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P. J. Hirschfeld

Publications and source records attributed to P. J. Hirschfeld.

At least 235 records · Page 13Linked to original sources
arXiv1999

Anisotropic thermodynamics of d-wave superconductors in the vortex state

We show that the density of states and the thermodynamic properties of a 2D d-wave superconductor in the vortex state with applied magnetic field $\bf H$ in the plane depend on the angle between $\bf H$ and the order parameter nodes. Within a semiclassical treatment of the extended quasiparticle states, we obtain fourfold oscillations of the specific heat, measurement of which provides a simple probe of gap symmetry. The frequency dependence of the density of states and the temperature dependence of thermodynamic properties obey different power laws for field in the nodal and anti-nodal direction. The fourfold pattern is changed to twofold when orthorhombicity is considered.

cond-mat.supr-con↗
arXiv1999

Effect of Order-Parameter Suppression on Scattering by Isolated Impurities in Asymmetric Bands

The single-impurity problem in d-wave superconductors with asymmetric bands is discussed. The effect of local order parameter suppression near the impurity is to shift the quasiparticle resonance. Contrary to previous work [A. Shnirman et al., Phys. Rev. B 60, 7517 (1999)] we find that the direction of the shift is not universally towards the strong scattering limit.

cond-mat.supr-con↗
arXiv1998

Is the nonlinear Meissner effect unobservable?

We examine the effects of nonlocal electrodynamics for a d-wave superconductor on the field dependence of the magnetic penetration depth. The linear field dependence predicted in the local limit, commonly known as the nonlinear Meissner effect, is instead found to be quadratic, $δλ\sim H^2$ for fields below a crossover scale $H^*$. This crossover is shown to be geometry dependent and for most orientations of the screening currents is of the same order as or greater than $H_{c1}$, implying that the nonlinear Meissner effect can not be observed. For special orientations where the current flows along the nodal directions, however, the nonlinear Meissner effect may be recovered.

cond-mat.supr-con↗
arXiv1998

Anisotropic thermodynamics and $T/\sqrt H$ scaling of d-wave superconductors in the vortex state

The density of states of a 2D d-wave superconductor in the vortex state with applied magnetic field $\bf H$ in the plane is shown to exhibit fourfold oscillations as a function of the angle of the field with respect to the crystal axes. We find further that the frequency dependence of the density of states and the temperature dependence of transport coefficients obey different power laws, thus leading to different magnetic scaling functions, for field in the nodal and anti-nodal direction. We discuss the consequences of this anisotropy for measurements of the specific heat.

cond-mat.supr-con↗
arXiv1998

Scattering by impurity-induced order parameter ``holes'' in d-wave superconductors

Nonmagnetic impurities in d-wave superconductors cause strong local suppressions of the order parameter. We investigate the observable effects of the scatterigng off such suppressions in bulk samples by treating the order parameter "hole" as a pointlike off-diagonal scatterer treated within a self-consistent t-matrix approximation. Strong scattering potentials lead to a finite-energy spectral feature in the d-wave "impurity band", the observable effects of which include enhanced low-temperature microwave power absorption and a stronger sensitivity of the London penetration depth to disorder than found previously in simpler ``dirty'' d-wave models.

cond-mat.supr-con↗
arXiv1998

Quasiparticle Transport in the Vortex State of Unconventional Superconductors

I consider the problem of the vortex contribution to quasiparticle transport in unconventional superconductors with line nodes, a nd argue that the magnetic field dependence of transport coefficients is fixed by the same scattering processes which limit low-temperature transport. I give no detailed calculations, but show that qualitatively correct results may be obtained in the limit of low temperatures and fields by simple physical arguments, based on estimates of the density of states and relaxation time in analogy with the zero-field case. I conclude with a brief discussion of the problem of anisotropy of the field dependence and influence of experimental geometry.

cond-mat.supr-con↗
arXiv1998

Magnetic field -induced phase transition in a $d_{x^2-y^2}$-wave superconductor at low temperatures

We consider, within BCS weak coupling theory, the instability of a $d_{x^2-y^2}$-wave superconductor to a state of mixed symmetry $d+iq$, $q=d_{xy},s$. In zero magnetic field we show that there is a large and physically reasonable range of interaction strengths for which a pure $d_{x^2-y^2}$ state is stable down to T=0. In this case a magnetic field, assumed to couple to quasiparticles via their Doppler shifts in the vortex superflow field, is shown to induce a phase transition at $T=T_c^*\sim \sqrt{H}$. Below $T_c^*$, the density of states remains gapless but its field dependence is substantially supressed. The theory explains many features of recent striking thermal conductivity measurements on BSCCO by Krishana et al.

cond-mat.supr-con↗
arXiv1998

Effects of Fermi Surface Anisotropy on Unconventional Superconductivity in UPt_3

We discuss the weak-coupling BCS theory of the heavy fermion superconductor UPt_3, accounting for that system's anisotropic, multisheeted Fermi surface by expanding the order parameter and pair potential in terms of appropriate basis functions of the irreducible representations of the D_6h crystal point group. Within a phenomenological model for the electronic structure of UPt_3 chosen to capture the qualitative features of local density functional calculations and de Haas-van Alphen measurements, we show how Fermi surface anisotropy can favor pairing in certain symmetry classes, and influence the phase diagram of unconventional superconductors. We also calculate the Ginzburg-Landau coefficients, focussing on those coefficients relevant to current theories of the UPt_3 phase diagram.

cond-mat.supr-con↗
arXiv1998

Quasiparticles in the Vortex State of Dirty d-Wave Superconductors

We consider the problem of the vortex contribution to thermal properties of dirty d-wave superconductors. In the clean limit, Volovik has argued that 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)\ltsim 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, H_{c1}\ll H\ll H_{c2}. This crossover may explain recent discrepancies in specicific heat measurements at low temperatures and fields in the cuprate superconductors. We further discuss the field dependence of transport properties within the same model.

cond-mat.supr-con↗
arXiv1998

Vortex Contribution to Specific Heat of Dirty $d$-Wave Superconductors: Breakdown of Scaling

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)\sim 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, H_{c1}\ltsim H\ll H_{c2}. 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.

cond-mat.supr-con↗
arXiv1998

Transport Properties of d-Wave Superconductors in the Vortex State

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.

cond-mat.supr-con↗
arXiv1997

Reply to the Comment by A.A. Nersesyan and A.M. Tsvelik on the "Non--Zero Fermi Level Density of States for a Disordered d-Wave Superconductor in Two Dimensions" (PRL 77, 3013 (1996)) by K. Ziegler, M.H. Hettler and P.J. Hirschfeld

In a recent Comment (cond-mat/9701197) on our Letter (PRL 77, 3013 (1996), cond-mat/9604176) Nersesyan and Tsvelik questioned the relevance of our exact calculation of the density of states (DOS) of a 2D d-wave superconductor using a Lorentzian disorder distribution, claiming ``that models with Lorentzian and Gaussian disorder belong to different universality classes'', on grounds of a comparison with a straightforward perturbation expansion in the disorder potential. We showed in a very recent paper (cond-mat/9703047) that a rigorous nonzero lower bound for DOS can be established without relying on the tails of the disorder distribution, i.e. both the Gaussian and Lorentzian distributions belong to a large class of distributions which give a nonzero lower bound for the DOS. This proves that the result of our Letter is generic.

cond-mat.supr-con↗
arXiv1997

Lower Bound for the Fermi Level Density of States of a Disordered D-Wave Superconductor in Two Dimensions

We consider a disordered d--wave superconductor in two dimensions. Recently, we have shown in an exact calculation that for a lattice model with a Lorentzian distributed random chemical potential the quasiparticle density of states at the Fermi level is nonzero. As the exact result holds only for the special choice of the Lorentzian, we employ different methods to show that for a large class of distributions, including the Gaussian distribution, one can establish a nonzero lower bound for the Fermi level density of states. The fact that the tails of the distributions are unimportant in deriving the lower bound shows that the exact result obtained before is generic.

cond-mat.supr-con↗
arXiv1996

Theory of Thermal Conductivity in YBa_2Cu_3O_{7-δ}

We calculate the electronic thermal conductivity in a d-wave superconductor, including both the effect of impurity scattering and inelastic scattering by antiferromagnetic spin fluctuations. We analyze existing experiments, particularly with regard to the question of the relative importance of electronic and phononic contributions to the heat current, and to the influence of disorder on low-temperature properties. We find that phonons dominate heat transport near T_c, but that electrons are responsible for most of the peak observed in clean samples, in agreement with a recent analysis of Krishana et al. In agreement with recent data on YBa_2(Cu_1-xZn_x)_3O_7-δthe peak position is found to vary nonmonotonically with disorder.

cond-mat.supr-con↗
arXiv1996

c-Axis Infrared Conductivity of a d_{x^2-y^2}-Wave Superconductor with Impurity and Spin-Fluctuation Scattering

Results of a calculation of the c-axis infrared conductivity sigma_c for a d_{x^2-y^2}-wave superconductor which include both elastic impurity and inelastic spin-fluctuation scattering are presented and compared with the ab-plane conductivity sigma_{ab} in the same model. In this model,the interlayer c-axis coupling is taken to be weak and diffusive. While in clean systems, inelastic scattering leads to a peak at omega = 4*Delta_0 in sigma_{ab} for T < T_c, it has little effect on the corresponding sigma_c, which exhibits structure only at omega = 2*Delta_0 and is directly related to the single-particle density of states N(omega). The c-axis penetration depth lambda_c in the same model is predicted to vary as T^3 at low temperatures in clean samples. We discuss recent optical experiments on the cuprates and compare with these predictions.

supr-con↗
arXiv1995

Infrared conductivity of a d_{x^2-y^2}-wave superconductor with impurity and spin-fluctuation scattering

Calculations are presented of the in-plane far-infrared conductivity of a d_{x^2-y^2}-wave superconductor, incorporating elastic scattering due to impurities and inelastic scattering due to spin fluctuations. The impurity scattering is modeled by short-range potential scattering with arbitrary phase shift, while scattering due to spin fluctuations is calculated within a weak-coupling Hubbard model picture. The conductivity is characterized by a low-temperature residual Drude feature whose height and weight are controlled by impurity scattering, as well as a broad peak centered at 4 Delta_0 arising from clean-limit inelastic processes. Results are in qualitative agreement with experiment despite missing spectral weight at high energies.

cond-mat↗