arXiv subjects

A. P. Mackenzie

Publications and source records attributed to A. P. Mackenzie.

At least 55 records · Page 3Linked to original sources

arXiv2016

Detection of a Cooper-Pair Density Wave in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$

The quantum condensate of Cooper-pairs forming a superconductor was originally conceived to be translationally invariant. In theory, however, pairs can exist with finite momentum $Q$ and thereby generate states with spatially modulating Cooper-pair density. While never observed directly in any superconductor, such a state has been created in ultra-cold $^{6}$Li gas. It is now widely hypothesized that the cuprate pseudogap phase contains such a 'pair density wave' (PDW) state. Here we use nanometer resolution scanned Josephson tunneling microscopy (SJTM) to image Cooper-pair tunneling from a $d$-wave superconducting STM tip to the condensate of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. Condensate visualization capabilities are demonstrated directly using the Cooper-pair density variations surrounding Zn impurity atoms and at the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ crystal-supermodulation. Then, by using Fourier analysis of SJTM images, we discover the direct signature of a Cooper-pair density modulation at wavevectors $Q_{p} \approx (0.25,0)2π/ a_{0}$;$(0,0.25)2π/ a_{0}$ in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. The amplitude of these modulations is ~5% of the homogenous condensate density and their form factor exhibits primarily $s$/$s'$-symmetry. This phenomenology is expected within Ginzburg-Landau theory when a charge density wave with $d$-symmetry form factor and wave vector $Q_{c}=Q_{p}$ coexists with a homogeneous $d$-symmetry superconductor ; it is also encompassed by several contemporary microscopic theories for the pseudogap phase.

cond-mat.supr-con↗

arXiv2015

Nearly-free electrons in a 5d delafossite oxide metal

Understanding the role of electron correlations in strong spin-orbit transition-metal oxides is key to the realisation of numerous exotic phases including spin-orbit assisted Mott insulators, correlated topological solids, and prospective new high-temperature superconductors. To date, most attention has been focussed on the $5d$ iridium-based oxides. Here, we instead consider the Pt-based delafossite oxide PtCoO$_2$. Our transport measurements, performed on single-crystal samples etched to well-defined geometries using focussed ion-beam techniques, yield a room-temperature resistivity of only 2.1~$μΩ$cm, establishing PtCoO$_2$ as the most conductive oxide known. From angle-resolved photoemission and density-functional theory, we show that the underlying Fermi surface is a single cylinder of nearly hexagonal cross-section, with very weak dispersion along k$_z$. Despite being predominantly composed of $d$-orbital character, the conduction band is remarkably steep, with an average effective mass of only 1.14$m_e$. Moreover, the sharp spectral features observed in photoemission remain well-defined with little additional broadening for over 500~meV below E$_F$, pointing to suppressed electron-electron scattering. Together, our findings establish PtCoO$_2$ as a model nearly-free electron system in a $5d$ delafossite transition-metal oxide.

cond-mat.str-el↗

arXiv2015

Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State

Extensive research into high temperature superconducting cuprates is now focused upon identifying the relationship between the classic 'pseudogap' phenomenon$^{1,2}$ and the more recently investigated density wave state$^{3-13}$. This state always exhibits wave vector $Q$ parallel to the planar Cu-O-Cu bonds$^{4-13}$ along with a predominantly $d$-symmetry form factor$^{14-17}$ (dFF-DW). Finding its microscopic mechanism has now become a key objective$^{18-30}$ of this field. To accomplish this, one must identify the momentum-space ($k$-space) states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization$^{14}$ of electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy $Δ_{1}$. Moreover, we demonstrate that the dFF-DW modulations at $E=-Δ_{1}$ (filled states) occur with relative phase $π$ compared to those at $E=Δ_{1}$ (empty states). Finally, we show that the dFF-DW $Q$ corresponds directly to scattering between the 'hot frontier' regions of $k$-space beyond which Bogoliubov quasiparticles cease to exist$^{31,32,33}$. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in $k$-space where the pseudogap opens.

cond-mat.supr-con↗

arXiv2014

Muon-spin rotation measurements of the vortex state in Sr$_2$RuO$_4$: type-1.5 superconductivity, vortex clustering and a crossover from a triangular to a square vortex lattice

Muon-spin rotation has been used to probe vortex state in Sr$_2$RuO$_4$. At moderate fields and temperatures a lattice of triangular symmetry is observed, crossing over to a lattice of square symmetry with increasing field and temperature. At lower fields it is found that there are large regions of the sample that are completely free from vortices which grow in volume as the temperature falls. Importantly this is accompanied by {\it increasing} vortex density and increasing disorder within the vortex-cluster containing regions. Both effects are expected to result from the strongly temperature-dependent long-range vortex attractive forces arising from the multi-band chiral-order superconductivity.

cond-mat.supr-con↗

arXiv2014

Pressure study of nematicity and quantum criticality in Sr$_3$Ru$_2$O$_7$ for an in-plane field

We study the relationship between the nematic phases of Sr$_3$Ru$_2$O$_7$ and quantum criticality. At ambient pressure, one nematic phase is associated with a metamagnetic quantum critical end point (QCEP) when the applied magnetic field is near the \textit{c}-axis. We show, however, that this metamagnetic transition does not produce the same nematic signatures when the QCEP is reached by hydrostatic pressure with the field applied in the \textit{ab}-plane. Moreover, a second nematic phase, that is seen for field applied in the \textit{ab}-plane close to, but not right at, a second metamagnetic anomaly, persists with minimal change to the highest applied pressure, 16.55 kbar. Taken together our results suggest that metamagnetic quantum criticality may not be necessary for the formation of a nematic phase in Sr$_3$Ru$_2$O$_7$.

cond-mat.str-el↗

arXiv2013

Evidence from Tunneling Spectroscopy for a Quasi-One Dimensional Origin of Superconductivity in Sr2RuO4

To establish the mechanism of unconventional superconductivity in Sr$_2$RUO$_4$, a prerequisite is direct information concerning the momentum-space structure of the energy gaps $Δ_i(k)$, and in particular whether the pairing strength is stronger ("dominant") on the quasi-1D ($α$ and $β$) or on the quasi-2D ($γ$) Fermi surfaces. We present scanning tunneling microscopy (STM) measurements of the density-of-states spectra in the superconducting state of Sr$_2$RuO$_4$ for $0.1 T_C<T<T_C$, and analyze them, along with published thermodynamic data, using a simple phenomenological model. We show that our observation of a single superconducting gap scale with maximum value $2Δ\approx 5 T_C$ along with a spectral shape indicative of line nodes is consistent, within a weak-coupling model, with magnetically mediated odd-parity superconductivity generated by dominant, near-nodal Cooper pairing on the $α$ and $β$ bands.

cond-mat.supr-con↗

arXiv2013

Study of the electronic nematic phase of Sr$_3$Ru$_2$O$_7$ with precise control of the applied magnetic field vector

We report a study of the magnetoresistivity of high purity Sr$_3$Ru$_2$O$_7$, in the vicinity of its electronic nematic phase. By employing a triple-axis (9/1/1T) vector magnet, we were able to precisely tune both the magnitude and direction of the in-plane component of the magnetic field (H$_\parallel$). We report the dependence of the resistively determined anisotropy on H$_\parallel$ in the phase, as well as across the wider temperature-field region. Our measurements reveal a high-temperature anisotropy which mimics the behaviour of fluctuations from the underlying quantum critical point, and suggest the existence of a more complicated phase diagram than previously reported.

cond-mat.str-el↗

arXiv2013

Imaging Cooper Pairing of Heavy Fermions in CeCoIn5

The Cooper pairing mechanism of heavy-fermion superconductors, while long hypothesized as due to spin fluctuations, has not been determined. It is the momentum space (k-space) structure of the superconducting energy gap delta(k) that encodes specifics of this pairing mechanism. However, because the energy scales are so low, it has not been possible to directly measure delta(k) for any heavy-fermion superconductor. Bogoliubov quasiparticle interference (QPI) imaging, a proven technique for measuring the energy gaps of high-Tc superconductors, has recently been proposed as a new method to measure delta(k) in heavy-fermion superconductors, specifically CeCoIn5. By implementing this method, we immediately detect a superconducting energy gap whose nodes are oriented along k||(+-1, +-1)pi/a0 directions. Moreover, we determine the complete k-space structure of the delta(k) of a heavy-fermion superconductor. For CeCoIn5, this novel information includes: the complex band structure and Fermi surface of the hybridized heavy bands, the fact that highest magnitude delta(k) opens on a high-k band so that gap nodes occur at quite unanticipated k-space locations, and that the Bogoliubov quasiparticle interference patterns are most consistent with dx2-y2 gap symmetry. The availability of such quantitative heavy band- and gap-structure data will be critical in identifying the microscopic mechanism of heavy fermion superconductivity in this material, and perhaps in general.

cond-mat.supr-con↗

arXiv2012

Formation and consequences of heavy d-electron quasiparticles in Sr3Ru2O7

We report angle-resolved photoelectron spectroscopy measurements of the quantum critical metal Sr3Ru2O7 revealing itinerant Ru 4d-states confined over large parts of the Brillouin zone to an energy range of < 6 meV, nearly three orders of magnitude lower than the bare band width. We show that this energy scale agrees quantitatively with a characteristic thermodynamic energy scale associated with quantum criticality and illustrate how it arises from the hybridization of light and strongly renormalized, heavy quasiparticle bands. For the largest Fermi surface sheet we find a marked k-dependence of the renormalization and show that it correlates with the Ru 4d - O 2p hybridization.

cond-mat.str-el↗

arXiv2012

Quantum criticality and the formation of a putative electronic liquid crystal in Sr3Ru2O7

We present a brief review of the physical properties of Sr3Ru2O7, in which the approach to a magnetic-field-tuned quantum critical point is cut off by the formation of a novel phase with transport characteristics consistent with those of a nematic electronic liquid crystal. Our goal is to summarize the physics that led to that conclusion being drawn, describing the key experiments and discussing the theoretical approaches that have been adopted. Throughout the review we also attempt to highlight observations that are not yet understood, and to discuss the future challenges that will need to be addressed by both experiment and theory.

cond-mat.str-el↗

arXiv2012

Anisotropic Energy Gaps of Iron-based Superconductivity from Intra-band Quasiparticle Interference in LiFeAs

If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps Δ_i(k) should appear on the different electronic bands i. Here we introduce intra-band Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of Δ_i(k) in such materials, focusing on LiFeAs. We identify the three hole-like bands assigned previously as γ, α_2 and α_1, and we determine the anisotropy, magnitude and relative orientations of their Δ_i(k). These measurements will advance quantitative theoretical analysis of the mechanism of Cooper pairing in iron-based superconductivity.

cond-mat.supr-con↗

arXiv2011

Sr3Ru2O7: Thermodynamics of Phase Formation in a Quantum Critical Metal

The behaviour of matter near zero temperature continuous phase transitions, or 'quantum critical points' (QCPs) is a central topic of study in condensed matter physics. In fermionic systems, fundamental questions remain unanswered: the nature of the quantum critical regime is unclear because of the apparent breakdown of the concept of the quasiparticle, a cornerstone of existing theories of strongly interacting metals. Even less is known experimentally about the formation of ordered phases from such a quantum critical 'soup'. Here, we report a study of the specific heat across the phase diagram of the model system Sr3Ru2O7, which features an anomalous phase whose transport properties are consistent with those of an electronic nematic. We show that this phase, which exists at low temperatures in a narrow range of magnetic fields, forms directly from a quantum critical state, and contains more entropy than mean-field calculations predict. Our results suggest that this extra entropy is due to remnant degrees of freedom from the highly entropic state above T_c. The associated quantum critical point, which is 'concealed' by the nematic phase, separates two Fermi liquids, neither of which has an identifiable spontaneously broken symmetry, but which likely differ in the topology of their Fermi surfaces.

cond-mat.str-el↗

arXiv2011

Quantum critical metamagnetism of Sr3Ru2O7 under hydrostatic pressure

Using ac susceptibility, we have determined the pressure dependence of the metamagnetic critical end point temperature T* for field applied in the ab-plane in the itinerant metamagnet Sr3Ru2O7. We find that T* falls monotonically to zero as pressure increases, producing a quantum critical end point (QCEP) at Pc~13.6 kbar. New features are observed near the QCEP -- the slope of T* vs pressure changes at ~12.8 kbar, and weak subsidiary maxima appear on either side of the main susceptibility peak at pressures near Pc -- indicating that some new physics comes into play near the QCEP. Clear signatures of a nematic phase, however, that were seen in field-angle tuning of T*, are not observed. As T* is suppressed by pressure, the metamagnetic peak in the susceptibility remains sharp as a function of applied magnetic field. As a function of temperature, however, the peak becomes broad with only a very weak maximum, suggesting that, near the QCEP, the uniform magnetization density is not the order parameter for the metamagnetic transition.

cond-mat.str-el↗

arXiv2010

Unconventional magnetization processes and thermal runaway in spin-ice Dy$_2$Ti$_2$O$_7$

We investigate the non-equilibrium behavior of the spin-ice material Dy$_2$Ti$_2$O$_7$ by studying its magnetization as a function of the rate at which an external field is swept. At temperatures below the enigmatic "freezing" temperature $T_{\rm equil}\approx600$ mK, we find that even the slowest sweeps fail to yield the equilibrium magnetization curve and instead give a smooth, initially much flatter curve. For higher sweep rates, the magnetization develops sharp steps accompanied by similarly sharp peaks in the temperature of the sample. We ascribe the former behavior to the energy barriers encountered in the magnetization process, which proceeds via flipping of spins on filaments traced out by the field-driven motion of the gapped, long-range interacting magnetic monopole excitations. In contrast, the peaks in temperature result from the released Zeeman energy not being carried away efficiently into the bath, with the resulting heating triggering a chain reaction.

cond-mat.mtrl-sci↗

arXiv2010

Quantum oscillations near the metamagnetic transition in Sr3Ru2O7

We report detailed investigation of quantum oscillations in Sr3Ru2O7, observed inductively (the de Haas-van Alphen effect) and thermally (the magnetocaloric effect). Working at fields from 3 T to 18 T allowed us to straddle the metamagnetic transition region and probe the low- and high-field Fermi liquids. The observed frequencies are strongly field-dependent in the vicinity of the metamagnetic transition, and there is evidence for magnetic breakdown. We also present the results of a comprehensive rotation study. The most surprising result concerns the field dependence of the measured quasiparticle masses. Contrary to conclusions previously drawn by some of us as a result of a study performed with a much poorer signal to noise ratio, none of the five Fermi surface branches for which we have good field-dependent data gives evidence for a strong field dependence of the mass. The implications of these experimental findings are discussed.

cond-mat.str-el↗

arXiv2010

Quantum oscillations in the anomalous phase in Sr3Ru2O7

We report measurements of quantum oscillations detected in the putative nematic phase of Sr3Ru2O7. Significant improvements in sample purity enabled the resolution of small amplitude dHvA oscillations between two first order metamagnetic transitions delimiting the phase. Two distinct frequencies were observed, and their amplitudes follow the normal Lifshitz-Kosevich profile. The Fermi surface sheets seem to correspond to a subset of those detected outside the phase. Variations of the dHvA frequencies are explained in terms of a chemical potential shift produced by reaching a peak in the density of states, and an anomalous field dependence of the oscillatory amplitude provides information on domains.

cond-mat.str-el↗

arXiv2009

Heavy d-Electron Quasiparticle Interference and Real-space Electronic Structure of Sr3Ru2O7

The intriguing idea that strongly interacting electrons can generate spatially inhomogeneous electronic liquid crystalline phases is over a decade old, but these systems still represent an unexplored frontier of condensed matter physics. One reason is that visualization of the many-body quantum states generated by the strong interactions, and of the resulting electronic phases, has not been achieved. Soft condensed matter physics was transformed by microscopies that allowed imaging of real-space structures and patterns. A candidate technique for obtaining equivalent data in the purely electronic systems is Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM). The core challenge is to detect the tenuous but 'heavy' k-space components of the many-body electronic state simultaneously with its r-space constituents. Sr3Ru2O7 provides a particularly exciting opportunity to address these issues. It possesses (i) a very strongly renormalized 'heavy' d-electron Fermi liquid and (ii) exhibits a field-induced transition to an electronic liquid crystalline phase. Finally, as a layered compound, it can be cleaved to present an excellent surface for SI-STM.

cond-mat.str-el↗

arXiv2009

Microscopic theory of the nematic phase in Sr$_3$Ru$_2$O$_7$

In an externally applied magnetic field, ultra-pure crystals of the bilayer compound Sr$_3$Ru$_2$O$_7$ undergo a metamagnetic transition below a critical temperature, $T^*$, which varies as a function of the angle between the magnetic field $H$ and the Ru-O planes. Moreover, $T^*$ approaches zero when $H$ is perpendicular to the planes. This putative "metamagnetic quantum critical point", however, is preempted by a nematic fluid phase with order one resistive anisotropy in the {\it ab} plane. In a "realistic" bilayer model with moderate strength local Coulomb interactions, the existence of a sharp divergence of the electronic density of states near a van Hove singularity of the quasi-one-dimensional bands, and the spin-orbit couplings permitted by the presence of multiple orbitals result in a mean-field phase diagram which accounts for many of these experimentally observed phenomena. Although the spin-orbit coupling is not overly strong, it destroys the otherwise near perfect Fermi surface nesting and hence suppresses spin-density-wave (SDW) ordering.

cond-mat.str-el↗