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Physical review. B, Condensed matter

Quantum critical point associated with the electronic topological transition in a two-dimensional electron system as a driving force for anomalies in underdoped high- Tc cuprates

F. P. Onufrieva, Pierre M. Pfeuty

Published Jan 1, 2000• 28 citations
Publisher

Abstract

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-${T}_{c}$ cuprates) and have a striking similarity with the anomalies observed in the high-${T}_{c}$ 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).

DOI
10.1103/physrevb.61.799

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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 \ensuremathδ=1\ensuremath−n).\ensuremath{\delta}=1\ensuremath{-}n).\ensuremathδ=1\ensuremath−n). We show that the ETT point (\ensuremathδ=\ensuremathδc,T=0)(\ensuremath{\delta}={\ensuremath{\delta}}_{c}, T=0)(\ensuremathδ=\ensuremathδc​,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,\ensuremathδ>\ensuremathδc)(T=0, \ensuremath{\delta}>{\ensuremath{\delta}}_{c})(T=0,\ensuremathδ>\ensuremathδc​) 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{t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}Jt\ensuremath−t\ensuremath′\ensuremath−J model.) The anomalies take place on one side of the ETT (\ensuremathδ<\ensuremathδc(\ensuremath{\delta}<{\ensuremath{\delta}}_{c}(\ensuremathδ<\ensuremathδc​ in the case of t\ensuremath′/t<0{t}^{\ensuremath{'}}/t<0t\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∗(\ensuremathδ)\ensuremath∝\ensuremathδc\ensuremath−\ensuremathδ,{T}^{*}(\ensuremath{\delta})\ensuremath{\propto}{\ensuremath{\delta}}_{c}\ensuremath{-}\ensuremath{\delta},T∗(\ensuremathδ)\ensuremath∝\ensuremathδc​\ensuremath−\ensuremathδ, which grows from the point \ensuremathδ=\ensuremathδc\ensuremath{\delta}={\ensuremath{\delta}}_{c}\ensuremathδ=\ensuremathδc​ on the side \ensuremathδ<\ensuremathδc.\ensuremath{\delta}<{\ensuremath{\delta}}_{c}.\ensuremathδ<\ensuremathδc​. 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).
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=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=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- Tc{T}_{c}Tc​ cuprates reveals a striking similarity to the behavior observed experimentally in the underdoped regime.
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.
We show that a two-dimensional (2D) metal in a superconducting (SC) state with wave-vector-dependent gap behaves as a quantum-spin liquid characterized by a collective mode of resonance type. Formally the mode exists whatever is a form of Fermi surface (FS). However, when the latter is spherical the effect is rather formal: any factor leading to an even weak electron scattering, like finite T, impurity, etc., easily kills the mode. On the contrary, for the type of FS observed in the high-Tc{T}_{c}Tc​ cuprates (characterized by a proximity to the saddle-point wave vectors) the resonance mode exists in a true sense being well separated from the electron-hole continuum and well defined. The effect is due to the effective 1D dimension in a proximity of electronic topological transition quantum critical point. The physical nature of the collective mode varies progressively between two possibilities. In the case of a weak interaction, the resonance mode is a typical effect of a two-particle bound state that appears slightly below the bottom of the two-particle continuum. The effect exists even in the case of infinitesimally weak interaction (of relevant sign). In the case of a strong or intermediate interaction, it is a critical mode existing as a precursor of spin-density wave (SDW) instability. The gap of the collective mode is not related directly to the value of the SC gap (being, however, limited by the latter from above) but rather to a proximity to SDW instability. We predict also a second collective mode lying inside the two-particle continuum. The existence of these two modes and the particular form of their dispersion in the case corresponding to the underdoped cuprates ${(d}_{{x}^{2}\ensuremath{\sim}{y}^{2}}$ symmetry of SC gap, exchange interaction of antiferromagnetic sign, etc.) allows one to understand the main features observed experimentally in the underdoped cuprates, namely the so-called ``41 meV resonance peak'' and ``24 meV incommensurability'' and their two-dimensional wave vector dependences, the doping evolution of the spin dynamics and many other features. The theory also predicts new features to be tested experimentally.
Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a nonFermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t � , we find a classical critical point at temperature Tc. This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature Tc extrapolates to zero
Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two-dimensional Hubbard model with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. At ${t}^{\ensuremath{'}}\ensuremath{\le}0$, we identify a line of Lifshitz transition points associated with a change in the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects and becomes more singular when ${t}^{\ensuremath{'}}$ becomes more negative. The resulting temperature dependence on the bare ddd-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at ${t}^{\ensuremath{'}}\ensuremath{\le}0$ extends our understanding of the quantum critical region in the phase diagram and shines lights on future investigations of the nature of the quantum critical point in the two-dimensional Hubbard model.
Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t', we find a classical critical point at temperature Tc. This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature Tc extrapolates to zero as t' vanishes, we conclude that a QCP connects the Fermi liquid to the pseudo-gap region, and that the marginal Fermi-liquid behaviour in its vicinity is the analogue of the supercritical region in the liquid-gas transition. © 2011 The Royal Society.