Structure of the intermediate state in type-I superconducting lead (Pb) is shown to be very sensitive to the ramp rate of an applied magnetic field. The configurations of resulting static patterns depend sensitively on the shape of the specimen. In particular, geometric barrier, present in the samples with rectangular cross-section, plays an important role in determining the sharp boundary between the phases of different topology. We propose that seemingly laminar (stripe) pattern obtained as a result of the fast field ramp is simply an imprint left behind by the fast-moving flux tubes. Our results confirm that flux tube phase is topologically favorable.
We present a phenomenological model for the vortex dynamics in the peak effect region of weakly pinned superconductors. We explain the history dependent dynamic response of the metastable vortex states subjected to a transport current and the hysteretic voltage-current characteristics observed in the vicinity of peak effect in weakly pinned superconductors. A strong variation in voltage current characteristics with the current sweep rate and the anomalous dependence of critical current density $J_c$ on the magnetic field sweep rate have also been accounted for by this model.
We investigated transient optical responses in an optimally-doped high-Tc superconductor La2-xSrxCuO4 (x=0.15) by using 800-nm optical pump and terahertz probe spectroscopy. With increasing the photoexcitation intensities, the Josephson plasma resonance shows a gradual redshift, indicating the suppression of superconductivity by the photoexcitation. With further increasing the photoexcitation intensities, a new longitudinal mode in the loss function spectrum appears and grows from the high energy side, accompanied by a new transverse mode as manifested in the conductivity spectrum. The observe…
The interaction between the telegraph noise and background voltage fluctuations in the current induced dissipative state of high-Tc BiSrCaCuO thin films has been investigated. Experimental time records of the voltage drop across current biased thin film strips show markedly different background noise traces in the up and down telegraph states. Detailed analysis demonstrates that fluctuations around the telegraph voltage levels are due to a unique background noise process. The apparent quiet and noisy voltage states are due only to differences in the effective frequency bandwidth at which backg…
Intense debate has recently arisen regarding the photoinduced changes to the iron-chalcogenide superconductors, including the enhancement of superconductivity and a metastable state. Here, by employing high energy resolution, we directly observe the melting of superconductivity on ultrafast timescales. We demonstrate a distinctly nonequilibrium response on short timescales, where the gap fills in prior to the destruction of the superconducting peak, followed by a metastable response. We propose that the former is due to pair phase decoherence and speculate that the latter is due to the increas…
We present here some newer characteristics pertaining to paramagnetic Meissner effect like response in a single crystal of the low Tc superconducting compound 2H-NbSe2 via a detailed study of effects of perturbation on the field-cooled magnetization response. In the temperature range, where an anomalous paramagnetic magnetization occurs, the field-cooled magnetization response is found to be highly metastable: it displays a curious tendency to switch randomly from a given paramagnetic value to a diamagnetic or to a different paramagnetic value, when the system is perturbed by an impulse of an …
The flux lattice driven by a uniform driving force in a superconductor with hot, strong, sharp and randomly distributed pinning centers, with applied magnetic field half the matching field is simulated. At low temperature both a non activated regime, where flux motion occurs within a robust percolative flux flow channel, and an activated regime are obtained depending on the sample preparation. These two regimes exhibit distinct resistivity and magnetic induction. In the non activated regime, a clear fingerprint is observed in the autocorrelation function of the longitudinal resitivity, which o…
We examine a contact between a superconductor whose order parameter changes sign across the Brillioun zone, and an ordinary, uniform-sign superconductor. Within a Ginzburg-Landau type model, we find that if the the barrier between the two superconductors is not too high, the frustration of the Josephson coupling between different portions of the Fermi surface across the contact can lead to surprising consequences. These include time-reversal symmetry breaking at the interface and unusual energy-phase relations with multiple local minima. We propose this mechanism as a possible explanation for …
A15 Nb$_3$Si is, until now, the only high temperature superconductor produced at high pressure (~110 GPa) that has been successfully brought back to room pressure conditions in a metastable condition. Based on the current great interest in trying to create metastable-at-room-pressure high temperature superconductors produced at high pressure, we have restudied explosively compressed A15 Nb$_3$Si and its production from tetragonal Nb$_3$Si. First, diamond anvil cell pressure measurements up to 88 GPa were performed on explosively compressed A15 Nb$_3$Si material to trace Tc as a function of pre…
Sr2RuO4, a leading-candidate spin-triplet superconductor and a highly anisotropic quasi-two-dimensional type-II superconductor, provides unique opportunity to study unconventional as well as conventional vortex phases. To investigate its vortex-matter phases, we studied the ac susceptibility of Sr2RuO4 for fields parallel to the RuO2 plane by adapting two different thermal processes: In addition to the ordinary field sweep (FS) process, we newly employed the "each-point field cooling (EPFC)" process, in which the superconductivity is once thermally destroyed before collecting the data. We find…
Photoexcitations on a superconductor using ultrafast nir-infrared (NIR) pulses, whose energy is much higher than the superconducting energy gap, are expected to suppress/destroy superconductivity by breaking Cooper pairs and excite quasiparticles from occupied state to unoccupied state far above the Fermi level. This appears to be true only for small pumping fluence. Here we show that the intense NIR pumping has different effect. We perform an intense NIR pump, c-axis terahertz probe measurement on an electron-doped cuprate superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$ with T$_c$=22 K. The me…
The peak effect in weakly pinned superconductors is accompanied by metastable vortex states. Each metastable vortex configuration is characterized by a different critical current density J_c, which mainly depends on the past thermomagnetic history of the superconductor. A recent model [G. Ravikumar, et al, Phys. Rev. B 61, R6479 (2000)] proposed to explain the history dependent J_c postulates a stable state of vortex lattice with a critical current density J_c^{st}, determined uniquely by the field and temperature. In this paper, we present evidence for the existence of the stable state of the…
We present a study of the behaviour of metastable vortex states in mesoscopic superconductors. Our analysis relies on the London limit within which it is possible to derive closed analytical expressions for the magnetic field and the Gibbs free energy. We consider in particular the situation where the vortices are symmetrically distributed along a closed ring. There, we obtain expressions for the confining Bean-Livingston barrier and for the magnetization which turns out to be paramagnetic away from thermodynamic equilibrium. At low temperature, the barrier is high enough for this regime to be…
We study the effect of a strong electric field on the fluctuation conductivity within the time-dependent Ginzburg-Landau theory for the case of arbitrary dimension. Our results are based on the analytical derivation of the velocity distribution law for the fluctuation Cooper pairs, from the Boltzmann equation. Special attention is drawn to the case of small nonlinearity of conductivity, which can be investigated experimentally. We obtain a general relation between the nonlinear conductivity and the temperature derivative of the linear Aslamazov-Larkin conductivity, applicable to any supercondu…
The breakdown of crystalline order in a disordered background connects to some of the most challenging problems in condensed matter physics. For a superconducting vortex lattice, the equilibrium state in the presence of impurities is predicted to be a "Bragg glass" (BG), where the local crystalline order is maintained everywhere and yet the global positional order decays algebraically. Here, using scanning tunnelling spectroscopy (STS) we image the vortex lattice in a weakly pinned NbSe2 single crystal. We present direct evidence that the ordered state of the VL is a BG, consisting of a large …
The large increase in voltage noise, commonly observed in the vicinity of the peak-effect in superconductors, is ascribed to a novel noise mechanism. A strongly pinned metastable disordered vortex phase, which is randomly generated at the edges and annealed into ordered phase in the bulk, causes large fluctuations in the integrated critical current of the sample. The excess noise due to this dynamic admixture of two distinct phases is found to display pronounced reentrant behavior. In the Corbino geometry the injection of the metastable phase is prevented and, accordingly, the excess noise dis…
The attenuation of ultrasound (the geometric resonance) in an intermediate state of the type I superconductors at kaN >> 1 is researched. The oscillating dependence of ultrasound attenuation, which has an amplitude modulation as a result of presence of the Andreev reflec-tions by the electronic excitations on the boundaries between the normal metal layer and the superconducting layer in an intermediate state of the type I superconductor, is obtained. The derived theoretical equation explains the nature of experimental results in [1, 2].
Intermediate state (IS) flux structures in mesoscopic type-I superconductors are investigated within the Ginzburg-Landau theory. In addition to well-established tubular and laminar structures, the strong confinement leads to the formation of (i) a phase of singly quantized vortices, which is typical for type-II superconductors and (ii) a ring of a normal domain at equilibrium. The stability region and the formation process of these IS flux structures are strongly influenced by the geometry of the sample.
M. Tinkham and P. G. de Gennes, described in their books the existence of an intermediate type-I superconductor as a consequence of an external surface that affects the well known classification of superconductors into type-I and II. Here we consider the mesoscopic superconductor where the ratio volume to area is small and the effects of the external surface are enhanced. By means of the standard Ginzburg-Landau theory the Tinkham-de Gennes scenario is extended to the mesoscopic type-I superconductor. We find new features of the transition at the passage from the genuine to the intermediate ty…
Using a powerful combination of Coleman's instanton technique and the method of Banks and Bender, the exponential factor for the zero temperature rate of tunneling out of metastable vacuum in a system of two identical capacitively coupled phase qubits is calculated in closed form to second order in asymmetry parameter for a special case of intermediate coupling C=C_J/2.
The magnetic vortices in superconductors usually repel each other. Several cases are discussed when the vortex interaction has an attractive tail and thus a minimum, leading to vortex clusters and chains. Decoration pictures then typically look like in the intermediate state of type-I superconductors, showing lamellae or islands of Meissner state or surrounded by Meissner state, but with the normal regions filled with Abrikosov vortices that are typical for type-II superconductors in the mixed state. Such intermediate-mixed state was observed and investigated in detail in pure Nb, TaN and othe…
Magneto-optical imaging of thick stress-free lead samples reveals two distinct topologies of the intermediate state. Flux tubes are formed upon magnetic field penetration (closed topology) and laminar patterns appear upon flux exit (open topology). Two-dimensional distributions of shielding currents were obtained by applying an efficient inversion scheme. Quantitative analysis of the magnetic induction distribution and correlation with magnetization measurements indicate that observed topological differences between the two phases are responsible for experimentally observable magnetic hysteres…
In a composite superconductor in uniform rotation, the London field strength at equilibrium is given by the usual expression B_L = 2m Omega/e; here m corresponds to the bare electron mass, although the effective mass m* can be different in different layers. In the presence of strong angular accelerations, however, transient phases and differences in m* can become relevant. In particular, if the layers are orthogonal to the rotation axis and one of them is much thinner than the others, the superconductor may enter metastable states characterized by intense "slide" supercurrents in this layer. W…
We study s-wave superconductivity in the attractive Hubbard model in an applied magnetic field and assume the extreme Pauli limit where the orbital critical field is much greater than the Zeeman critical field. We work at a coupling corresponding roughly to the peak $T_c$ in the BCS to BEC crossover window and retain the crucial amplitude and phase fluctuations. At low field, as expected, the superconductor undergoes a second order thermal transition to the normal state, and is only weakly magnetized near $T_c$. At intermediate fields the thermal transition is still second order, but the magne…
Hydrogen-rich compounds have been extensively studied both theoretically and experimentally in the quest for novel high-temperature superconductors. Reports on sulfur-hydride attaining metallicity under pressure and exhibiting superconductivity at temperatures as high as 200 K have spurred an intense search for room-temperature superconductors in hydride materials. Recently, compressed phosphine was reported to metallize at pressures above 45 GPa, reaching a superconducting transition temperature (T$_{c}$) of 100 K at 200 GPa. However, neither the exact composition nor the crystal structure of…
Dynamic structure of the intermediate state was studied in pinning-free thick Pb strips using real-time magneto-optical visualization. It is found that topological hysteresis can be lifted by applying sufficiently large current. Namely, laminar structure that appears on flux exit in a static case is turned into tubular when the sufficiently large transport current is present. Size and distribution of the flux tubes in static and dynamic regimes are different. Temperature, magnetic field and current phase diagram is discussed.
We present simulations of the intermediate state of type-I superconducting films solving the time dependent Ginzburg-Landau equations, which include the demagnetizing fields via the Biot-Savart law. For small square samples we find that, when slowly increasing the applied magnetic field $H_a$, there is a saw-tooth behavior of the magnetization and very geometric patterns, due to the influence of surface barriers; while when slowly decreasing $H_a$, there is a positive magnetization and symmetry-breaking structures. When random initial conditions are considered, we obtain droplet and laberynthi…
The geometric structure of an intermediate state in the high pure Gallium single crys-tal at the external magnetic field Hext at the temperature T=0.4 K is researched, using the longi-tudinal ultrasonic signal attenuation method at the ultrasonic signal frequency of 30 MHz. It is experimentally shown that the edge inhomogeneities of the magnetic field distribution have an influence on the structure of an intermediate state in the cylindrical superconductor samples at the transverse orientation of external magnetic field Hext. It is shown that the use of the super-conducting plane screens of Nb…
The vortex lattice (VL) symmetry and orientation in clean type-II superconductors depends sensitively on the host material anisotropy, vortex density and temperature, frequently leading to rich phase diagrams. Typically, a well-ordered VL is taken to imply a ground state configuration for the vortex-vortex interaction. Using neutron scattering we studied the VL in MgB2 for a number of field-temperature histories, discovering an unprecedented degree of metastability in connection with a known, second-order rotation transition. This allows, for the first time, structural studies of a well-ordere…
We present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction $U$ and (ii) the intersite charge exchange term $I$, determining the hopping of electron pairs between nearest-neighbour sites. In the analysis of the phase diagrams and thermodynamic properties of this model we treat the intersite interactions within the mean-field approximation. In this report we focus on metastable phases and determine their ranges of occurrence. Our investiga…
High-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres and discs. Combined with the measurements of macroscopic magnetization these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to geometric barrier that results in a topological hysteresis -- flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have geometric barrie…
To address unsolved fundamental problems of the intermediate state (IS), the equilibrium magnetic flux structure and the critical field in a high purity type-I superconductor (indium film) are investigated using magneto-optical imaging with a 3D vector magnet and electrical transport measurements. The least expected observation is that the critical field in the IS can be as small as nearly 40% of the thermodynamic critical field $H_c$. This indicates that the flux density in the \textit{bulk} of normal domains can be \textit{considerably} less than $H_c$, in apparent contradiction with the lon…
The self-consistent solutions of a nonlinear Ginzburg--Landau equations, which describe the behavior of a superconducting plate of thickness 2D in a magnetic field H parallel to its surface (provided that there are no vortices inside the plate), are studied. We distinguish two types of superconductors according to the behavior of their magnetization M(H) in an increasing field. The magnetization can vanish either by a first order phase transition (type-I superconductors), or by a second order (type-II). The boundary S_{I-II}, which separates two regions (I and II) on the plane of variables (D,…
To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the meltin…
In the intermediate state of a thin type-I superconductor magnetic flux penetrates in a disordered set of highly branched and fingered macroscopic domains. To understand these shapes, we study in detail a recently proposed "current-loop" (CL) model that models the intermediate state as a collection of tense current ribbons flowing along the superconducting-normal interfaces and subject to the constraint of global flux conservation. The validity of this model is tested through a detailed reanalysis of Landau's original conformal mapping treatment of the laminar state, in which the superconducto…
We show that, based on the critical state model for flux-line pinning in hard superconductors, one can assess the magnetic moment relaxation induced by the oscillations of a perpendicular magnetic field. Our theory follows a recent proposal of using phenomenological 2D modeling for the description of crossed field dynamics in high-T$_c$ superconductors [{\tt arXiv:cond-mat/0703330}]. Stationary regimes with either saturation to metastable configurations, or complete decay to the thermodynamic equilibrium are obtained. The transition between both types of response is related to the disappearanc…
Two experiments are described which are related to the problem of localized Cooper pairs. Magnetic-field-tuned superconductor-insulator transition was studied in amorphous In--O films with onset of the superconducting transition in zero field near 2 K. Experiments performed in the temperature range T>0.3 K indicate that at the critical field, B=B_c, the first derivative of the resistance dR/dT is non-zero at T=0 and hence the scaling relations should be written in more general form. Study of the magnetotransport of high-resistance metastable alloy Cd-Sb on the insulating side of the supercondu…
The importance of accounting for the inhomogeneity of the magnetic field distribution and roundness of domain walls near the surface of type-I superconductors in the intermediate state for forming the equilibrium flux structure was predicted by Landau eight decades ago. Further studies confirmed this prediction and extended it to all equilibrium properties of this state. Here we report on direct depth-resolved measurements of the field distribution and shape of domains near the surface of high-purity type-I (indium) films in a perpendicular field using Low-Energy Muon Spin Rotation spectroscop…
The hole doped Fe-based superconductors Ba$_{1-x}$A$_x$Fe$_2$As$_2$ (where A=Na or K) show a particular rich phase diagram. It was observed that an intermediate re-entrant tetragonal phase forms within the orthorhombic antiferromagnetically-ordered stripe-type spin density wave state above the superconducting transition [S. Avci et al., Nature Comm. 5, 3845 (2014), A. E. Böhmer et al., arXiv:1412.7038v2]. A similar intermediate phase was reported to appear if pressure is applied to underdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ [E. Hassinger et al., Phys. Rev. B 86, 140502(R) (2012)]. Here we report d…
Relaxation Dynamics of Superconducting/Normal Interfaces in the Intermediate State of a type-I superconductor
Low Temperature Physics Laboratory, College of Physics & Center of Quantum Materials and Devices, Chongqing University（重庆大学物理学院低温物理实验室与量子材料与器件中心）；Materials Genome Institute, Shanghai University（上海大学材料基因组研究院）
The formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains surrounded by the superconducting phase. The distribution of domain surface areas is found to exhibit a threshold, above which only the lamellar shape is observed. We show that this threshold coincides with the predicted critical surface area for the elongation instability of the circular shape. The partition of the normal phase into circular and lamellar d…
A simplified model of c axis transport in the high T_c superconductors is presented. Expressions are found for the c axis optical conductivity, the d.c. resistivity, and the c axis penetration depth. Within the framework of this model, the pseudogap in the optical conductivity arises naturally as a result of the layered band structure of the high T_c materials. We discuss the occurence of the pseudogap in terms of three parameters: a band gap Delta_{ps}, a temperature dependent scattering rate Gamma(T), and the strength of the interlayer coupling t_{perp}. We are also able to find analytic exp…
We report the synthesis and superconducting properties of a metastable form of the known superconductor NaxCoO2*yH2O (x ~ 1/3, y ~ 4x). Instead of using the conventional bromine-acetonitrile mixture for sodium deintercalation, we use an aqueous bromine solution. Using this method, we oxidize the sample to a point that the sodium cobaltate becomes unstable, leading to formation of other products if not controlled. This compound has the same structure as the reported superconductor, yet it exhibits a systematic variation of the superconducting transition temperature (Tc) as a function of time. I…
We investigate two-dimensional Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to an additional depletion of the superfluid density. We demonstrate the existence of the intermediate superfluid state where the condensate and localized bosons present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto the three dimensiona…
Superconductors have the potential to revolutionize technology due to their ability to have zero electrical resistance. However, superconductor materials require either low temperatures or high pressures to function in a superconductive state. Thus, researchers are now on the search for the first-ever room temperature, ambient pressure superconductor. Yet, recent discoveries have only shown superconductors that work at low temperatures with ambient pressure or room temperature with high pressures. The region between these two extremes has not been identified due to the number of variables that…
We suggest a mechanism which promotes the existence of a phase soliton -- topological defect formed in the relative phase of superconducting gaps of a two-band superconductor with s+- type of pairing. This mechanism exploits the proximity effect with a conventional s-wave superconductor which favors the alignment of the phases of the two-band superconductor which, in the case of s+- pairing, are pi-shifted in the absence of proximity. In the case of a strong proximity such effect can be used to reduce soliton's energy below the energy of a soliton-free state thus making the soliton thermodynam…
We study the thermodynamics of the diffusive SFS trilayer composed of thin superconductor (S) and ferromagnet (F) layers. On the basis the self-consistent solutions of nonlinear Usadel equations in the F and S layers we obtain the Ginzburg--Landau expansion and compute the condensation free energy and entropy of the $0$ (even) and $π$ (odd) order parameter configurations. The first order $0-π$ transition as a function of temperature $T$ occurs, which is responsible for a jump of the averaged magnetic field penetration depth $λ(T)$ recently observed on experiments [N.Pompeo, et. al., Phys. Rev.…
We analyze the local density of states (LDOS) of heterostructures consisting of alternating ferromagnet, $F$, and superconductor, $S$, layers. We consider structures of the $SFS$ and $SFSFSFS$ type, with thin nanometer scale $F$ and $S$ layers, within the ballistic regime. The spin-splitting effects of the ferromagnet and the mutual coupling between the $S$ regions, yield several nontrivial stable and metastable pair amplitude configurations, and we find that the details of the spatial behavior of the pair amplitude govern the calculated electronic spectra. These are reflected in discernible s…
Normal state bubble patterns in Type I superconducting Indium and Lead slabs are studied by the high resolution magneto-optical imaging technique. The size of bubbles is found to be almost independent of the long-range interaction between the normal state domains. Under bubble diameter and slab thickness proper scaling, the results gather onto a single master curve. On this basis, in the framework of the "current-loop" model [R.E. Goldstein, D.P. Jackson and A.T. Dorsey, Phys. Rev. Lett. 76, 3818 (1996)], we calculate the equilibrium diameter of an isolated bubble resulting from the competitio…
The calculation of spatial structure of a quantum intermediate state in high pure type I superconductors in external magnetic field at low temperatures is completed. The theoretical model of thermodynamics of intermediate state in type I superconductors was proposed by Andreev. It is shown, that in the quantum case, the period of structure of quantum intermediate state appears to be significantly shorter and it has different dependences on the magnetic field H and temperature T in comparison with the classical intermediate Landau state. The decrease of thickness of normal layers results in the…
In this work we study by numerical methods the phase dynamics in ballistic graphene-based short Josephson junctions. The supercurrent through a graphene junction shows a non-sinusoidal phase-dependence, unlike a conventional junction ruled by the well-known d.c. Josephson relation. A superconductor-graphene-superconductor system exhibits superconductive quantum metastable states similar to those present in normal current-biased JJs. We explore the effects of thermal and correlated fluctuations on the escape time from these metastable states, when the system is stimulated by an oscillating bias…
Controlled Manipulation of Intermediate State in a Type-I Superconductor
Materials Genome Institute, Shanghai University（上海大学材料基因组研究院）；Department of Physics, Shanghai Key Laboratory for High Temperature Superconductors, Shanghai University（上海大学物理系高温超导上海市重点实验室）；Institute for Quantum Science and Technology, Shanghai University（上海大学量子科学与技术研究院）
We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anom…
We investigate the magnetization processes of a standard Ginzburg-Landau model for chiral p-wave superconducting states in an applied magnetic field. We find that the phase diagram is dominated by triangular lattices of doubly quantized vortices. Only in close vicinity to the upper critical field, the lattice starts to dissociate into a structure of single-quanta vortices. The degeneracy between states with opposite chirality is broken in a nonzero field. If the magnetization starts with an energetically unfavorable chirality, the process of chirality-inversion induced by the external magnetic…
We explore a BCS Bose Einstein crossover scenario for $0 \leq T \leq T_c$ and its implications for the superfluid density and specific heat. The low lying excitations consist of nodal (fermionic) quasi-particles as well as excited (bosonic) pair states. Semi-quantitative comparison with cuprate data is reasonable, with no compelling indications for Landau parameter effects.
