates for momentum-conserving and momentum-relaxing scattering, deriving closed-form expressions for $σ(q)$ and $σ(x)$ -- beyond generalizing from circular to arbitrary Fermi surface geometry, this represents an improvement over existing methods which solve the relevant differential equation numerically rather than in closed form. For the specific case of a diamond Fermi surface, we show that, if transport signatures were interpreted via a model for a circular Fermi surface, the diagnosis of the underlying transport regime would differ based on experimental orientation and based on whether $σ(q)$ or $σ(x)$ was considered. Finally, we discuss the bulk conductivity. While the common lore is that ``momentum''-conserving scattering does not affect bulk resistivity, we show that \textit{crystal momentum}-conserving scattering -- such as normal electron-electron scattering -- can affect the bulk resistivity for an anisotropic Fermi surface. We derive a simple formula for this contribution.

cond-mat.mes-hall↗
arXiv2023

Constraints on the superconducting state of Sr$_2$RuO$_4$ from elastocaloric measurements

Strontium ruthenate Sr$_2$RuO$_4$ is an unconventional superconductor whose pairing symmetry has not been fully clarified, despite more than two decades of intensive research. Recent NMR Knight shift experiments have rekindled the Sr$_2$RuO$_4$ pairing debate by giving strong evidence against all odd-parity pairing states, including chiral $p$-wave pairing that was for a long time the leading pairing candidate. Here, we exclude additional pairing states by analyzing recent elastocaloric measurements [YS. Li et al., Nature 607, 276--280 (2022)]. To be able to explain the elastocaloric experiment, we find that unconventional even-parity pairings must include either large $d_{x^2 - y^2}$-wave or large $\{d_{xz} \mid d_{yz}\}$-wave admixtures, where the latter possibility arises because of the body-centered point group symmetry. These $\{d_{xz} \mid d_{yz}\}$-wave admixtures take the form of distinctively body-centered-periodic harmonics that have horizontal line nodes. Hence $g_{xy(x^2-y^2)}$-wave and $d_{xy}$-wave pairings are excluded as possible dominant even pairing states.

cond-mat.supr-con↗
arXiv2023

Anisotropic Seebeck coefficient of $\mathrm{Sr}_2\mathrm{Ru}\mathrm{O}_4$ in the incoherent regime

Intuitive entropic interpretations of the thermoelectric effect in metals predict an isotropic Seebeck coefficient at high temperatures in the incoherent regime even in anisotropic metals since entropy is not directional. $\mathrm{Sr}_2\mathrm{Ru}\mathrm{O}_4$ is an enigmatic material known for a well characterised anisotropic normal state and unconventional superconductivity. Recent ab-initio transport calculations of $\mathrm{Sr}_2\mathrm{Ru}\mathrm{O}_4$ that include the effect of strong electronic correlations predicted an enhanced high-temperature anisotropy of the Seebeck coefficient at temperatures above 300 K, but experimental evidence is missing. From measurements on clean $\mathrm{Sr}_2\mathrm{Ru}\mathrm{O}_4$ single crystals along both crystallographic directions, we find that the Seebeck coefficient becomes increasingly isotropic upon heating towards room temperature as generally expected. Above 300 K, however, $S$ acquires a new anisotropy which rises up to the highest temperatures measured (750 K), in qualitative agreement with calculations. This is a challenge to entropic interpretations and highlights the lack of an intuitive framework to understand the anisotropy of thermopower at high temperatures.

cond-mat.str-el↗
arXiv2023

$T-$linear resistivity from magneto-elastic scattering: application to PdCrO$_2$

An electronic solid with itinerant carriers and localized magnetic moments represents a paradigmatic strongly correlated system. The electrical transport properties associated with the itinerant carriers, as they scatter off these local moments, has been scrutinized across a number of materials. Here we analyze the transport characteristics associated with ultra-clean PdCrO$_2$ -- a quasi two-dimensional material consisting of alternating layers of itinerant Pd-electrons and Mott-insulating CrO$_2$ layers -- which shows a pronounced regime of $T-$linear resistivity over a wide-range of intermediate temperatures. By contrasting these observations to the transport properties in a closely related material PdCoO$_2$, where the CoO$_2$ layers are band-insulators, we can rule out the traditional electron-phonon interactions as being responsible for this interesting regime. We propose a previously ignored electron-magnetoelastic interaction between the Pd-electrons, the Cr local-moments and an out-of-plane phonon as the main scattering mechanism that leads to the significant enhancement of resistivity and a $T-$linear regime in PdCrO$_2$ at temperatures far in excess of the magnetic ordering temperature. We suggest a number of future experiments to confirm this picture in PdCrO$_2$, as well as other layered metallic/Mott-insulating materials.

cond-mat.str-el↗
arXiv2023

Observation of the anomalous Hall effect in a layered polar semiconductor

Progress in magnetoelectric materials is hindered by apparently contradictory requirements for time-reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes could be provided by recent discoveries of a time-reversal symmetry breaking anomalous Hall effect in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, we report the observation of a spontaneous anomalous Hall effect in doped AgCrSe$_2$, a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3 $μΩ$ cm is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to $\sim 80^{\circ}$ from the crystalline $c$-axis. Our ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the $p$-type carrier density. We also present theoretical results that suggest the anomalous Hall effect is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe$_2$. Our results open the possibility to study the interplay of magnetic and ferroelectric-like responses in this fascinating class of materials.

cond-mat.mtrl-sci↗
arXiv2023

Giant lattice softening at a Lifshitz transition in Sr$_{2}$RuO$_{4}$

The interplay of electronic and structural degrees of freedom in solids is a topic of intense research. Experience and intuition suggest that structural changes drive conduction electron behavior, because the large number of valence electrons dominate the structural properties. As part of a seminal paper written over sixty years ago, Lifshitz discussed an alternative possibility: lattice softening driven by conduction electrons at topological Fermi surface transitions. The effect he predicted, however, was small, and has not been convincingly observed. Using measurements of the stress-strain relationship in the ultra-clean metal Sr$_{2}$RuO$_{4}$, we reveal a huge softening of the Young's modulus at a Lifshitz transition of a two-dimensional Fermi surface, and show that it is indeed entirely driven by the conduction electrons of the relevant energy band.

cond-mat.str-el↗
arXiv2023

Elastocaloric effect of the heavy-fermion system YbPtBi

YbPtBi is one of the heavy-fermion systems with largest Sommerfeld coefficient $γ$ and is thus classified as a `super'-heavy fermion material. In this work, we resolve the long-debated question about the hierarchy of relevant energy scales, such as crystal-electric field (CEF) levels, Kondo and magnetic ordering temperature, in YbPtBi. Through measurements of the a.c. elastocaloric effect and generic symmetry arguments, we identify an \textit{elastic level splitting} that is uniquely associated with the symmetry-allowed splitting of a quartet CEF level. This quartet, which we identify to be the first excited state at $Δ/k_\text B\approx1.6\,\rm K$ above the doublet ground state at ambient pressure, is well below the Kondo temperature $T_\text K\approx10\,\rm K$. Thus, our analysis provides strong support for models that predict that the heavy electron mass is a result of an enhanced degeneracy of the CEF ground state, i.e., a quasi-sextet in YbPtBi. At the same time, our study shows the potential of the a.c. elastocaloric effect to control and quantify strain-induced changes of the CEF schemes, opening a different route to disentangle the CEF energy scales from other relevant energy scales in correlated quantum materials.

cond-mat.str-el↗
arXiv2023

Non-local electrodynamics in ultra-pure PdCoO$_{2}$

The motion of electrons in the vast majority of conductors is diffusive, obeying Ohm's law. However, the recent discovery and growth of high-purity materials with extremely long electronic mean free paths has sparked interest in non-ohmic alternatives, including viscous and ballistic flow. Although non-ohmic transport regimes have been discovered across a range of materials, including two-dimensional electron gases, graphene, topological semimetals, and the delafossite metals, determining their nature has proved to be challenging. Here, we report on a new approach to the problem, employing broadband microwave spectroscopy of the delafossite metal PdCoO$_{2}$ in three distinct sample geometries that would be identical for diffusive transport. The observed differences, which go as far as differing power laws, take advantage of the hexagonal symmetry of PdCoO$_{2}$. This permits a particularly elegant symmetry-based diagnostic for non-local electrodynamics, with the result favouring ballistic over strictly hydrodynamic flow. Furthermore, it uncovers a new effect for ballistic electron flow, owing to the highly facetted shape of the hexagonal Fermi surface. We combine our extensive dataset with an analysis of the Boltzmann equation to characterize the non-local regime in PdCoO$_{2}$. More broadly, our results highlight the potential of broadband microwave spectroscopy to play a central role in investigating exotic transport regimes in the new generation of ultra-high conductivity materials.

cond-mat.mes-hall↗
arXiv2023

Hierarchy of Lifshitz transitions in the surface electronic structure of Sr$_2$RuO$_4$ under uniaxial compression

We report the evolution of the electronic structure at the surface of the layered perovskite Sr$_2$RuO$_4$ under large in-plane uniaxial compression, leading to anisotropic $B_{1g}$ strains of ${\varepsilon_{xx}-\varepsilon_{yy}=-0.9\pm0.1\%}$. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of Sr$_2$RuO$_4$ hosts. From comparison to tight-binding modelling, we find that the strain is accommodated predominantly by bond-length changes rather than modifications of octahedral tilt and rotation angles. Our study sheds new light on the nature of structural distortions at oxide surfaces, and how targeted control of these can be used to tune density of states singularities to the Fermi level, in turn paving the way to the possible realisation of rich collective states at the Sr$_2$RuO$_4$ surface.

cond-mat.str-el↗
arXiv2023

Probing momentum-dependent scattering in uniaxially stressed Sr$_2$RuO$_4$ through the Hall effect

Under in-plane uniaxial stress, the largest Fermi surface sheet of the correlated metal Sr$_2$RuO$_4$ undergoes a Lifshitz transition from an electron-like to an open geometry. We investigate the effects of this transition on transport through measurement of the longitudinal resistivity $ρ_{xx}$ and the Hall coefficient $R_\text{H}$. At temperatures where scattering is dominated by electron-electron scattering, $R_\text{H}$ becomes more negative across the Lifshitz transition, opposite to expectations from the change in Fermi surface topology. We show that this change in $R_\text{H}$ is explainable only if scattering changes throughout the Brillouin zone, not just at the point in $k$-space where the Lifshitz transition occurs. In a model of orbital-dependent scattering, the electron-electron scattering rate on sections of Fermi surface with $xy$ orbital weight decreases dramatically. On the other hand, at temperatures where defect scattering dominates $ρ_{xx}$ and $R_\text{H}$ are essentially constant across the Lifshitz transition.

cond-mat.str-el↗
arXiv2023

Upper Critical Field of Sr$_2$RuO$_4$ under In-Plane Uniaxial Pressure

In-plane uniaxial pressure has been shown to strongly tune the superconducting state of Sr2RuO4 by approaching a Lifshitz transition and associated Van Hove singularity (VHS) in the density of states. At the VHS, $T_c$ and the in- and out-of-plane upper critical fields are all strongly enhanced, and the latter has changed its curvature as a function of temperature from convex to concave. However, due to strain inhomogeneity it has not been possible so far to determine how the upper critical fields change with strain. Here, we show the strain dependence of both upper critical fields, which was achieved due to an improved sample preparation. We find that the in-plane upper critical field is mostly linear in $T_c$. On the other hand, the out-of-plane upper critical field varies with a higher power in $T_c$, and peaks strongly at the VHS. The strong increase in magnitude and the change in form of $H_\mathrm{c2||c}$ occur very close to the Van Hove strain, and points to a strong enhancement of both the density of states and the gap magnitude at the Lifshitz transition.

cond-mat.supr-con↗
arXiv2023

Investigation of Planckian behavior in a high-conductivity oxide: PdCrO$_2$

The layered delafossite metal PdCrO$_2$ is a natural heterostructure of highly conductive Pd layers Kondo coupled to localized spins in the adjacent Mott insulating CrO$_2$ layers. At high temperatures $T$ it has a $T$-linear resistivity which is not seen in the isostructural but non-magnetic PdCoO$_2$. The strength of the Kondo coupling is known, as-grown crystals are extremely high purity and the Fermi surface is both very simple and experimentally known. It is therefore an ideal material platform in which to investigate 'Planckian metal' physics. We do this by means of controlled introduction of point disorder, measurement of the thermal conductivity and Lorenz ratio and studying the sources of its high temperature entropy. The $T$-linear resistivity is seen to be due mainly to elastic scattering and to arise from a sum of several scattering mechanisms. Remarkably, this sum leads to a scattering rate within 10$\%$ of the Planckian value of $k_BT/$$\hbar$.

cond-mat.str-el↗
arXiv2023

Microstructuring YbRh2Si2 for resistance and noise measurements down to ultra-low temperatures

The discovery of superconductivity in the quantum critical Kondo-lattice system YbRh2Si2 at an extremely low temperature of 2 mK has inspired efforts to perform high-resolution electrical resistivity measurements down to this temperature range in highly conductive materials. Here we show that control over the sample geometry by microstructuring using focused-ion-beam (FIB) techniques allows to reach ultra-low temperatures and increase signal-to-noise ratios (SNR) tenfold, without adverse effects to sample quality. In five experiments we show four-terminal sensing resistance and magnetoresistance measurements which exhibit sharp phase transitions at the Néel temperature, and Shubnikov-de-Haas (SdH) oscillations between 13 T and 18 T where we identified a new SdH frequency of 0.39 kT. The increased SNR allowed resistance fluctuation (noise) spectroscopy that would not be possible for bulk crystals, and confirmed intrinsic 1/f-type fluctuations. Under controlled strain, two thin microstructured samples exhibited a large increase of T_N from 67 mK up to 188 mK while still showing clear signatures of the phase transition and SdH oscillations. SQUID-based thermal noise spectroscopy measurements in a nuclear demagnetisation refrigerator down to 0.95 mK, show a sharp superconducting transition at T_c = 1.2 mK. These experiments demonstrate microstructuring as a powerful tool to investigate the resistance and the noise spectrum of highly conductive correlated metals over wide temperature ranges.

cond-mat.str-el↗
arXiv2022

Atomic-scale imaging of emergent order at a magnetic-field-induced Lifshitz transition

The phenomenology and radical changes seen in materials properties traversing a quantum phase transition has captivated condensed matter research over past decades. Strong electronic correlations lead to novel electronic ground states, including magnetic order, nematicity and unconventional superconductivity. Providing a microscopic model for these requires detailed knowledge of the electronic structure in the vicinity of the Fermi energy, promising a complete understanding of the physics of the quantum critical point. Here, we demonstrate such a measurement at the surface of Sr$_3$Ru$_2$O$_7$. Our results show that, even in zero field, the electronic structure is strongly $C_2$ symmetric and that a magnetic-field drives both a Lifshitz transition and induces a charge-stripe order. We track the changes of the electronic structure as a function of field via quasi-particle interference imaging at ultralow temperatures. Our results provide a complete microscopic picture of the field-induced changes of the electronic structure across the Lifshitz transition.

cond-mat.str-el↗
arXiv2022

Observation of an Anomalous Hall Effect in Single-crystal Mn3Pt

The Mn3X family of compounds was the first in which a large anomalous Hall effect (AHE) was predicted to arise from a purely antiferromagnetic structure, due to the Berry curvature in momentum space. Nearly simultaneously with this prediction, a large AHE was observed experimentally in one of the hexagonal members of this family, Mn3Sn. Aligning antiferromagnetic domains, a necessary step for observation of the AHE, is more challenging for the cubic members of the Mn3X family, due to a combination of a smaller spontaneous ferromagnetic moment and much stronger magnetic anisotropy. Here, we use a combination of uniaxial stress and applied magnetic field to align domains of bulk single-crystal Mn3Pt, and demonstrate for the first time a substantial AHE in a bulk sample of a cubic member of the Mn3X family. The AHE remains locked in with essentially no quantitative variation when the stress is ramped back to zero, which shows that it is not a consequence of any stress-induced ferromagnetic moment.

cond-mat.mtrl-sci↗
arXiv2022

Elastocaloric determination of the phase diagram of Sr$_2$RuO$_4$

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr$_2$RuO$_4$. Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr$_2$RuO$_4$.

cond-mat.supr-con↗
arXiv2022

Planckian Dissipation in Metals

We review the appearance of the Planckian time $τ_\text{Pl} = \hbar/(k_B T)$ in both conventional and unconventional metals. We give a pedagogical discussion of the various different timescales (quasiparticle, transport, many-body) that characterize metals, emphasizing conditions under which these times are the same or different. Throughout, we have attempted to clear up aspects of the problem that had been confusing us, in the hope that this helps the reader as well. We discuss the possibility of a Planckian bound on dissipation from both a quasiparticle and a many-body perspective. Planckian quasiparticles can arise naturally from a combination of inelastic scattering and mass renormalization. Many-body dynamics, on the other hand, is constrained by the basic time- and length- scales of local thermalization.

cond-mat.str-el↗