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arXiv:cond-mat/9804189 · Physical Review Letters

New Scenario for High- Tc Cuprates: Electronic Topological Transition as a Motor for Anomalies in the Underdoped Regime

F. P. Onufrieva, Pierre M. Pfeuty, Mikhail N. Kiselev

Published Mar 15, 1999• 58 citations
arXivHTMLPDF

Abstract

We have discovered a new nontrivial aspect of electronic topological transition (ETT) in a 2D free fermion system on a square lattice. The corresponding exotic quantum critical point, $\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\delta}}_{c}$, $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ ( $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\ensuremath{-}\ensuremath{\delta}$ is the electron concentration), is at the origin of anomalous behavior in the interacting system on one side of ETT, $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}$. Most important is the appearance of the line of characteristic temperatures, ${T}^{*}(\ensuremath{\delta})\ensuremath{\propto}{\ensuremath{\delta}}_{c}\ensuremath{-}\ensuremath{\delta}$. Application of the theory to high- ${T}_{c}$ cuprates reveals a striking similarity to the behavior observed experimentally in the underdoped regime.

DOI
10.1103/physrevlett.82.2370

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We have discovered a new nontrivial aspect of electronic topological transition (ETT) in a 2D free fermion system on a square lattice. The corresponding exotic quantum critical point, \ensuremathδ=\ensuremathδc\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\delta}}_{c}\ensuremathδ=\ensuremathδc​, T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 ( n=1\ensuremath−\ensuremathδn\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\ensuremath{-}\ensuremath{\delta}n=1\ensuremath−\ensuremathδ is the electron concentration), is at the origin of anomalous behavior in the interacting system on one side of ETT, \ensuremathδ<\ensuremathδc\ensuremath{\delta}<{\ensuremath{\delta}}_{c}\ensuremathδ<\ensuremathδc​. Most important is the appearance of the line of characteristic temperatures, T∗(\ensuremathδ)\ensuremath∝\ensuremathδc\ensuremath−\ensuremathδ{T}^{*}(\ensuremath{\delta})\ensuremath{\propto}{\ensuremath{\delta}}_{c}\ensuremath{-}\ensuremath{\delta}T∗(\ensuremathδ)\ensuremath∝\ensuremathδc​\ensuremath−\ensuremathδ. Application of the theory to high- Tc{T}_{c}Tc​ cuprates reveals a striking similarity to the behavior observed experimentally in the underdoped regime.
We study an electronic topological transition (ETT) (the transition due to change in topology of Fermi surface) that occurs in a two-dimensional electron system on a square lattice with hopping beyond nearest neighbors under a change of electronic concentration n (or of hole doping $\ensuremath{\delta}=1\ensuremath{-}n).$ We show that the ETT point $(\ensuremath{\delta}={\ensuremath{\delta}}_{c}, T=0)$ is an exotic quantum critical point (QCP) with several aspects of criticality. The first trivial one is related to singularities in thermodynamic properties. A nontrivial and never considered aspect concerns a behavior of the electron-hole response function: the ETT point is a quantum multicritical point, the end point of the critical line $(T=0, \ensuremath{\delta}>{\ensuremath{\delta}}_{c})$ of static Kohn singularities. We show that the existence of this QCP results in global anomalies of the system in the presence of interaction. (We consider the interaction corresponding to the ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}J$ model.) The anomalies take place on one side of the ETT $(\ensuremath{\delta}<{\ensuremath{\delta}}_{c}$ in the case of ${t}^{\ensuremath{'}}/t<0$ corresponding to the high-Tc{T}_{c}Tc​ cuprates) and have a striking similarity with the anomalies observed in the high-Tc{T}_{c}Tc​ cuprates in the underdoped regime. The most important consequence of the ETT (besides the appearance of superconducting instability of the d-wave symmetry) is the existence of the pseudocritical zone, ${T}^{*}(\ensuremath{\delta})\ensuremath{\propto}{\ensuremath{\delta}}_{c}\ensuremath{-}\ensuremath{\delta},$ which grows from the point $\ensuremath{\delta}={\ensuremath{\delta}}_{c}$ on the side $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}.$ Below and around this zone the metal state is anomalous. Some anomalies are considered in the present paper and compared with experiment (NMR, neutron scattering).
Theoretical attempts to explain the origin of high temperature superconductivity are challenged by the complexity of the normal state, which exhibits three regimes with increasing hole doping: a pseudo-gap regime when underdoped, strange power laws near optimal doping and more conventional metallic behavior when heavily overdoped. We suggest that the origin of this behavior is linked to a zero temperature quantum phase transition separating the overdoped Fermi liquid from a spin-charge separated underdoped phase. Central to our analysis is a new Z2Z_2Z2​ gauge theory formulation, which supports topological vortex excitations - dubbed visons. The visons are gapped in the underdoped phase, splitting the electron's charge and Fermi statistics into two separate excitations. Superconductivity occurs when the resulting charge eee boson condenses. The visons are condensed in the overdoped phase, thereby confining the charge and statistics of the electron leading to a Fermi liquid phase. Right at the quantum confinement transition the visons are in a critical state, leading to power law behavior for both charge and spin.
We have discovered a new example of quantum spin liquid which is a superconducting (SC) phase in 2D electron system close to electronic topological transition. As a quantum spin liquid in low dimensional localized spin systems it is characterized by a resonance spin mode and a well separated two-particle continuum. Application of the theory to the high-T_c cuprates allows to shed light on many observed in the underdoped regime features such as the so called 40 meV resonance peak, incommensurability at lower ω, spin gap etc.
We show that the presence of two topological quantum critical points (QCP's) in 2D electronic system on a square lattice imposes strong constraints on density-wave (DW) correlations in the high-T(c) cuprates. Electronic properties of the corresponding strongly correlated system are highly reminiscent of the experimental trends in the high-T(c) cuprates. The most interesting results are the existence at low doping of two single-particle gaps different by order of magnitude both increasing towards low doping and of the specific insulating state characterized by a small chemical potential jump.
The microscopical analysis of the unconventional and puzzling physics of the underdoped cuprates, as carried out lately by means of the composite operator method (COM) applied to the 2D Hubbard model, is reviewed and systematized. The 2D Hubbard model has been adopted as it has been considered the minimal model capable of describing the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundation, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying noncanonical algebras. In this case (underdoped cuprates—2D Hubbard model), the residual interactions—beyond a 2-pole approximation—between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the noncrossing approximation. Given this recipe and exploiting the few unknowns to enforce the Pauli principle content in the solution, it is possible to qualitatively describe some of the anomalous features of high-Tc cuprate superconductors such as large versus small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal versus antinodal physics, pseudogap(s), and kinks in the electronic dispersion. The resulting scenario envisages a smooth crossover between an ordinary weakly interacting metal sustaining weak, short-range antiferromagnetic correlations in the overdoped regime to an unconventional poor metal characterized by very strong, long-but-finite-range antiferromagnetic correlations leading to momentum-selective non-Fermi liquid features as well as to the opening of a pseudogap and to the striking differences between the nodal and the antinodal dynamics in the underdoped regime.