We calculate the magnetic field dependence of quasiparticle transport properties in the vortex state of a d-wave superconductor arising solely from the quasiparticle's Doppler shift in the superflow field surrounding the vortex. Qualitative features agree well with experiments on cuprate and heavy fermion superconductors at low fields and temperatures. We derive scaling relations in the variable T /H 1/2 valid at sufficiently low temperatures T and fields H, but show that these relations depend on the scattering phase shift, and are in general fulfilled only approximately even in the clean limit, due to the energy dependence of the quasiparticle relaxation time.PACS Numbers: 74.25.Fy,74.60.Ec Introduction. While the origins of high-temperature superconductivity and the non-Fermi liquid nature of the normal state in the cuprates are not understood, recently a consensus has been emerging that the superconducting state itself is not particularly exotic, in the sense that it consists of a BCS-like pair state with well-defined quasiparticle excitations above it. Although the order parameter in these materials is now thought to display d-wave symmetry, ranking them among the few known "unconventional" superconductors, it has been argued that the prediction of observable properties in the superconducting state is now a relatively routine task.In the study of transport properties, however, questions arise which prevent one from drawing such sanguine conclusions. Recent measurements of thermal conductivity in both the LSCO-214 and BSCCO-2212 systems have hinted at qualitatively new physics in the vortex state at low temperatures and fields. [1,2] In the LSCO case, a logarithmic dependence on field has been found suggestive of quantum interference effects; in the BSCCO case, a kink in the thermal conductivity as a function of field occurs, apparently signaling a transition to a new superconducting phase at higher fields.In order to extract which aspects of the new phenomena are due to qualitatively "new" physics, one needs first to understand which aspects can be attributed to the perhaps more mundane but still largely unexplored phenomenology of quasiparticles in the d-wave vortex state. A fundamental observation regarding the thermodynamics of this state was made by Volovik, who pointed out that, in contrast to classic superconductors, in d-wave systems the entropy and density of states was dominated by contributions from extended quasiparticle states rather than the bound states associated with vortex cores. The remarkable consequence of this observation, which occurs due to the existence of order parameter nodes in the clean d-wave state, is a term in the specific heat of the superconductor in a field varying as √ HT rather than as HT as in the classic case. Other calculations, dependent only on the Dirac-like spectrum of nodal quasiparticles excited at low temperature, gave the field dependence of the density of states N (ω; H) [4] and predicted the specific heat should scale as C(T ; H)/T 2 ∼ F C (X), where X ≡ T...

We consider the problem of the vortex contribution to thermal properties of dirty d-wave superconductors. In the clean limit, the main contribution to the density of states in a d-wave superconductor arises from extended quasiparticle states which may be treated semiclassically, giving rise to a specific heat contribution δC(H) ∼ H 1/2 . We show that the extended states continue to dominate the dirty limit, but lead to a H log H behavior at the lowest fields, Hc1 < ∼ H ≪ Hc2. This crossover may explain recent discrepancies in specific heat measurements at low temperatures and fields in the cuprate superconductors. We discuss the range of validity of recent predictions of scaling with H 1/2 /T in real samples.PACS Numbers: 74.25.Fy,74.25.Jb Introduction. With the growing consensus that the symmetry of the cuprate superconductors is d-wave [1] has come a renewed interest in the properties of the vortex state in "unconventional" superconductors with order parameter nodes. Many of the basic ideas about how this state differs from the conventional Abrikosov state in classic superconductors were worked out already in the context of rotating 3 He and heavy fermion superconductors. Recently, however, a number of novel features of the problem peculiar to those systems with Dirac spectrum (line nodes in 3D or point nodes in 2D with order parameter vanishing linearly with angle on the Fermi surface) have been pointed out. Volovik [2] showed that, in contrast to conventional superconductors, extended quasiparticle states with momentum k near order parameter nodal directions k n dominate the density of states at zero energy. This leads to a specific heat which varies as δC(H) ∼ H 1/2 , in contrast to classic superconductors, where localized quasiparticle states in vortex cores lead to a scaling of δC(H) ∼ H since the number of vortices scales proportionally to the field. Simon and Lee [3] then showed that thermal and transport properties exhibit a scaling with H 1/2 /T , again arising simply from the low-energy Dirac form of the electronic spectrum.The predicted proportionality of the electronic specific heat to √ H was in fact identified in measurements on high quality single crystals by Moler et al.,[4] one of the crucial early experiments lending credence to the d-wave hypothesis. However, the interpretation of the observed √ H dependence has been questioned by Ramirez [5] who points out that there are well-known cases where classic superconductors show a similar "nonanalytic" behavior sufficiently close to the lower critical field H c1 . Furthermore, experimental results of Fisher et al [6] and Revaz et al. [7] cannot be well fit by a √ H form. The above scaling predictions hold, strictly speaking, for clean d-wave superconductors and for energy scales small compared to the maximum gap scale ∆ 0 . To make realistic predictions for experiments, deviations from scaling due to disorder and other real-materials effects must be accounted for. In this work, we study the

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A quantitative description of the transition to a quantum disordered phase in a doped antiferromagnet is obtained with a U(1) gauge-theory, where the gap in the spin-wave spectrum determines the strength of the gauge-fields. They mediate an attractive long-range interaction whose possible bound-states correspond to charge-spin separation and pairing.

We study a doped antiferromagnet (AF) using a rotating reference-frame. Whereas in the laboratory reference-frame with a globally fixed spin-quantization axis (SQA) the long-wavelength, lowenergy physics is given by the O(3) non-linear σ-model with current-current interactions between the fermionic degrees of freedom and the order-parameter field for the spin-background, an alternative description in form of an U(1) gauge theory can be derived by choosing the SQA defined by the local direction of the order-parameter field via a SU(2) rotation of the fermionic spinor. Within a large-N expansion of this U(1) gauge theory we obtain the phase diagram for the doped AF and identify the relevant terms due to doping that lead to a quantum phase transition at T = 0 from the antiferromagnetically ordered Néel phase to the quantum-disordered (QD) spin-liquid phase. Furthermore, we calculate the propagator of the corresponding U(1) gauge field, which mediates a long-range transverse interaction between the bosonic and fermionic fields. It is found that the strength of the propagator is proportional to the gap of the spin-excitations. Therefore, we expect as a consequence of this long-range interaction the formation of bound states when the spin-gap opens, i.e. in the QD spin-liquid phase. The possible bound states are spin-waves with a (spin-) gap in the excitation spectrum, spinless fermions and pairs of fermions. Thus, an alternative picture for charge-spin separation emerges, with composite charge-separated excitations. Moreover, the present treatment shows an intimate connection between the opening of the spin-gap and charge-spin separation as well as pairing.