Strange Metal Phase Research Articles

Viable phenomenologies of the normal state of cuprates

We revisit the problem of constructing an elusive scaling theory of the strange metal phase of the cuprates. By using the four robust experimentally established temperature dependencies as the constitutive relations we then predict the scaling behaviors of a number of other observables, all those for which the reliable data are available being in agreement with experiment. Such predictions are also contrasted against the recent proposal inspired by the holographic approach, thus allowing one to critically assess the status of the latter.

Nonequilibrium transport in the strange metal and pseudogap phases of the cuprates

We propose that the non-equilibrium current measured in the $a-b$ plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively one expects the strange metal to be more different from a Fermi liquid than is the pseudogap. We compute the expected non-equilibrium transport signal with the three Green functions that are available in the literature: 1) marginal Fermi liquid theory, 2) the phenomenological ansatz for the pseudogap regime and 3) the Wilsonian reduction of the Hubbard model which contains both the strange metal and pseudogap. All three give linear IV curves at low bias voltages. Significant deviations from linearity at higher voltages obtain only in the marginal Fermi liquid approach. The key finding, however, is that IV curves for the strange metal/Fermi liquid contact that exceed that of the pseudogap/Fermi liquid system. If this is borne out experimentally, this implies that the strange metal is less orthogonal to a Fermi liquid than is the pseudogap. Within the Wilsonian reduction of the Hubbard model, this result is explained in terms of a composite-particle picture. Namely, the pseudogap corresponds to a confinement transition of the charge degrees of freedom present in the strange metal. In the strange metal the composite excitations break up and electron quasiparticles scatter off bosons. The bosons here, however, do not arise from phonons but from the charge degrees of freedom responsible for dynamical spectral weight transfer.

Origin of Strange Metallic Phase in Cuprate Superconductors

The origin of strange metallic phase is shown to exist due to these two conditions: (i) the electrons are strongly correlated such that there are neither band nor Mott–Hubbard gaps, and (ii) the electronic energy levels are crossed in such a way that there is an electronic energy gap between two energy levels associated with two different wave functions. The theory is also exploited to explain (i) the upward- and downward-shifts in the T-linear resistivity curves, and (ii) the spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements of the La–Sr–Cu–O Mott insulator.

Semi-local quantum liquids

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.

A phenomenological description of an incoherent Fermi liquid near optimal doping in high Tc cuprates

Marginal Fermi-liquid physics near optimal doping in high Tc cuprates has been explained within two competing scenarios such as the spin-fluctuation theory based on an itinerant picture and the slave-particle approach based on a localized picture. In this study we propose an alternative scenario for the anomalous transport within the context of the slave-particle approach. Although the marginal Fermi-liquid phenomenology was interpreted previously within deconfinement of the compact gauge theory, referred to as the strange metal phase, we start from confinement, introducing the Polyakov loop parameter into an SU(2) gauge theory formulation of the t–J model. The Polyakov loop parameter gives rise to incoherent electrons through the confinement of spinons and holons, which result from huge imaginary parts of self-energy corrections for spinons and holons. This confinement scenario serves a novel mechanism for the marginal Fermi-liquid transport in the respect that the scattering source has nothing to do with symmetry breaking. Furthermore, the incoherent Fermi-liquid state evolves into the Fermi-liquid phase through crossover instead of an artificial second-order transition as temperature is lowered, where the crossover phenomenon does not result from the Anderson–Higgs mechanism but originates from an energy scale in the holon sector. We fit experimental data for the electrical resistivity around the optimal doping and find a reasonable match between our theory and the experiment.

Mott physics, sign structure, ground state wavefunction, and high-T c superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-Tc superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature "strange metal phase" of the doped Mott insulator.

Zero sound in strange metallic holography

One way to model the strange metal phase of certain materials is via a holographic description in terms of probe D-branes in a Lifshitz spacetime, characterised by a dynamical exponent z. The background geometry is dual to a strongly-interacting quantum critical theory while the probe D-branes are dual to a finite density of charge carriers that can exhibit the characteristic properties of strange metals. We compute holographically the low-frequency and low-momentum form of the charge density and current retarded Green's functions in these systems for massless charge carriers. The results reveal a quasi-particle excitation when z<2, which in analogy with Landau Fermi liquids we call zero sound. The real part of the dispersion relation depends on momentum k linearly, while the imaginary part goes as k^2/z. When z is greater than or equal to 2 the zero sound is not a well-defined quasi-particle. We also compute the frequency-dependent conductivity in arbitrary spacetime dimensions. Using that as a measure of the charge current spectral function, we find that the zero sound appears only when the spectral function consists of a single delta function at zero frequency.

Strange Metal Transport Realized by Gauge/Gravity Duality

Fermi liquid theory explains the thermodynamic and transport properties of most metals. The so-called non-Fermi liquids deviate from these expectations and include exotic systems such as the strange metal phase of cuprate superconductors and heavy fermion materials near a quantum phase transition. We used the anti-de-Sitter/conformal field theory correspondence to identify a class of non-Fermi liquids; their low-energy behavior is found to be governed by a nontrivial infrared fixed point, which exhibits nonanalytic scaling behavior only in the time direction. For some representatives of this class, the resistivity has a linear temperature dependence, as is the case for strange metals.

Consistent theory of underdoped cuprates: Evolution of the resonating valence bond state from half filling

We have been able to resolve two long-standing issues that are central to the theory of high Tc superconductivity: (1) How is the physics of the doped region connected to that of the Mott insulator? (2) What is the origin of the two-dimensionality of the normal state? Specifically, based on the t-J model, we derive a renormalized Hamiltonian to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the bosonic RVB state of Arovas and Auerbach. Moving holes are assumed to destroy long-range magnetic order, which leads to a gap in the spinon spectrum. The presence of the spin gap allows us to derive a constrained Hamiltonian which describes sublattice-preserving hopping by renormalized holons and holon pairs, accompanied by spinon singlet backflows. Below the singlet condensation, i.e, the psudogap (as distinct from the spin gap), temperature T*, holons form a spinless Fermi liquid without an observable small Fermi surface. Above T* holons are localized, giving rise to a (gauge) insulator, which we identify with the strange metal phase. Holon pair hopping leads to a robust d-wave superconductor, its symmetry determined primarily by the symmetry of the RVB state at half filling. The predictions of the theory are shown to be consistent with the results of nmr, tunneling and transport experiments. Remarkably, the existence of the spin gap provides a natural explanation for the two-dimensionality of the normal state. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.

Where is the quantum critical point in the cuprate superconductors?

AbstractTransport measurements in the hole‐doped cuprates show a “strange metal” normal state with an electrical resistance which varies linearly with temperature. This strange metal phase is often identified with the quantum critical region of a zero temperature quantum critical point (QCP) at hole density $x = x_{\rm m} $, near optimal doping. A long‐standing problem with this picture is that low temperature experiments within the superconducting phase have not shown convincing signatures of such an optimal doping QCP (except in some cuprates with small superconducting critical temperatures). I review theoretical work which proposes a simple resolution of this enigma. The crossovers in the normal state are argued to be controlled by a QCP at xm linked to the onset of spin density wave (SDW) order in a “large” Fermi surface metal, leading to small Fermi pockets for $x &gt; x_{\rm m} $. A key effect is that the onset of superconductivity at low temperatures disrupts the simplest canonical quantum critical crossover phase diagram. In particular, the competition between superconductivity and SDW order shifts the actual QCP to a lower doping $x_{\rm s} &gt; x_{\rm m} $ in the underdoped regime, so that SDW order is only present for $x &gt; x_{\rm s} $. I review the phase transitions and crossovers associated with the QCPs at xm and xs: the resulting phase diagram as a function of x, temperature, and applied magnetic field consistently explains a number of recent experiments.

Transport anomalies of the strange metal: Resolution by hidden Fermi liquid theory

The strange metal phase of optimally and overdoped cuprates exhibits a number of anomalous transport properties: unsaturating linear T resistivity, distinct relaxation times for Hall angle and resistivity, temperature dependent anisotropic relaxation times, and a characteristic crossover from supposed Fermi Liquid to linear T behavior. All receive natural explanations and quantitative fits in terms of the Hidden Fermi Liquid theory.

Transport properties of HTS cuprates via spin–charge gauge approach

We show that the spin–charge gauge approach to the 2D t– J model can naturally explain many experimental features of transport properties for HTS cuprates, in particular temperature crossover phenomena in the “pseudogap phase” (PG) and 1/ T behavior of conductivities in the “strange metal phase” (SM) at higher T or x (doping concentration).

Superconductivity emerging near U(1) topological critical point and the strange metal phase in cuprates

Topological excitations are examined to establish an effective theory of the superconducting state evolving from the Mott insulator in high- T c cuprates. We emphasise the Coulomb interaction U that is governed by the electromagnetic U(1) compact group. The results are obtained for the layered t− t′− t ⊥− U− J system of strongly correlated electrons relevant for cuprates. We exploit the U(1) instanton phase field configurations for the cuprate phase diagram which displays the “hidden” quantum critical point covered by the superconducting lobe in addition to a sharp crossover between a compressible normal “strange metal” state and a region characterized by a vanishing compressibility, which marks the Mott insulator. The existence of robust topological quantum numbers explains the stability against small perturbation of the system and attributes to the topological “quantum protectorate” as observed in strongly correlated systems.

Spin-charge gauge symmetry: A way to tackle HTS cuprates?

We propose an explanation of several experimental features of transport phenomena in the normal state of high Tc cuprates in terms of a spin-charge gauge theory of the 2D t-J model. The calculated doping-temperature dependence for a number of physical quantities is found in qualitative agreement with data. In particular, we recover: in the ``pseudogap phase'' the metal-insulator crossover of the in-plane resistivity and of the NMR ``relaxation time'' and the insulating behavior of the out-of-plane resistivity; in the ``strange metal phase'' (at higher temperature or doping) the linear in T behavior of the above quantities; the appearance of maxima in the in-plane far-infrared conductivity in strongly underdoped and overdoped samples.

Transport properties in the strange-metal phase of high-Tccuprates: Spin-charge gauge theory versus experiments

The SU(2)xU(1) Chern-Simons spin-charge gauge approach developed earlier to describe the transport properties of the cuprate superconductors in the ``pseudogap'' regime, in particular, the metal-insulator crossover of the in-plane resistivity, is generalized to the ``strange metal'' phase at higher temperature/doping. The short-range antiferromagnetic order and the gauge field fluctuations, which were the key ingredients in the theory for the pseudogap phase, also play an important role in the present case. The main difference between these two phases is caused by the existence of an underlying statistical $\pi$-flux lattice for charge carriers in the former case, whereas the background flux is absent in the latter case. The Fermi surface then changes from small ``arcs'' in the pseudogap to a rather large closed line in the strange metal phase. As a consequence the celebrated linear in T dependence of the in-plane and out-of-plane resistivity is shown explicitly to recover. The doping concentration and temperature dependence of theoretically calculated in-plane and out-of-plane resistivity, spin-relaxation rate and AC conductivity are compared with experimental data, showing good agreement.

Superconductivity and high‐Tc superconductors

Superconductivity and high‐T_<i>c</i> superconductors

SU(2) formulation of thet−Jmodel: Application to underdoped cuprates

We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain $d$-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.

Theory of underdoped cuprates.

We develop a slave-boson theory for the t-J model at finite doping which respects an SU(2) symmetry -- a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contains d-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.