Bragg Glass Phase Research Articles

Dynamic phase diagram of driven colloid systems

Using Langevin simulations, we numerically investigate the dynamics phases of driven two-dimensional colloids subject to randomly distributed point-like pinning centers and present phase diagram. For weak disorder strength, the colloid systems form an ordered state and depin into moving Bragg glass phase by increasing driving force. With increasing the strength of pinning, we find a sharp crossover from elastic to plastic depinning where a substantial increase in the depinning force is observed, accompanied by an order to disorder state transition. Increasing the strength of pinning further, a transition to a smectic flow phase occurs where longitudinal order is lost while transverse order remains. Four dynamic phases are found in strong pinning regime upon increasing applied driving force: creeping disordered, plastic flow, smectic flow, and moving Bragg glass phase.

Lindemann criterion and vortex lattice phase transitions in type-II superconductors

We discuss the destruction of vortex lattice order in type-II superconductors by random point pinning and thermal fluctuations based on Lindemann criteria. The location of the melting line and the order-disorder transition, which marks the destruction of the topologically ordered Bragg glass phase and is the reason for the second peak effect, is calculated. We focus on a comparative discussion of different versions of Lindemann criteria and, with regard to experiment, on a comparative discussion of three classes of type-II superconductors---low-${T}_{c},$ anisotropic high-${T}_{c},$ and layered high-${T}_{c}$ materials. Specific attention is paid to the role of nonlocal magnetic interlayer couplings and the softening of elastic moduli at high magnetic fields, which is crucial for low-${T}_{c}$ materials. We also discuss in detail the competing mechanisms of thermal depinning and temperature dependence of the pinning strength through microscopic parameters as well as the crossover between single vortex and bundle pinning for low-${T}_{c}$ materials.

X-ray diffraction of a disordered charge density wave

We study the X-ray diffraction spectrum produced by a collectively pinned charge density wave (CDW), for which one can expect a Bragg glass phase. The spectrum consists of two asymmetric divergent peaks. We compute the shape of the peaks, and discuss the experimental consequences.

Two-Step Melting of the Vortex Solid in Layered Superconductors with Random Columnar Pins

We consider the melting of the vortex solid in highly anisotropic layered superconductors with a small concentration of random columnar pinning centers. Using large-scale numerical minimization of a free-energy functional, we find that melting of the low-temperature, nearly crystalline vortex solid (Bragg glass) into a vortex liquid occurs in two steps as the temperature increases: the Bragg glass and liquid phases are separated by an intermediate Bose glass phase. A suitably defined local melting temperature exhibits spatial variation similar to that observed in experiments.

Specific heat of classical disordered elastic systems.

We study the thermodynamics of disordered elastic systems, applied to vortex lattices in the Bragg glass phase. Using the replica variational method we compute the specific heat of pinned vortons in the classical limit. We find that the contribution of disorder is positive, linear at low temperature, and exhibits a maximum. It is found to be important compared to other contributions, e.g., core electrons, mean field, and nonlinear elasticity that we evaluate. The contribution of droplets is subdominant at weak disorder in d=3.

Evidence of Bragg glass phase in high-Tc vortex states with columnar defects

High-Tc vortex states with sparse and weak columnar defects are investigated numerically, and a new phase characterized by Bragg peaks associated with hexagonal symmetry is found. This new phase corresponds to the Bragg glass phase in high-Tc vortex states with point defects. As the number of columnar defects increases, the melting temperature of this new phase also increases owing to “partial trap” of flux lines to columnar defects. The phase transition from the Bragg glass phase to the Bose glass phase occurs when the number of columnar defects further increases. The “interstitial liquid” phase is also observed between these two glass phases and the vortex liquid phase.

Point-defects-induced vortex phase diagram in high-Tc superconductors: Monte Carlo simulation study

We investigated the vortex phase diagram of high-Tc copper-oxide superconductors in the presence of dense point defects (PDs), by using a Monte Carlo simulation based on the Lawrence–Doniach model. We found a temperature-driven depinning line within the Bragg and vortex glass phases, well below the melting line in the case of high anisotropy. We also found a field-driven transition line from the Bragg-to-vortex glass at low temperatures, accompanied by an abrupt reduction in the interlayer vortex correlation. The complex phase boundaries are drastically controlled by the pinning force of PDs, defect density, and anisotropy.

Vortex- and Bragg-glass phases in bulk MgB 2

A more complete magnetic field–temperature ( H– T) phase diagram, containing the upper critical field H c2( T), the vortex-glass melting line H g( T), and the magnetic irreversibility line H irr( T) has been established for bulk MgB 2 ( T c=38.5 K), synthesized under 200 MPa pressure by hot isostatic pressing (HIPing). Scaling analysis of resistivity data, J c data, and electric field vs current density ( E– J) isotherms in the mixed-state suggest that a Bragg-glass state exists for H< 8 kOe. The critical scaling exponents are dependent upon field and change from ν≈0.6, z≈3.1 in low fields ( H<8 kOe) to ν≈0.9, z≈3.4 in high fields. Magnetization data reveal distinctly different critical current density ( J c) behaviors in high and low magnetic field critical scaling regions.

Vortex Phase Transition and Oxygen Vacancy in YBa2Cu3Oy Single Crystals

The atomic images of YBa 2 Cu 3 O y (YBCO, y ≃ 6.94) single crystals are measured by low-temperature scanning tunneling microscopy (LT-STM). We find that the oxygen vacancies form clusters along the b-axis in the CuO chain layer. Near the clusters, the strong atomic distortion is observed along the a-axis. The vortex phase diagram is very sensitive to the amount of oxygen vacancies in the region between optimal and overdoped regions. For optimally doped untwinned YBCO (y ≃ 6.92), we find a first-order transition T L (H) in the vortex liquid above the terminal point H mcp (≃ 7 T) of both the vortex glass line T g (H) and the field-driven disordering transition line H * (T). The obtained small entropy change (∼ 0.02 k B /vortex/layer) and the critical endpoint H cep (≃ 11 T) of T L (H) indicate that the vortex liquid undergoes the vortex slush regime before the solidification into the vortex glass phase. Below H mcp , the vortex liquid phase shows the first-order melting transition into the Bragg glass phase.

Phase transition in the vortex liquid and the critical endpoint inYBa2Cu3Oy

The vortex phase diagram of optimally doped untwinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ is studied. We find a first-order transition ${T}_{\mathrm{L}}(H)$ in the vortex liquid above the terminal point ${H}_{\mathrm{mcp}}$ $(\ensuremath{\simeq}7\mathrm{T})$ of both the vortex glass line ${T}_{\mathrm{g}}(H)$ and the field-driven disordering transition line ${H}^{*}(T).$ The obtained small entropy change $(\ensuremath{\sim}0.02$ ${k}_{\mathrm{B}}/\mathrm{vortex}/\mathrm{layer})$ and the critical endpoint ${H}_{\mathrm{cep}}$ $(\ensuremath{\simeq}11\mathrm{T})$ of the ${T}_{\mathrm{L}}(H)$ line indicate that the vortex liquid undergoes the vortex slush regime before the solidification into the vortex glass phase. Below ${H}_{\mathrm{mcp}},$ the vortex liquid phase shows the first-order melting transition into the Bragg glass phase. We also study the oxygen content y dependence of the vortex phase diagram and find that the vortex slush regime is located in the borderline (i.e., $6.90&lt;~y&lt;~6.92)$ below which the vortex lattice melting transition disappears. The result indicates that the point disorder with the intermediate strength plays an important role in the vortex slush regime.

Thermodynamics of disordered elastic systems in the Bragg glass phase

We study the thermodynamics of a pinned quantum object when the elastic description applies, e.g. in the Bragg glass phase for a crystal with point disorder or for a single elastic line. Using the replica variational method we compute the specific heat both in the quantum and classical limits. In the quantum regime, we show that the specific heat behaves - at low temperature - as T3 in dimension $d = 2$ and $d = 3$.

Disordered elastic systems and electronic crystals

Electrons can crystallize to form a Wigner crystal. This crystallization is particularly effective in two dimensions. The effect of disorder on such electronic crystals can be taken into account using the same techniques and concepts, in particular the notion of Bragg glass phase, than the one developed to tackle classical disordered elastic systems. We analyze the properties of such a disordered Wigner crystal and discuss the physical consequences, both for the thermodynamics (compressibility etc.) and for the transport properties. This approach allows a good description of the optical conductivity and in particular to obtain correctly the density and field dependence of the pinning frequency. Relevance to experimental systems is discussed.

The effect of pointlike disorder on current-driven vortex state of Bi 2Sr 2CaCu 2O 8+ δ

We studied the DC current-driven vortex state of a Bi 2Sr 2CaCu 2O 8+ δ model in the presence of pointlike disorder via a Monte Carlo simulation. We found that the vortex drift velocity v as a function of temperature T drastically changes twice at a depinning ( T dp) and a melting ( T m) temperature, as is consistent with our two-stage melting scenario. At the low field region, whereas v remains almost zero for T< T dp, it rapidly grows for T dp< T< T m and the Bragg peak intensity survives for T< T m. We thus give numerical evidence that a moving Bragg glass phase exists for the intermediate temperature regime of T dp< T< T m.

No ending point on the Bragg glass phase transition line at low temperatures

We have measured the magnetic hysteresis loops and the magnetic relaxation for $Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi-2212) single crystals which exhibit the second magnetization peak effect. Although no second peak effect is observed below 20 K in the measurement with fast field sweeping rate, it is found that the second peak effect will appear again after long time relaxation or in a measurement with very slow field sweeping rate at 16 K. It is anticipated that the peak effect will appear at very low temperatures (approaching zero K) when the relaxation time is long enough. We attribute this phenomenon to the profile of the interior magnetic field and conclude that the phase transition line of Bragg glass to vortex glass has no ending point at low temperatures.

Probing phase transitions of vortex matter by Josephson plasma resonance

The Josephson plasma resonance is the most powerful means to study the vortex state in high-Tc superconductors. In this paper we report the detailed and quantitative study of the interlayer quantum phase coherence in the vortex liquid, Bragg glass and vortex glass phases of Bi2Sr2CaCu2O8+δ by the Josephson plasma resonance. We also provide a quantitative discussion on the nature of the phase transitions among these vortex phases.

Vortex phase diagram of a weakly pinned YBa2Cu3O7−δ crystal for H || c

The vortex phase diagram in a weakly pinned crystal of YBa2Cu3O7−δ (YBCO) for H || c is reviewed in the light of a recent elucidation of the process of ‘inverse melting’ in a bismuth cuprate system and the imaging of an interface between the ordered and the disordered regions across the peak effect in 2H-NbSe2. In the given YBCO crystal, a clear distinction can be made between the second magnetization peak and the peak effect in between 65 K and 75 K. The field region between the peak fields of the second magnetization peak (Hmsmp) and the onset fields of the peak effect (Honpe) is not only continuously connected to the Bragg glass phase at lower fields, but it is also sandwiched between the higher temperature vortex liquid phase and the lower temperature vortex glass phase. Thus, an ordered vortex state between (Hmsmp) and (Honpe) can get transformed to the (disordered) vortex liquid state on heating as well as to the (disordered) vortex glass state on cooling, a situation analogous to the thermal melting and the inverse melting phenomenon seen in a bismuth cuprate.

Josephson plasma resonance in underdoped Bi 2Sr 2CaCu 2O 8+ δ crystals

Using two methods, the bolometric method and the cavity perturbation technique, we have observed the Josephson plasma resonance (JPR) in heavily underdoped Bi 2Sr 2CaCu 2O 8+ δ crystals ( T c=69.4 K) in the Bragg-glass phase in different magnetic fields. From these data, we obtain the penetration depth along the c-axis, λ c (0)=229±10 μm. The JPR results yielded an experimental estimate of the wandering length r w of vortex pancakes in the samples ( r w≈300–550 nm at 52 K depending on the magnetic field applied). We observe an increase of r w with increasing applied dc magnetic field applied.

Pinned Wigner crystals

We study the effects of weak disorder on a Wigner crystal in a magnetic field. We show that an elastic description of the pinned Wigner crystal provides an excellent framework to obtain most of the physically relevant observables. Using such a description, we compute the static and dynamical properties. We find that, akin to the Bragg glass phase, a good degree of translational order survives (up to a large lengthscale in $d=2$, infinite in $d=3$). Using a gaussian variational method, we obtain the full frequency dependence of the conductivity tensor. The zero temperature Hall resistivity is independent of frequency and remains unaffected by disorder at its classical value. We show that the characteristic features of the conductivity in the pinned Wigner crystal are dramatically different from those arising from the naive extrapolations of Fukuyama-Lee type theories for charge density waves. We determine the relevant scales and find that the physical properties depend crucially on whether the disorder correlation length is larger than the cyclotron length or not. We analyse, in particular, the magnetic field and density dependence of the optical conductivity. Within our approach the pinning frequency can increase with increasing magnetic field and varies as $n^{-3/2}$ with the density $n$. We compare our predictions with recent experiments on transport in two dimensional electron gases under strong magnetic fields. Our theory allows for a consistent interpretation of these experiments in terms of a pinned WC.

Vortex state of high- Tc superconductors studied by Josephson plasma resonance

The Josephson plasma resonance (JPR), which is a phase collective excitation mode representing the Cooper-pair oscillation mode, is a most powerful means to study the vortex state in Josephson coupled high- T c superconductors (HTSC). In this paper, we report the detailed and quantitative study of the interlayer quantum phase coherence in the vortex liquid, Bragg glass and vortex glass phases of Bi 2Sr 2CaCu 2O 8+ δ by the JPR. We also provide a quantitative discussion on the nature of the phase transitions among these vortex phases. On the basis of these results, we discuss the vortex phase diagram of HTSC.

Effect of electron irradiation on vortex dynamics inYBa2Cu3O7−δsingle crystals

We report on drastic change of vortex dynamics with increase of quenched disorder: for rather weak disorder we found a single vortex creep regime, which we attribute to a Bragg-glass phase, while for enhanced disorder we found an increase of both the depinning current and activation energy with magnetic field, which we attribute to entangled vortex phase. We also found that introduction of additional defects always increases the depinning current, but it increases activation energy only for elastic vortex creep, while it decreases activation energy for plastic vortex creep.