Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session N32: Focus Session: Superconductivity: Theory and Computations |
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Sponsoring Units: DCOMP DCMP Chair: Richard Scalettar, University of California-Davis Room: LACC 507 |
Wednesday, March 23, 2005 8:00AM - 8:12AM |
N32.00001: Chiral symmetry breaking in QED$_3$ in presence of irrelevant interactions: a renormalization group study Kamrab Kaveh, Igor Herbut Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics (QED$_3$) in presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of large number of fermion flavors $N$. We find that the critical number of fermions $N_c$ below which the mass becomes dynamically generated depends continuously on a weak chiral-symmetry-breaking interaction. One-loop calculation in our gauge-invariant approach yields $N_{c0} = 6$ in pure QED$_3 $. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure QED$_3$. [Preview Abstract] |
Wednesday, March 23, 2005 8:12AM - 8:24AM |
N32.00002: Thermal melting of density wave order on the square lattice Adrian Del Maestro, Subir Sachdev We present a theory of thermal fluctuations which melt a commensurate $p \times p$ density wave ordered state on the square lattice. A phase diagram is constructed which will act as a springboard to a variety of interesting phases and phase transitions. The commensurate lock-in solid can in general melt to either an incommensurate floating solid or by a second order phase transition to an anisotropic (striped) floating state with $p$-periodic order along one direction and incommensurate quasi long range order in the other direction. In either case, this transition will be accompanied by the proliferation of domain walls, with the adjacent state being distinguished by the sign of the domain wall interaction energy. The fully disordered high temperature state can be reached from the floating solid by a second order transition mediated by dislocations. For $p = 4$, and at special commensurate densities, the $p \times p$ commensurate state can melt directly into the disordered state via a self-dual critical point with non-universal exponents. [Preview Abstract] |
Wednesday, March 23, 2005 8:24AM - 8:36AM |
N32.00003: Solution for the dynamics of the BCS and central spin problems Emil Yuzbashyan We develop an explicit description of a time-dependent response of fermionic condensates to perturbations. The dynamics of Cooper pairs at times shorter than the energy relaxation time can be described by the BCS model. We obtain a general explicit solution for the dynamics of the BCS model. We also solve a closely related dynamical problem - the central spin model, which describes a localized spin coupled to a ``spin bath''. A typical dynamics of the BCS and central spin models is quasi-periodic with a large number of frequencies and stable under small perturbations. [Preview Abstract] |
Wednesday, March 23, 2005 8:36AM - 8:48AM |
N32.00004: Spin gap phase in the strong coupling limit of the hole-doped 2D Emery model Kai Sun, Eduardo Fradkin, Steven Kivelson We investigate the strong coupling limit of the three-band Emery model of a CuO plane. Starting from the nematic phase of this model [1], an effective Hamiltonian is constructed to leading order in the strong coupling expansion and for a range of hole doping. We show that the effective Hamiltonian we found is equivalent to a Kondo lattice model which can be solved exactly. We find that this model exhibits a quantum phase transition from a spin gapless phase to a spin gap phase as a function of doping. We will discuss the implications of these results for the phase diagram. [1] E. Fradkin, S.A. Kivelson and T.H. Geballe, Phys. Rev. B 69, 144505 (2004) [Preview Abstract] |
Wednesday, March 23, 2005 8:48AM - 9:00AM |
N32.00005: Theories that try to describe pairing fluctuations above T$_c$: a critical evaluation Frank Marsiglio, Simona Verga, Robert J. Gooding Over the past couple of decades many attempts have been made to understand the pairing instability crossover from weak coupling to strong coupling, particularly at finite temperature. While the physics is {\it qualitatively} understood, there is still dispute over what theoretical framework accurately represents this physics. We offer our two cents worth by examining the strong coupling limit in a weak coupling framework, and find one prescription, used extensively by Levin and coworkers, and based on a modified proposal dating back to Kadanoff and Martin, works remarkably well. [Preview Abstract] |
Wednesday, March 23, 2005 9:00AM - 9:12AM |
N32.00006: Gauge Theory of Pairing and Spin Fluctuations Near the Quantum Critical Point J.R. Schrieffer We have solved the spin Fermion (periodic Kondo) model for the superconductor transition temperature $T_c $ and for the electron energy gap function $\phi $ as $T\to T_c $. We find for realistic parameters$W$, the electron band width, $N_{B} \left( \omega \right)$, the Boson density of states and $J_q ,$ the Kondo exhange interaction, that $T_c =1.14{\kern 1pt}\,\omega _s \;\,e-\frac{(1+\lambda _Z )}{\lambda _\phi }$ where $\lambda _Z $ is the normal state renormalization constant and $\lambda _\phi $ is the pairing interaction strength. We find $T_c $ is exponentially higher for $\ell =1$ (p-wave), $S=1$ (spin triplet) pairing than for $s$- wave pairing $S=0$. We note $\lambda _Z =0$ for $p$-wave pairing due to the odd parity of the relevant. For realistic parameters the solution of Eliashberg's equation for $T_c $ predicts $T_c \tilde {-}\;5\times 10^5\,^0K$ with $H_{c2} \sim 10^8T$ and$j_c \sim 10^8\,Amps/cm^2$. When $T_c $ and $\phi $ are simultaneously maximized, with respect to $N_B \left( \omega \right)$ and $J_q $ considerably high $T_c ,H_{c2} ,j_c $ values are predicted, namely $T_c $ of order $5\times 10^8\,^0K \quad H_{c2} \sim 10^{13}T$ and $j_c \sim 10^{13}\,Amps/cm^2$There values are predicted to exist in systems such as the Heusler alloys, e.g. for $Au_2 \left( {Mn_{2-x} \;A\ell _x } \right)$ for $x\tilde {-}0.1-0.5.$ [Preview Abstract] |
Wednesday, March 23, 2005 9:12AM - 9:24AM |
N32.00007: Problem of Gauge Invariance in the BCS theory: Revisited Yong-Jihn Kim It is well known that the derivation of the Meissner effect in the BCS theory is not gauge invariant. We reconsider this fundamental problem from a few different aspects. First, we point out that the gauge invariance is basically one particle property, although we are dealing with the many body BCS wavefunction. Second, if the field operators are transformed due to the gauge change, it is trivial to show the gauge invariance. Third, if the BCS state is changed instead according to the gauge transformation, we need to pair the states which include the effects of the perturbation. In fact, this point was realized by Bogoliubov, Blatt, and Ambegaokar and Kadanoff. However, their investigations were only formal and didn't pursue the implications of this generalized pairing on the electrodynamics of the BCS superconductors. We show that the generalized pairing leads to a gauge invariant derivation of the Meissner effect. We also discuss the resulting refinement of the electrodynamics of the BCS superconductors. [Preview Abstract] |
Wednesday, March 23, 2005 9:24AM - 9:36AM |
N32.00008: 4D-XY quantum criticality in a doped Mott insulator Marcel Franz, Andrew Iyengar We argue that the low energy, long wavelength physics of the underdoped cuprate superconductors is governed by a 4D-XY quantum critical point situated at the $T=0$ terminus of the $T_c(x)$ line. We derive the effective action for a d-wave superconductor in the vicinity of this point and show that much of the experimentally observed phenomenology follows from it. Most notably our theory explains the puzzling features of the recent magnetic penetration depth data on YBCO crystals, such as the apparent absence of the classical thermal fluctuation regime and the observed violations of Uemura scaling. [Preview Abstract] |
Wednesday, March 23, 2005 9:36AM - 9:48AM |
N32.00009: Statistics of Cooper's pairs Ilya Kaplan, Oracio Navarro It is well known that the Cooper pair~(pairon) operators may not be considered either as the Bose operators nor as the Fermi operators. The analysis of trilinear commutation relations for the pairon operators reveals that they correspond to the modified parafermi statistics of rank p=1. Two different expressions for the Cooper pair number operator are presented. We demonstrate that the calculations with a Hamiltonian expressed via pairon operators is more convenient using the commutation properties of these operators without presenting them as a product of fermion operators. This allows to study problems in which the interactions between Cooper's pairs are also included. The problem with two interacting Cooper's pairs is resolved and its generalization in the case of large systems is discussed$^{1}$. $^{1}$ I.G. Kaplan, O. Navarro, and J.A. S\'{a}nchez, Physica C (in Press). Key Words: Cooper's pairs interaction, commutation relations, parastatistics [Preview Abstract] |
Wednesday, March 23, 2005 9:48AM - 10:00AM |
N32.00010: Theory of magic dopings in high Tc superconductors Handong Chen, Shou-Cheng Zhang Based on an effective bosonic model, we predict checkerboard- type ordering of the Cooper pairs at magic rational doping fractions $(2m+1)/2^n$, where m and n are integers. At the magic doping fraction $x = (2m+1)/2^n$, the charge unit-cell is $2^ {(n+1)/2}a \times 2^{(n+1)/2}a$, pointing along the original CuO bond direction when $n$ is odd, and along the diagonal direction when $n$ is even. It is generally expected that the charge ordering tendencies are stronger at higher levels of the hierarchy, with smaller n. Recently, a tendency towards charge ordering at particular rational hole doping fractions, 1/16, 3/32, 1/8, and 3/16, is reported in transport measurements of $La_{2-x}Sr_xCuO_4$ samples[1]. This observation is most consistent with our predicted hierarchy of charge ordering of hole-pairs. [Preview Abstract] |
Wednesday, March 23, 2005 10:00AM - 10:12AM |
N32.00011: Some Comparisons of RVB Theories and High Tc Cu-oxides Kaiyu Yang, C.T. Shih, C.P. Chou, S.M. Huang, T.K. Lee, T. Xiang, F.C. Zhang We report extensive comparisons of the doping dependences of physical properties of the RVB theories and the high Tc Cu- oxides. We study an extended t-J model with the second and third-nearest-neighboring hopping terms by using the renormalized mean field theory and the variational Monte Carlo and the power Lanczos methods. We calculate the quantites related to the nodal quasiparticle physics as well as the thermal and spectral properties of the model and compare them to the available experiments [Preview Abstract] |
Wednesday, March 23, 2005 10:12AM - 10:24AM |
N32.00012: Antiferromagnetism and charged vortices in high-Tc superconductors Daniel Knapp, Catherine Kallin, Amit Ghosal, Sarah Mansour We present the results of a detailed mean-field study of the effect of the long-range Coulomb interaction on charge accumulation in antiferromagnetic vortices in high-$T_c$ superconductors. We have found that antiferromagnetism is associated with an accumulation of charge in the vortex core, even in the presence of the long-range Coulomb interaction and that the local density of states in the vortex core, as described by a simple theory of competing $d$SC and AFM orders, is in excellent qualitative agreement with experimental data. We also touch on the manifestation of $\Pi$-triplet pairing in the presence of coexisting $d$SC and AFM order, and the intriguing appearance of one-dimensional stripe-like ordering. [Preview Abstract] |
Wednesday, March 23, 2005 10:24AM - 10:36AM |
N32.00013: Maximization of a Superconductor's Transition Temperature in a Boson - Fermion Model by Variation of the Boson Density of States and the Boson - Fermion Coupling Constants or for Spin Vector or Scalar Couplings Respective Arno Kampf, J.R. Schrieffer We have solved the problem of maximizing a superconductors transition temperature $T_c $ by varying the Boson (spin fluctuation or phonon) density of states $N_B \left( \omega \right)$ and coupling constants, $J_q $ or$g_{kq\lambda } $. We find that $T_c \sim 10^9\;{ }^0K$ can be obtained, for example in Heusler alloys, such as$Au_2 \left( {Mn_{2-x} \;A\ell _x } \right)$, with$x\sim 0.1-0.5$. Also values of $H_{c2} \sim 10^{13}T$ and$j_c \sim 10^{13}\,Amps/cm^2$are predicted. Additionally results for the tunneling density of states$N_T \left( {eV} \right)$, the arpes cross section,${d\Delta } \mathord{\left/ {\vphantom {{d\Delta } {d\Omega d\omega }}} \right. \kern-\nulldelimiterspace} {d\Omega d\omega }$, $e.m.,{\kern 1pt}\,I.R.$ and transport coefficients arising from these models will be presented. Also we will present a discussion of the 36 Leggett modes which our theory predicts to exist, whose energies are in the optical frequency range$\left[ {\omega \sim 1-3eV} \right]$, versus the microwave frequency range for superfluid $^{3}$He-A phase. [Preview Abstract] |
Wednesday, March 23, 2005 10:36AM - 10:48AM |
N32.00014: Exact summation of vertex corrections to the penetration depth in $d$-wave superconductors Andrew Iyengar, Marcel Franz In high-purity YBCO single crystals, the impurity scattering may be dominated by slowly varying potentials due to dopant oxygen atoms. A d-wave superconductor presents an unusual situation in which such extended disorder potentials are essentially unable to change the charge current carried by nodal quasiparticles. We find that the inclusion of the important vertex corrections leads to a remarkably simple relationship between the normal fluid density and the quasiparticle density of states in the disordered system. This result is extremely general and allows the interpretation of the temperature dependence of the penetration depth in a model-independent fashion. [Preview Abstract] |
Wednesday, March 23, 2005 10:48AM - 11:00AM |
N32.00015: Slave-boson approach to the $t$-$t'$-$t''$-$U$ model applied to electron-doped cuprates Qingshan Yuan, Feng Yuan, Chin-Sen Ting By applying Hartree-Fock (HF) mean-field theory to the $t$-$t'$-$t''$-$U$ model, Kusko {\it et al.} have studied the Fermi surface evolution with doping in the antiferromagnetic (AF) phase for electron-doped cuprates. Although they reached consistent results with ARPES data, a doping-dependent effective $U$ was adopted, specifically, $U$ drops from $6t$ at $x=0$ to $3t$ at $x=0.15$. The strong doping dependence of $U$ and its small value at $x=0.15$ are both in disagreement with the analysis on the optical conductivity [A. J. Millis {\it et al.}, cond-mat/0411172]. In view that the HF theory often overestimates the AF order, we re-study the model analytically by Kotliar-Ruckenstein slave-boson approach which improves the consideration of fluctuations. A quicker decreasing of the staggered magnetization (and AF gap) with increasing doping than in HF theory is obtained, thus the ARPES results are possibly reproduced even under a doping-independent constant $U$. We have further considered superconductivity and its interplay with antiferromagnetism by introducing an attractive intersite $V$. [Preview Abstract] |
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