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AIP conference proceedings

QED3 as an effective theory of the pseudogap phase in underdoped cuprates

Iorwerth O. Thomas

Published Jan 1, 2007• 0 citations
Publisher

Abstract

A version of non‐compact QED in 2+1 dimensions (QED3), with anisotropies introduced by differing Fermi and gap velocities in the spatial directions has been proposed as an effective theory of the SDW‐pseudogap phase transition in underdoped cuprates at T=0. Preliminary simulations using lattice gauge theory techniques suggest that matters are a little more complicated than previously thought; in particular, measurements of the fermion propagator in Landau gauge indicate that one should be cautious in inferring properties of this form of QED3 from those of isotropic QED3.

DOI
10.1063/1.2752004

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Chinese Physics C•Jan 1, 2007•0 citations
A version of non‐compact QED in 2+1 dimensions (QED3), with anisotropies introduced by differing Fermi and gap velocities in the spatial directions has been proposed as an effective theory of the SDW‐pseudogap phase transition in underdoped cuprates at T=0. Preliminary simulations using lattice gauge theory techniques suggest that matters are a little more complicated than previously thought; in particular, measurements of the fermion propagator in Landau gauge indicate that one should be cautious in inferring properties of this form of QED3 from those of isotropic QED3.
The low-lying excitations at the nodes of the d-wave gap in the normal state for underdoped cuprates, close to the superconducting phase transition, may be described by an effective QED3 theory. There are three characteristic velocities: v_F, v_Delta and c. For v_Delta=v_F=c, the model reduces to N-flavour QED3. Here, in the isotropic limit, for N100. However, we argue that N_c=N_0c, when we go beyond the approximations used to derive our mass gap equations. We expect, though, that our solution for N=2 is roughly correct, at low momentum, for large enough anisotropies. Implications and possible extensions to this work are also discussed.
Within the phase fluctuation model for the pseudogap state of cuprate superconductors we identify a novel statistical "Berry phase" interaction between the nodal quasiparticles and fluctuating vortex-antivortex excitations. The effective action describing this model assumes the form of an anisotropic Euclidean quantum electrodynamics in (2+1) dimensions (QED (3)) and naturally generates non-Fermi liquid behavior for its fermionic excitations. The doping axis in the x -T phase diagram emerges as a quantum critical line which regulates the low energy fermiology.
The ubiquitous phase diagram of the cuprate superconductors has a phase where the density of states still has a gap above the superconducting transition temperature. Due to the presence of a gap without any other superconducting characteristics, this phase is known as the pseudogap (PG) state. Emery and Kivelson proposed that in this state the superconducting order parameter still has a finite amplitude, however the quantal phase is disordered in such a way that it does not possess long range order. Using these ideas, Franz and Tesanovic developed a theory to explain the pseudogap phase that is identical to three dimensional quantum electrodynamics (QED3 ) apart from an intrinsic anisotropy. Amazingly, this theory can easily explain the antiferromagnetic region. The main purpose of this thesis is twofold. First, to explore some finite temperature properties of QED3 . We do this by calculating a Bosonic polarization bubble at finite temperature in the Matsubara formalism. Secondly we wish to derive some experimentally testable predictions of QED3 . To this end we calculate the modification to the Patrick Lee universal conductivity in the pseudogap state.
We comment on the recent attempt by M. Franz et al [1] to further justify their earlier calculation of the gauge-invariant electron propagator in the context of the QED_3 theory of the pseudogap phase in cuprates [2]. First, we use the method of "reductio ad absurdum" to demonstrate the inconsistency of the argument offered in [2] and then present a direct calculation of the disputed fermion amplitudes, thus unequivocally proving that the previously proposed form of the electron propagator: 1) does exhibit a negative anomalous dimension, as pointed out in [3]; 2) is different from the so-called Brown's function whose anomalous dimension turns out to be positive when computed in a covariant gauge. Lastly, we conjecture that the true physical electron propagator (whose exact form still remains to be found) may feature a "super-Luttinger" behavior characterized by a faster than a power-law decay G(x)~exp(-const\ln^2|x|).
We present finite temperature (T) extension of the (2+1)-dimensional QED (QED3) theory of under-doped cuprates. The theory describes nodal quasiparticles whose interactions with quantum proliferated hc/2e vortex-antivortex pairs are represented by an emergent U(1) gauge field. Finite T introduces a scale beyond which the spatial fluctuations of vorticity are suppressed. As a result, the spin susceptibility of the pseudogap state is bounded by T2 at low T and crosses over to approximately T at higher T, while the low-T specific heat scales as T2, reflecting the thermodynamics of QED3. The Wilson ratio vanishes as T-->0; the pseudogap state is a "thermal (semi)metal" but a "spin-charge dielectric." This non-Fermi liquid behavior originates from two general principles: spin correlations induced by "gauge" interactions of quasiparticles and fluctuating vortices and the "relativistic" scaling of the T=0 fixed point.
With the coupled Dyson-Schwinger equations in the framework of the unified QED3 theory,we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0.By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion,we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi- fermion flavors N■4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region.By comparing the pressure between the coexistent AF-dSC phase and dSC phase,we find that AF-dSC coexisting phase is the stable phase,the AF phase can then coexist with the dSC phase.