Thermodynamic signatures of quantum criticality in cuprate superconductors.

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram1. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range2 that includes p*. As a function of doping, we find that Cel/T is strongly peaked at p* (where Cel is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point3-5, as observed in heavy-fermion6 and iron-based7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

Magnetically Hidden State on the Ground Floor of the Magnetic Devil's Staircase.

We investigated the low-temperature and high-field thermodynamic and ultrasonic properties of SrCu_{2}(BO_{3})_{2}, which exhibits various plateaux in its magnetization curve above 27 T, called a magnetic Devil's staircase. The results of the present study confirm that magnetic crystallization, the first step of the staircase, occurs above 27 T as a first-order transition accompanied by a sharp singularity in heat capacity C_{p} and a kink in the elastic constant. In addition, we observe a thermodynamic anomaly at lower fields around 26 T, which has not been previously detected by any magnetic probes. At low temperatures, this magnetically hidden state has a large entropy and does not exhibit Schottky-type gapped behavior, which suggests the existence of low-energy collective excitations. Based on our observations and theoretical predictions, we propose that magnetic quadrupoles form a spin-nematic state around 26 T as a hidden state on the ground floor of the magnetic Devil's staircase.

Unusual Interplay between Superconductivity and Field-Induced Charge Order in YBa_{2}Cu_{3}O_{y}.

We present a detailed study of the temperature (T) and magnetic field (H) dependence of the electronic density of states (DOS) at the Fermi level, as deduced from specific heat and Knight shift measurements in underdoped YBa_{2}Cu_{3}O_{y}. We find that the DOS becomes field independent above a characteristic field H_{DOS}, and that the H_{DOS}(T) line displays an unusual inflection near the onset of the long-range 3D charge-density wave order. The unusual S shape of H_{DOS}(T) is suggestive of two mutually exclusive orders that eventually establish a form of cooperation in order to coexist at low T. On theoretical grounds, such a collaboration could result from the stabilization of a pair-density wave state, which calls for further investigation in this region of the phase diagram.

Superconductivity in doped cubic silicon.

Although the local resistivity of semiconducting silicon in its standard crystalline form can be changed by many orders of magnitude by doping with elements, superconductivity has so far never been achieved. Hybrid devices combining silicon's semiconducting properties and superconductivity have therefore remained largely underdeveloped. Here we report that superconductivity can be induced when boron is locally introduced into silicon at concentrations above its equilibrium solubility. For sufficiently high boron doping (typically 100 p.p.m.) silicon becomes metallic. We find that at a higher boron concentration of several per cent, achieved by gas immersion laser doping, silicon becomes superconducting. Electrical resistivity and magnetic susceptibility measurements show that boron-doped silicon (Si:B) made in this way is a superconductor below a transition temperature T(c) approximately 0.35 K, with a critical field of about 0.4 T. Ab initio calculations, corroborated by Raman measurements, strongly suggest that doping is substitutional. The calculated electron-phonon coupling strength is found to be consistent with a conventional phonon-mediated coupling mechanism. Our findings will facilitate the fabrication of new silicon-based superconducting nanostructures and mesoscopic devices with high-quality interfaces.

First-order transition in the magnetic vortex matter in superconducting MgB2 tuned by disorder.

The field-driven transition from an ordered Bragg glass to a disordered vortex phase in single-crystalline MgB2 is tuned by an increasing density of point defects, introduced by electron irradiation. The discontinuity observed in magnetization attests to the first-order nature of the transition. The temperature and defect density dependences of the transition field point to vortex pinning mediated by fluctuations in the quasiparticle mean free path, and reveal the mechanism of the transition in the absence of complicating factors such as layeredness or thermal fluctuations.

Field-induced Bose-Einstein condensation of triplons up to 8 K in Sr3Cr2O8.

Single crystals of the spin dimer system Sr(3)Cr(2)O(8) have been grown for the first time. Magnetization, heat capacity, and magnetocaloric effect data up to 65 T reveal magnetic order between applied fields of H(c1) approximately 30.4 T and H(c2) approximately 62 T. This field-induced order persists up to T(c)(max) approximately 8 K at H approximately 44 T, the highest observed in any quantum magnet where H(c2) is experimentally accessible. We fit the temperature-field phase diagram boundary close to H(c1) using the expression T(c) = A(H-H(c1))(nu). The exponent nu = 0.65(2), obtained at temperatures much smaller than T(c)(max), is that of the 3D Bose-Einstein condensate (BEC) universality class. This finding strongly suggests that Sr(3)Cr(2)O(8) is a new realization of a triplon BEC where the universal regimes corresponding to both H(c1) and H(c2) are accessible at (4)He temperatures.

Coexistence and interplay of superconductivity and ferromagnetism in URhGe.

As ferromagnetism and superconductivity are usually considered to be antagonistic, the discovery of their coexistence in UGe(2), URhGe, UIr and UCoGe has attracted a lot of interest. The mechanism to explain such a state has, however, not yet been fully elucidated. In these compounds superconductivity may be unconventional: Cooper pairs could be formed by electrons with parallel spins and magnetic fluctuations might be involved in the pairing mechanism. URhGe becomes ferromagnetic below a Curie temperature of 9.5 K, with a spontaneous moment aligned to the c-axis. For temperatures below 260 mK and fields lower than 2 T, superconductivity was first observed in 2001. Recently, we discovered a second pocket of superconductivity. This new pocket of superconductivity appears at higher fields applied close to the b-axis, enveloping a sudden magnetic moment rotation transition at H(R) = 12 T. Detailed studies of the field induced metamagnetic transition and superconductivity are presented. The possibility that magnetic fluctuations emerging from a quantum critical point provide the pairing mechanism for superconductivity is discussed.

Calorimetric determination of the magnetic phase diagram of underdoped ortho II YBa2Cu3O6.54 single crystals.

The recent discovery of a charge order in underdoped YBa2Cu3Oy raised the question of the interplay between superconductivity and this competing phase. Understanding the normal state of high-temperature superconductors is now an essential step towards the description of the pairing mechanism in those materials and determining the upper critical field is therefore of fundamental importance. We present here a calorimetric determination of the field-temperature phase diagram in underdoped YBa2Cu3Oy single crystals. We show that the specific heat saturates in high magnetic fields. This saturation is consistent with a normal state without any significant superconducting contribution and a total Sommerfeld coefficient γN∼6.5±1.5 mJ mol(-1) K(-2) putting strong constraints on the theoretical models for the Fermi surface reconstruction.

Non-Debye normalization of the glass vibrational density of states in mildly densified silicate glasses.

The evolution of the boson peak with densification at medium densification rates (up to 2.3%) in silicate glasses was followed through heat capacity measurements and low frequency Raman scattering. It is shown that the decrease of the boson peak induced by densification does not conform to that expected from a continuous medium; rather it follows a two step behaviour. The comparison of the heat capacity data with the Raman data shows that the light-vibration coupling coefficient is almost unaffected in this densification regime. These results are discussed in relation to the inhomogeneity of the glass elastic network at the nanometre scale.

Metal-to-insulator transition and superconductivity in boron-doped diamond.

The experimental discovery of superconductivity in boron-doped diamond came as a major surprise to both the diamond and the superconducting materials communities. The main experimental results obtained since then on single-crystal diamond epilayers are reviewed and applied to calculations, and some open questions are identified. The critical doping of the metal-to-insulator transition (MIT) was found to coincide with that necessary for superconductivity to occur. Some of the critical exponents of the MIT were determined and superconducting diamond was found to follow a conventional type II behaviour in the dirty limit, with relatively high critical temperature values quite close to the doping-induced insulator-to-metal transition. This could indicate that on the metallic side both the electron-phonon coupling and the screening parameter depend on the boron concentration. In our view, doped diamond is a potential model system for the study of electronic phase transitions and a stimulating example for other semiconductors such as germanium and silicon.

Anisotropy of the Sommerfeld coefficient in magnesium diboride single crystals.

The anisotropic field dependence of the Sommerfeld coefficient gamma has been measured down to B-->0 by combining specific heat and Hall probe magnetization measurements in MgB2 single crystals. We find that gamma(B,theta) is the sum of two contributions arising from the sigma and pi band, respectively. We show that gammasigma(B,theta)=B/Bc2(theta) where Bc2(theta)=Bc2ab/sqrt[sin2theta+Gamma2cos2theta] with Gamma approximately 5.4 (theta being the angle between the applied field and the c axis) and gammapi(B,theta)=gammapi(B)=B/Bpi(B). The "critical field" of the pi band Bpi is fully isotropic but field dependent increasing from approximately 0.25 T for B< or =0.1 T up to 3 T approximately Bc2c for B-->3 T. Because of the coupling of the two bands, superconductivity survives in the pi band up to 3 T but is totally destroyed above for any orientation of the field.

Tunneling spectroscopy and vortex imaging in boron-doped diamond.

We present the first scanning tunneling spectroscopy study of single-crystalline boron-doped diamond. The measurements were performed below 100 mK with a low temperature scanning tunneling microscope. The tunneling density of states displays a clear superconducting gap. The temperature evolution of the order parameter follows the weak-coupling BCS law with Delta(0)/kBTc approximately 1.74. Vortex imaging at low magnetic field also reveals localized states inside the vortex core that are unexpected for such a dirty superconductor.

Dependence of the superconducting transition temperature on the doping level in single-crystalline diamond films.

Homoepitaxial diamond layers doped with boron in the 10(20)-10(21) cm(-3) range are shown to be type II superconductors with sharp transitions (approximately 0.2 K) at temperatures increasing from 0 to 2.1 K with boron contents. The critical concentration for the onset of superconductivity in those 001-oriented single-crystalline films is about 5-7 10(20) cm(-3). The H-T phase diagram has been obtained from transport and ac-susceptibility measurements down to 300 mK.

Anisotropic enhancement of superconductivity in heavy-ion irradiated (K, Ba)BiO3.

We have measured the specific heat, resistivity, and ac susceptibility of (K,Ba)BiO3 single crystals before and after introduction of either point or columnar defects by electron (EI) or heavy-ion irradiation (HII). While the magnetic field dependence of these properties remains mainly unaffected by EI, the irreversibility line and the location of the specific heat anomaly are both shifted up in temperature after HII. The shift is apparent only if the magnetic field is applied parallel to the ion tracks. For perpendicularly applied fields, both lines lie at the same field as in the pristine sample. These experiments call the nature of the vortex liquid state into question.

Entropy of vortex cores near the superconductor-insulator transition in an underdoped cuprate.

We present a study of Nernst effect in underdoped La(2-x)Sr(x)CuO4 in magnetic fields as high as 28 T. At high fields, a sizable Nernst signal was found to persist in the presence of a field-induced nonmetallic resistivity. By simultaneously measuring resistivity and the Nernst coefficient, we extract the entropy of vortex cores in the vicinity of this field-induced superconductor-insulator transition. Moreover, the temperature dependence of the thermoelectric Hall angle provides strong constraints on the possible origins of the finite Nernst signal above T(c), as recently discovered by Xu et al. [Nature (London) 406, 486 (2000)].

Anomalous magnetic field dependence of the thermodynamic transition line in the isotropic superconductor (K,Ba)BiO3.

Thermodynamic (specific heat, reversible magnetization, tunneling spectroscopy) and transport measurements have been performed on high quality (K,Ba)BiO3 single crystals. The temperature dependence of the magnetic field H(C(p)) corresponding to the onset of the specific heat anomaly presents a clear positive curvature. H(C(p)) is significantly smaller than the field H(Delta) for which the superconducting gap vanishes but is closely related to the irreversibility line deduced from transport data. Moreover, the temperature dependence of the reversible magnetization presents a strong deviation from the Ginzburg-Landau theory emphasizing the peculiar nature of the superconducting transition in this material.

Anisotropies of the lower and upper critical fields in MgB2 single crystals.

The temperature dependence of the upper (H(c2)) and lower (H(c1)) critical fields has been deduced from Hall probe magnetization measurements of high quality MgB2 single crystals along the two main crystallographic directions. We show that Gamma(H(c2))=H(c2 axially ab)/H(c2 axially c) and Gamma(H(c1))=H(c1 axially c)/H(c1 axially ab) differ significantly at low temperature (being approximately 5 and approximately 1, respectively) and have opposite temperature dependencies. We suggest that MgB2 can be described by a single field dependent anisotropy parameter gamma(H) (=lambda(c)/lambda(ab)=xi(ab)/xi(c)) that increases from Gamma(H(c1)) at low field to Gamma(H(c2)) at high field.

Direct transition from Bose glass to normal state in the (K,Ba)BiO3 superconductor.

The introduction of columnar defects in (K,Ba )Bi O3 single crystals shifts both the irreversibility and thermodynamic transition lines, respectively, deduced from ac susceptibility (and/or transport) and specific heat measurements, upwards. This shift can be attributed to the defect-induced decrease of the difference (Delta F) between the free energies in the superconducting and the normal states, assuming that the position of the superconducting transition is given by the condition absolute value Delta F approximately k(B )T/xi(3 ). This criterion also perfectly reproduces the influence of the angle between the tracks and the external field. This result suggests that no vortex liquid phase exists in this system.

Evidence for two superconducting energy gaps in MgB(2) by point-contact spectroscopy.

Experimental support is found for the multiband model of the superconductivity in the recently discovered system MgB(2) with the transition temperature T(c) = 39 K. By means of Andreev reflection, evidence is obtained for two distinct superconducting energy gaps. The sizes of the two gaps ( Delta(S) = 2.8 meV and Delta(L) = 7 meV) are, respectively, smaller and larger than the expected weak coupling value. Because of the temperature smearing of the spectra the two gaps are hardly distinguishable at elevated temperatures, but when a magnetic field is applied the presence of two gaps can be demonstrated close to the bulk T(c) in the raw data.

An unusual phase transition to a second liquid vortex phase in the superconductor YBa2Cu3O7.

A magnetic field penetrates a superconductor through an array of 'vortices', each of which carries one quantum of flux that is surrounded by a circulating supercurrent. In this vortex state, the resistivity is determined by the dynamical properties of the vortex 'matter'. For the high-temperature copper oxide superconductors (see ref.1 for a theoretical review), the vortex phase can be a 'solid', in which the vortices are pinned, but the solid can 'melt' into a 'liquid' phase, in which their mobility gives rise to a finite resistance. (This melting phenomenon is also believed to occur in conventional superconductors, but in an experimentally inaccessible part of the phase diagram.) For the case of YBa2Cu3O7, there are indications of the existence of a critical point, at which the character of the melting changes. But neither the thermodynamic nature of the melting, nor the phase diagram in the vicinity of the critical point, has been well established. Here we report measurements of specific heat and magnetization that determine the phase diagram in this material to 26 T, well above the critical point. Our results reveal the presence of a reversible second-order transition above the critical point. An unusual feature of this transition-namely, that the high-temperature phase is the less symmetric in the sense of the Landau theory-is in accord with theoretical predictions of a transition to a second vortex-liquid phase.