arXiv subjects

R. Liang

Publications and source records attributed to R. Liang.

At least 37 records · Page 2Linked to original sources

arXiv2016

A global inversion-symmetry-broken phase inside the pseudogap region of YBa$_2$Cu$_3$O$_y$

The phase diagram of cuprate high-temperature superconductors features an enigmatic pseudogap region that is characterized by a partial suppression of low energy electronic excitations. Polarized neutron diffraction, Nernst effect, THz polarimetery and ultrasound measurements on YBa$_2$Cu$_3$O$_y$ suggest that the pseudogap onset below a temperature T* coincides with a bona fide thermodynamic phase transition that breaks time-reversal, four-fold rotation and mirror symmetries respectively. However, the full point group above and below T* has not been resolved and the fate of this transition as T* approaches the superconducting critical temperature T$_c$ is poorly understood. Here we reveal the point group of YBa$_2$Cu$_3$O$_y$ inside its pseudogap and neighboring regions using high sensitivity linear and second harmonic optical anisotropy measurements. We show that spatial inversion and two-fold rotational symmetries are broken below T* while mirror symmetries perpendicular to the Cu-O plane are absent at all temperatures. This transition occurs over a wide doping range and persists inside the superconducting dome, with no detectable coupling to either charge ordering or superconductivity. These results suggest that the pseudogap region coincides with an odd-parity order that does not arise from a competing Fermi surface instability and exhibits a quantum phase transition inside the superconducting dome.

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arXiv2016

Investigation of potential fluctuating intra-unit cell magnetic order in cuprates by muon spin relaxation

We report low temperature muon spin relaxation (muSR) measurements of the high-transition-temperature (Tc) cuprate superconductors Bi{2+x}Sr{2-x}CaCu2O{8+δ} and YBa2Cu3O6.57, aimed at detecting the mysterious intra-unit cell (IUC) magnetic order that has been observed by spin polarized neutron scattering in the pseudogap phase of four different cuprate families. A lack of confirmation by local magnetic probe methods has raised the possibility that the magnetic order fluctuates slowly enough to appear static on the time scale of neutron scattering, but too fast to affect $μ$SR or nuclear magnetic resonance (NMR) signals. The IUC magnetic order has been linked to a theoretical model for the cuprates, which predicts a long-range ordered phase of electron-current loop order that terminates at a quantum crictical point (QCP). Our study suggests that lowering the temperature to T ~ 25 mK and moving far below the purported QCP does not cause enough of a slowing down of fluctuations for the IUC magnetic order to become detectable on the time scale of muSR. Our measurements place narrow limits on the fluctuation rate of this unidentified magnetic order.

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arXiv2016

Observation of electronic bound states in charge-ordered YBa$_2$Cu$_3$O$_y$

Observing how electronic states in solids react to a local symmetry breaking provides insight into their microscopic nature. A striking example is the formation of bound states when quasiparticles are scattered off defects. This is known to occur, under specific circumstances, in some metals and superconductors but not, in general, in the charge-density-wave (CDW) state. Here, we report the unforeseen observation of bound states when a magnetic field quenches superconductivity and induces long-range CDW order in YBa$_2$Cu$_3$O$_y$. Bound states indeed produce an inhomogeneous pattern of the local density of states $N(E_F)$ that leads to a skewed distribution of Knight shifts which is detected here through an asymmetric profile of $^{17}$O NMR lines. We argue that the effect arises most likely from scattering off defects in the CDW state, which provides a novel case of disorder-induced bound states in a condensed-matter system and an insightful window into charge ordering in the cuprates.

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arXiv2016

Ideal charge density wave order in the high-field state of superconducting YBCO

The existence of charge density wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the ground state order has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to a dozen unit cells or less. Here we explore the CDW correlations in YBa2Cu3Ox (YBCO) ortho-II and ortho-VIII crystals, which belong to the cleanest available cuprate family, at magnetic fields in excess of the resistive upper critical field (Hc2) where the superconductivity is heavily suppressed. We find an incommensurate, unidirectional CDW with a well-defined onset at a critical field strength that is proportional to Hc2. It is related to but distinct from the short-range bidirectional CDW that exists at zero magnetic field. The unidirectional CDW possesses a long inplane correlation length as well as significant correlations between neighboring CuO2 planes, yielding a correlation volume that is at least 2 - 3 orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground-state of an "ideal" disorder-free cuprate.

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arXiv2016

Cu-NMR study of oxygen disorder in ortho-II YBa2Cu3Oy

We show that 63Cu NMR spectra place strong constraints on both the nature and the concentration of oxygen defects in ortho-II YBa2Cu3Oy. Systematic deviation from ideal ortho-II order is revealed by the presence of inequivalent Cu sites in either full or empty chains. The results can be explained by two kinds of defects: oxygen clustering into additional chains, or fragments thereof, most likely present at all concentrations (6.4<y<6.6) and oxygen vacancies randomly distributed in the full chains for y<6.50 only. Furthermore, the remarkable reproducibility of the spectra in different samples with optimal ortho-II order (y=6.55) shows that chain-oxygen disorder, known to limit electronic coherence, is ineluctable because it is inherent to these compounds.

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arXiv2016

Thermal Conductivity of the Iron-Based Superconductor FeSe : Nodeless Gap with Strong Two-Band Character

The thermal conductivity of the iron-based superconductor FeSe was measured at temperatures down to 50 mK in magnetic fields up to 17 T. In zero magnetic field, the electronic residual linear term in the T = 0 limit, κ_0/T, is vanishingly small. Application of a magnetic field H causes no increase in κ_0/T initially. Those two observations show that there are no zero-energy quasiparticles that carry heat and therefore no nodes in the superconducting gap of FeSe. The full field dependence of κ_0/T has the classic shape of a two-band superconductor, such as MgB2: it rises exponentially at very low field, with a characteristic field H* << Hc2, and then more slowly up to the upper critical field Hc2. This shows that the superconducting gap is very small on one of the pockets in the Fermi surface of FeSe.

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arXiv2016

Wiedemann-Franz law in the underdoped cuprate superconductor YBa2Cu3Oy

The recent detection of charge-density modulations in YBa2Cu3Oy and other cuprate superconductors raises new questions about the normal state of underdoped cuprates. In one class of theories, the modulations are intertwined with pairing in a dual state, expected to persist up to high magnetic fields as a vortex liquid. In support of such a state, specific heat and magnetisation data on YBa2Cu3Oy have been interpreted in terms of a vortex liquid persisting above the vortex-melting field Hvs at T = 0. Here we report high-field measurements of the electrical and thermal Hall conductivities in YBa2Cu3O6.54 that allow us to probe the Wiedemann-Franz law, a sensitive test of the presence of superconductivity in a metal. In the T = 0 limit, we find that the law is satisfied for fields immediately above Hvs. This rules out the existence of a vortex liquid and it places strict constraints on the nature of the normal state in underdoped cuprates.

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arXiv2016

Response to comment on "Broken translational and rotational symmetry via charge stripe order in underdoped YBa2Cu3O6+y"

Fine questions our interpretation of unidirectional-stripes over bidirectional-checkerboard, and illustrates his criticism by simulating a momentum space structure consistent with our data and corresponding to a checkerboard-looking real space density. Here we use a local rotational-symmetry analysis to demonstrate that the simulated image is in actuality composed of locally unidirectional modulations of the charge density, consistent with our original conclusions.

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arXiv2015

Two types of nematicity in the phase diagram of the cuprate superconductor YBa$_2$Cu$_3$O$_y$

Nematicity has emerged as a key feature of cuprate superconductors, but its link to other fundamental properties such as superconductivity, charge order and the pseudogap remains unclear. Here we use measurements of transport anisotropy in YBa$_2$Cu$_3$O$_y$ to distinguish two types of nematicity. The first is associated with short-range charge-density-wave modulations in a doping region near $p = 0.12$. It is detected in the Nernst coefficient, but not in the resistivity. The second type prevails at lower doping, where there are spin modulations but no charge modulations. In this case, the onset of in-plane anisotropy - detected in both the Nernst coefficient and the resistivity - follows a line in the temperature-doping phase diagram that tracks the pseudogap energy. We discuss two possible scenarios for the latter nematicity.

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arXiv2015

Change of carrier density at the pseudogap critical point of a cuprate superconductor

The pseudogap is a central puzzle of cuprate superconductors. Its connection to the Mott insulator at low doping $p$ remains ambiguous and its relation to the charge order that reconstructs the Fermi surface at intermediate $p$ is still unclear. Here we use measurements of the Hall coefficient in magnetic fields up to 88 T to show that Fermi-surface reconstruction by charge order in YBa$_2$Cu$_3$O$_y$ ends sharply at a critical doping $p = 0.16$, distinctly lower than the pseudogap critical point at $p^* = 0.19$. This shows that pseudogap and charge order are separate phenomena. We then find that the change of carrier density from $n = 1 + p$ in the conventional metal at high p to $n = p$ at low $p$ - a signature of the lightly doped cuprates - starts at $p^*$. This shows that pseudogap and antiferromagnetic Mott insulator are linked.

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arXiv2015

Onset field for Fermi-surface reconstruction in the cuprate superconductor YBCO

Quantum oscillations and negative Hall and Seebeck coefficients at low temperature and high magnetic field have shown the Fermi surface of underdoped cuprates to contain a small closed electron pocket. It is thought to result from a reconstruction by charge order, but whether it is the order seen by NMR and ultrasound above a threshold field or the short-range modulations seen by X-ray diffraction in zero field is unclear. Here we use measurements of the thermal Hall conductivity in YBCO to show that Fermi-surface reconstruction occurs only above a sharply defined onset field, equal to the transition field seen in ultrasound. This reveals that electrons do not experience long-range broken translational symmetry in the zero-field ground state, and hence in zero field there is no quantum critical point for the onset of charge order as a function of doping.

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arXiv2015

Three-Dimensional Charge Density Wave Order in YBa2Cu3O6.67 at High Magnetic Fields

Charge density wave (CDW) correlations have recently been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured by x-ray scattering at zero and low fields. Here we combine a pulsed magnet with an x-ray free electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields up to 28 Tesla. While the zero-field CDW order, which develops below T ~ 150 K, is essentially two-dimensional, at lower temperature and beyond 15 Tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW onsets around the zero-field superconducting transition temperature, yet the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

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arXiv2015

The symmetry of charge order in cuprates

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly-correlated states of matter. The recent discovery of charge order in various cuprate families fueled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-Tc superconductors. Here we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2201 and YBCO. We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum-structure of charge order. We also resolve the intra-unit-cell symmetry of the charge ordered state, which is revealed to be best represented by a bond-order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights on the microscopic description of charge order in cuprates, and on its origin and interplay with superconductivity.

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arXiv2015

Broken translational and rotational symmetry via charge stripe order in underdoped YBCO

Following the early discovery of stripe-like order in La-based copper-oxide superconductors, charge ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between uni- (stripes) and bi-directional (checkerboard) charge order in Y- and Bi-based materials. Here we use resonant x-ray scattering (RXS) to measure the two-dimensional structure factor in YBCO, in reciprocal space. Our data reveal the presence of charge stripe order, i.e. locally unidirectional density waves, suggesting it as the true microscopic nature of charge modulations in cuprates. At the same time, we find that the well-established competition between charge order and superconductivity is stronger for charge correlations across than along the stripes, which provides additional evidence for the intrinsic unidirectional nature of the charge order.

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arXiv2015

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy

The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order-parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.

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arXiv2015

Evidence for a small hole pocket in the Fermi surface of underdoped YBa2Cu3Oy

The Fermi surface of a metal is the fundamental basis from which its properties can be understood. In underdoped cuprate superconductors, the Fermi surface undergoes a reconstruction that produces a small electron pocket, but whether there is another, as yet undetected portion to the Fermi surface is unknown. Establishing the complete topology of the Fermi surface is key to identifying the mechanism responsible for its reconstruction. Here we report the discovery of a second Fermi pocket in underdoped YBa2Cu3Oy, detected as a small quantum oscillation frequency in the thermoelectric response and in the c-axis resistance. The field-angle dependence of the frequency demonstrates that it is a distinct Fermi surface and the normal-state thermopower requires it to be a hole pocket. A Fermi surface consisting of one electron pocket and two hole pockets with the measured areas and masses is consistent with a Fermi-surface reconstruction caused by the charge-density-wave order observed in YBa2Cu3Oy, provided other parts of the reconstructed Fermi surface are removed by a separate mechanism, possibly the pseudogap.

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arXiv2014

Direct measurement of the upper critical field in a cuprate superconductor

The upper critical field Hc2 is a fundamental measure of the pairing strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. We have used thermal conductivity as a direct probe of Hc2 in the cuprates YBa2Cu3Oy and YBa2Cu4O8 to show that there is no vortex liquid at T = 0, allowing us to use high-field resistivity measurements to map out the doping dependence of Hc2 across the phase diagram. Hc2(p) exhibits two peaks, each located at a critical point where the Fermi surface undergoes a transformation. The condensation energy obtained directly from Hc2, and previous Hc1 data, undergoes a 20-fold collapse below the higher critical point. These data provide quantitative information on the impact of competing phases in suppressing superconductivity in cuprates.

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arXiv2013

Lattice dynamical signature of charge density wave formation in underdoped YBa2Cu3O6+x

We report a detailed Raman scattering study of the lattice dynamics in detwinned single crystals of the underdoped high temperature superconductor YBa2Cu3O6+x (x=0.75, 0.6, 0.55 and 0.45). Whereas at room temperature the phonon spectra of these compounds are similar to that of optimally doped YBa2Cu3O6.99, additional Raman-active modes appear upon cooling below ~170-200 K in underdoped crystals. The temperature dependence of these new features indicates that they are associated with the incommensurate charge density wave state recently discovered using synchrotron x-ray scattering techniques on the same single crystals. Raman scattering has thus the potential to explore the evolution of this state under extreme conditions.

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