QED3theory of underdoped high-temperature superconductors

Abstract

Q E D 3 theory of underdoped high tem perature superconductors Igor F.H erbut D epartm ent ofPhysics,Sim on Fraser U niversity,B urnaby,B ritish C ol um bia, C anada V 5A 1S6T he l ow -energy theory ofd-w ave quasi parti cl es coupl ed to uctuati ng vortex l oopsthatdescri besthel ossofphase coherence i n a tw o di m ensi onald-w ave superconductor at T = 0 i s deri ved from rst pri nci pl es. T he theory has the form of2+ 1 di m ensi onal quantum el ectrodynam i cs (Q E D 3), and i s proposed asan e ecti ve descri pti on ofthe T = 0 superconductori nsul ator transi ti on and of the pseudogap phase i n underdoped cuprates. T he coupl i ng constant ("charge") i n thi s theory i s proporti onalto the dualorder param eter ofthe X Y m odel ,w hi ch i s assum ed to be descri bi ng uctuati ons ofthe phase ofthe superconducti ng order param eter. Fi ni teness of the charge i s then tantam ount to the appearance ofi n ni tel y l arge vortex l oops, i . e. to the l oss of phase coherence i n the system . T he pri nci palresul t i s thatthe destructi on ofsuperconducti ng phasecoherencei n thed-w avesuperconductors typi cal l y,and i m m edi atel y,l eadsto the appearance ofanti ferrom agneti sm . T hi s transi ti on can be understood i n term s of the spontaneous breaki ng ofan approxi m ate "chi ral " SUc(2) sym m etry, w hi ch m ay be di scerned at l ow enough energi es i n the standard d-w ave superconductor. T he m echani sm of thi s spontaneous sym m etry breaki ng i s form al l y anal ogous to the dynam i cal m ass generati on i n the Q E D 3, w i th the "m ass" here bei ng proporti onal to staggered m agneti zati on. O ther phases w i th broken chi ralsym m etry i ncl ude the transl ati onal l y i nvari ant "d+ i p" and "d+ i s" i nsul ators, and the one-di m ensi onalcharge-densi ty and spi n-densi ty w aves,w hi ch are al li nsul ati ng descendants ofthe d-w ave superconductor. A l lthe i nsul ati ng states have the neutralspi n-1=2 exci tati ons that one can i denti fy i n the superconductor con ned by the l ogari thm i c potenti al . El ectron repul si on i s i n thi s form ali sm represented by a parti cul ar quarti c perturbati on to the Q E D 3 acti on,w hi ch breaks the chi ralsym m etry and sel ects the anti ferrom agnet as the preferred broken sym m etry state. Iform ul ate the m ean-el d theory ofthe anti ferrom agneti c i nstabi l i ty i n presenceofa short-rangerepul si vei nteracti on,and nd the staggered m agneti zati on to be si gni cantl y enhanced deeperi nsi de the i nsul ati ng state. T he theory o ersan expl anati on for the rounded d-w ave-l i ke di spersi on seen i n A R PES experi m ents on the i nsul ati ng C a2C uO 2 C l2 (F.R onni ng et. al .,Sci ence 282,2067 (1998). ) R el ati ons to other theoreti cal approaches to the hi gh-Tc probl em are di scussed.

Chiral symmetry breaking in three-dimensional quantum electrodynamics in the presence of irrelevant interactions: A renormalization group study

“…Each of the insulators corresponds to a broken generator of the U(4) chiral symmetry of QED 3 , which emerges at low energies in the standard dSC [2], [5]. Most important among the insulating ground states is the spin-density-wave, which turns out to be favored by the repulsive interactions [2], [6]. This approach provides then a viable unified description of the known low-temperature phases of underdoped high-temperature superconductors.…”

“…It has been proposed recently that the low-energy theory of gapless quasiparticles in a two-dimensional d-wave superconductor (dSC) with strong phase fluctuations can be represented by the two-flavor massless quantum electrodynamics in three dimensions (QED 3 ) [1], [2]. The coupling constant (or the 'charge') in such an effective theory is the vortex condensate, i. e. the order parameter dual to the usual superconducting order parameter.…”

“…It is well known that QED 3 is inherently unstable towards the dynamical mass generation [3] [4], which in the context of d-wave superconductivity implies the transition into one of several possible insulating ground states. Each of the insulators corresponds to a broken generator of the U(4) chiral symmetry of QED 3 , which emerges at low energies in the standard dSC [2], [5]. Most important among the insulating ground states is the spin-density-wave, which turns out to be favored by the repulsive interactions [2], [6].…”

Topological order and the deconfinement transition in the(2+1)-dimensional compact Abelian Higgs model

“…It should be noted that a realistic theory of the high-T c cuprates would require also the inclusion of gapless nodal quasiparticles, which are here neglected. 19,20,21,22,23 We thus consider a (2+1)D compact U (1) gauge theory minimally coupled to a charge-q bosonic matter field, with an Euclidean action S = −J rµ cos(∇ µ θ r − qA rµ ) − 1 g rµ cos(B rµ ), (1) where θ r and A rµ are compact phases ∈ [0, 2π) living on the sites and links of a 3D simple cubic lattice, respectively. B rµ = ǫ µνλ ∇ ν A rλ is the dual field strength, with the lattice difference operators defined by ∇ µ f r = ∇ µ f r+eµ = f r+eµ − f r .…”

Birefringent breakup of Dirac fermions on a square optical lattice

“…Including spin would allow for on-site Hubbard interactions, which would be considerably complicate matters and require techniques similar to those that have been used to study high temperature superconductors [18].…”