Hidden Fermi Liquid: Self-Consistent Theory for the Normal State of High-TcSuperconductors

Abstract

Hidden Fermi liquid theory explicitly accounts for the effects of Gutzwiller projection in the t-J Hamiltonian, widely believed to contain the essential physics of the high-Tc superconductors. We derive expressions for the entire "strange metal", normal state relating angle-resolved photoemission, resistivity, Hall angle, and by generalizing the formalism to include the Fermi surface topologyangle-dependent magnetoresistance. We show this theory to be the first self-consistent description for the normal state of the cuprates based on transparent, fundamental assumptions. Our welldefined formalism also serves as a guide for further experimental confirmation.The anomalous "strange metal" properties of the normal, non-superconducting state of the high-T c cuprate superconductors have been extensively studied for over two decades. [1][2][3][4][5][6] The resistivity is robustly T-linear at high temperatures while at low T it appears linear near optimal doping and is T 2 at higher doping. The inverse Hall angle is strictly T 2 and hence has a distinct scattering lifetime from the resistivity. The transport scattering lifetime is highly anisotropic as directly measured by angle-dependent magnetoresistance (ADMR, or similarly AMRO) [7][8][9][10] and indirectly in more traditional transport experiments. The IR conductivity exhibits a non-integer power-law in frequency [11,12], which we take as a defining characteristic of the "strange metal".A phenomenological theory of the transport and spectroscopic properties at a self-consistent and predictive level has been much sought after, yet elusive. We demonstrate here that the hidden Fermi liquid theory (HFL) [13][14][15][16][17][18] is the effective low-energy theory for the normal state and no longer just a proposal. After reviewing the theory, we derive well-defined expressions relating ARPES, resistivity, Hall angle, and ADMR. Self-consistency is shown in the one system where most datasets are available, overdoped (OD) T l 2 Ba 2 CuO 6+δ .In the cuprate phase diagram, a line is usually drawn up and to the right from the edge of the superconducting dome in the OD region to separate the "strange metal" from a conventional Fermi liquid (FL) at high doping. We argue there is no crossover from the "strange metal" for high doping. HFL is valid for the entire normal state and we will show that the data only appears FL-like as the HFL bandwidth, W HF L , becomes large at high doping.Some proposals, which have neither demonstrated selfconsistency nor explained the IR conductivity, invoke the heuristic that there is single scattering lifetime in the problem with "hot" or "cold" spots [19][20][21] with different temperature dependences in different regions of the Fermi surface. However, the more recent experimental probe of ADMR allows a direct test of the anisotropic scattering predicted by any theory. We show that the anisotropy observed in the transport scattering rate in the ADMR is precisely reproduced by including the slight variation of v F and k F around the Fermi surface wi...

Weakly-correlated nodeless superconductivity in single crystals of Ca3Ir4Sn13 and Sr3Ir4Sn13 revealed by critical fields, Hall effect, and magnetoresistance measurements

“…where J is the bandwidth of spin excitations (or the spin exchange energy in Anderson's theory), and n is the planar carrier density. The spin exchange energy J for YBa 2 Cu 3−x Zn x O y was determined by the experimental value of Λ to be ∼830 K. A similar estimation for Tl 2 Ba 2 CuO y has recently shown J ≈ 800 K [32]. By substituting the experimental values of Λ and the carrier concentration derived from the Hall coefficient into equation (4), the analog exchange energy J for the superconducting CDW system of CIS and SIS can be determined to be 88 and 464 K, respectively.…”

Correlated Dirac particles and superconductivity on the honeycomb lattice

“…We shall also mention some theoretical progess accomplished close to the Mott state [91,119,[121][122][123][124][125].…”

Phases of the InfiniteUHubbard Model on Square Lattices

“…In the near future we also hope to study the apparent LL phase to determine whether there is a well-defined strong coupling limit [20] of the superconducting state that is known to arise at weak coupling [21].…”