arXiv subjects

Patrick A. Lee

Publications and source records attributed to Patrick A. Lee.

196 records · Page 11Linked to original sources

arXiv1997

Kondo Effect in High-T_c Cuprates

We study the Kondo effect due to the nonmagnetic impurity, e.g., Zn, in high-T_c cuprates based on the spin-change separated state. In the optimal or overdoped case with the Kondo screening, the residual resistivity is dominated by the spinons while the T-dependent part determined by the holons. This gives $ρ(T) = { {4 \hbar} /{e^2}} { { n_{imp.}} /{(1-x)}} + {{αT} / x}$ (x: hole concentration,$n_{imp.}$: impurity concentration, $α$: constant ), which is in agreement with experiments. In the underdoped region with the pseudo spin gap, an SU(2) formulation predicts that the holon phase shift is related to the formation of the local spin moment, and hence the residual resistivity is given by $ρ_{res.} = { {4 \hbar} /{ e^2}} { { n_{imp.}}/{x}} $, which is also consistent with the experiments. The magnetic impurity case, e.g., Ni, is also discussed.

cond-mat↗

arXiv1997

The Unusual Superconducting State of Underdoped Cuprates

There is increasing experimental evidence that the superconducting energy gap $Δ_0$ in the underdoped cuprates is independent of doping concentration $x$ while the superfluid density is linear in $x$. We show that under these conditions, thermal excitation of the quasiparticles is very effective in destroying the superconducting state, so that $T_c$ is proportional to $xΔ_0$ and part of the gap structure remains in the normal state. We then estimate $H_{c2}$ and predict it to be proportional to $x^2$. We also discuss to what extent the assumptions that go into the quasiparticle description can be derived in the U(1) and SU(2) formulations of the t-J model.

cond-mat.supr-con↗

arXiv1997

An SU(2) Formulation of the t-J model: Application to Underdoped Cuprates

We develop a slave-boson theory for the t-J model at finite doping which respect a SU(2) symmetry -- a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contains d-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping which continuously evolve into the large Fermi surface at high doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low energy effective theory for the low lying fluctuations is derived, and new lying modes (which were over looked in the U(1) theory) are identified.

cond-mat.str-el↗

arXiv1996

Scaling of the quasiparticle spectrum for d-wave superconductors

In finite magnetic field H, the excitation spectrum of the low energy quasiparticles in a 2 dimensional d-wave superconductor exhibits a scaling with respect to $H^{1/2}$. This property can be used to calculate scaling relations for various physical quantities at low temperature T. As examples, we make predictions for the scaling behavior of the finite magnetic field specific heat, quasiparticle magnetic susceptibility, optical conductivity tensor, and thermal conductivity tensor. These predictions are compatible with existing experimental data. Most notably, the thermal Hall coefficient $κ_{xy}$ measured by Krishana et al. in YBCO is found to scale as $κ_{xy} \sim T^2 F(αT/H^{1/2})$ for $T \lesssim 30 K$ in agreement with our predictions, where $α$ is a constant and F is a scaling function.

cond-mat.supr-con↗

arXiv1996

Transport phenomenology for a holon-spinon fluid

We propose that the normal-state transport in the cuprate superconductors can be understood in terms of a two-fluid model of spinons and holons. In our scenario, the resistivity is determined by the properties of the holons while magnetotransport involves the recombination of holons and spinons to form physical electrons. Our model implies that the Hall transport time is a measure of the electron lifetime, which is shorter than the longitudinal transport time. This agrees with our analysis of the normal-state data. We predict a strong increase in linewidth with increasing temperature in photoemission. Our model also suggests that the AC Hall effect is controlled by the transport time.

cond-mat.str-el↗

arXiv1996

Bosons, gauge fields, and high-Tc cuprates

A simple model of a degenerate two-dimensional Bose liquid interacting with a fluctuating gauge field is investigated as a possible candidate to describe the charge degree of freedom in the normal state of the cuprate superconductors. We show that the fluctuating gauge field destroys superfluidity even in the Bose degenerate regime. We discuss the nature of the resulting normal state in terms of the geometric properties of the imaginary-time paths of the bosons. We will also present numerical results on the transport properties and the density correlations in the system. We find a transport scattering rate of the order of 2T, consistent with experiments on the optimally-doped cuprates. We also find that the density correlations of our model resemble the charge correlations of the t-J model.

cond-mat↗

arXiv1996

Dephasing time of composite fermions

We study the dephasing of fermions interacting with a fluctuating transverse gauge field. The divergence of the imaginary part of the fermion self energy at finite temperatures is shown to result from a breakdown of Fermi's golden rule due to a faster than exponential decay in time. The strong dephasing affects experiments where phase coherence is probed. This result is used to describe the suppression of Shubnikov-de Haas (SdH) oscillations of composite fermions (oscillations in the conductivity near the half-filled Landau level). We find that it is important to take into account both the effect of dephasing and the mass renormalization. We conclude that while it is possible to use the conventional theory to extract an effective mass from the temperature dependence of the SdH oscillations, the resulting effective mass differs from the $m^\ast$ of the quasiparticle in Fermi liquid theory.

cond-mat↗

arXiv1996

Specific heat and validity of quasiparticle approximation in the half-filled Landau level

We calculate the specific heat of composite fermion system in the half-filled Landau level. Two different methods are used to examine validity of the quasiparticle approximation when the two-body interaction is given by $V(q) = V_0 / q^{2-η}$ ($1 \le η\le 2$). The singular part of the specific heat is calculated from the free energy of the gauge field, which is compared with the specific heat calculated from the quasiparticle approximation via the singular self-energy correction due to the gauge field fluctuations. It turns out that two results are in general different and they coincide only for the case of the Coulomb interaction ($η= 1$). This result supports the fact that the quasiparticle approximation is valid only for the case of the Coulomb interaction. It is emphasized that this result is obtained by looking at a gauge-invariant quantity -- the specific heat.

cond-mat↗

arXiv1996

Degenerate Bose liquid in a fluctuating gauge field

We study the effect of a strongly fluctuating gauge field on a degenerate Bose liquid, relevant to the charge degrees of freedom in doped Mott insulators. We find that the superfluidity is destroyed. The resulting metallic phase is studied using quantum Monte Carlo methods. Gauge fluctuations cause the boson world lines to retrace themselves. We examine how this world-line geometry affects the physical properties of the system. In particular, we find a transport relaxation rate of the order of 2kT, consistent with the normal state of the cuprate superconductors. We also find that the density excitations of this model resemble that of the full tJ model.

cond-mat↗

arXiv1995

Plaquette Resonating-Valence-Bond Ground State of CaV$_4$O$_9$

A theoretical model is presented to explain the spin gap observed for CaV$_4$O$_9$. The underlying lattice of the 1/5-depleted square lattice favors a formation of plaquette resonating valence bond state. Inclusion of the frustrating second neighbor interaction enhances this tendency, leading to a quantum disordered state of a two dimensional spin-1/2 Heisenberg model with a sufficiently big spin gap compatible with experiments.

cond-mat↗

arXiv1995

Theory of Underdoped Cuprates

We develop a slave-boson theory for the t-J model at finite doping which respects an SU(2) symmetry -- a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contains d-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.

cond-mat↗

arXiv1995

Quantum Boltzmann equation of composite fermions interacting with a gauge field

We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $ν= 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge field fluctuations suggests that there is no well defined Landau-quasi-particle. Therefore, we cannot assume the existence of the Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an alternative formulation, we derive the QBE for the generalized Fermi surface displacement which corresponds to the local variation of the chemical potential in momentum space. {}From this QBE, one can understand in a unified fashion the Fermi-liquid behaviors of the density-density and the current-current correlation functions at $ν= 1/2$ (in the long wave length and the low frequency limits) and the singular behavior of the energy gap obtained from the finite temperature activation behavior of the compressibility near $ν= 1/2$. Implications of these results to the recent experiments are also discussed.

cond-mat↗

arXiv1995

Energy Gap Structure in Bilayer Oxide Superconductors

We consider a model for bilayer superconductors where an interlayer pairing amplitude $Δ_\perp$ co-exists with intralayer pairing $Δ_\|$ of $d_{x^2 - y^2}$ symmetry. This model is motivated by a recent photoemission experiment reporting the splitting of the nodes of the energy gap. In addition to offering a natural explanation of this observation, the model has a number of new experimental consequences. We find that the new state is accompanied by a spontaneous breaking of the tetragonal symmetry. We also find that the out-of-phase oscillation of $Δ_\perp$ and $Δ_\|$ gives rise to a new Raman active mode. The phase of $Δ_\perp$ may also become imaginary, leading to a state which breaks time reversal symmetry, which may have important implications for tunnelling experiments.

cond-mat↗

arXiv1994

Gauge-invariant response functions of fermions coupled to a gauge field

We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be cancelled by those from the vertex correction for small $q$ and $Ω$. As a result, the remaining contributions are not singular enough to change the leading order results of the random phase approximation. It is also shown that the gauge field propagator is not renormalized up to two-loop order. We examine the resulting gauge-invariant two-particle Green's functions for small $q$ and $Ω$, but for all ratios of $Ω/ v_F q$ and we conclude that they can be described by Fermi liquid forms without a diverging effective mass.

cond-mat↗

arXiv1994

Influence of gauge-field fluctuations on composite fermions near the half-filled state

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field $ΔB = B - 2 n_e hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ${\partial n \over \partial μ} \propto e^{- Δω_c / 2 T} \left ( 1 + {A (η) \over η- 1} {(Δω_c)^{2 \over 1 + η} \over T} \right )$ for $T \ll Δω_c$, where $Δω_c = {e ΔB \over mc}$. Here we assume that the interaction between the fermions is given by $v ({\bf q}) = V_0 / q^{2 - η} \ (1 \le η\le 2)$, where $A (η)$ is a $η$ dependent constant. This result can be interpreted as a divergent correction to the activation energy gap and is consistent with the divergent renormalization of the effective mass of the composite fermions.

cond-mat↗

arXiv1993

Spin-gap formation in cuprates: gauge theory

We analyze the phase diagram of single and bi-layer cuprates using the gauge-field description of the t-J model. For $T>T_{\text{BE}}$ the in-plane fermion-pairing order parameter $Δ_{\scriptscriptstyle\parallel}$ is eliminated by gauge field fluctuations, leading us to predict the absence of a spin-gap phase in single-layer cuprates. For bi-layer cuprates the inter-layer order parameter $Δ_\perp$ is enhanced by spin correlations, and is less affected by gauge fluctuations. We believe that the spin gap in bi-layer materials is due to inter-layer fermion pairing, and that for these underdoped samples the superconducting gap may be nodeless.

cond-mat↗