Incoherent transport across the strange-metal regime of overdoped cuprates

Transport properties in non-Fermi liquid phases of nodal-point semimetals

In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid (NFL) phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable NFL phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g. optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-calledLuttinger-Abrikosov-Benelavskii phaseof isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity.

Hidden transport phenomena in an ultraclean correlated metal

Advancements in materials synthesis have been key to unveil the quantum nature of electronic properties in solids by providing experimental reference points for a correct theoretical description. Here, we report hidden transport phenomena emerging in the ultraclean limit of the archetypical correlated electron system SrVO3. The low temperature, low magnetic field transport was found to be dominated by anisotropic scattering, whereas, at high temperature, we find a yet undiscovered phase that exhibits clear deviations from the expected Landau Fermi liquid, which is reminiscent of strange-metal physics in materials on the verge of a Mott transition. Further, the high sample purity enabled accessing the high magnetic field transport regime at low temperature, which revealed an anomalously high Hall coefficient. Taken with the strong anisotropic scattering, this presents a more complex picture of SrVO3 that deviates from a simple Landau Fermi liquid. These hidden transport anomalies observed in the ultraclean limit prompt a theoretical reexamination of this canonical correlated electron system beyond the Landau Fermi liquid paradigm, and more generally serves as an experimental basis to refine theoretical methods to capture such nontrivial experimental consequences emerging in correlated electron systems.

Emergent normal fluid in the superconducting ground state of overdoped cuprates

The microscopic mechanism for the disappearance of superconductivity in overdoped cuprates is still under heated debate. Here we use scanning tunneling spectroscopy to investigate the evolution of quasiparticle interference phenomenon in Bi2Sr2CuO6+δ over a wide range of hole densities. We find that when the system enters the overdoped regime, a peculiar quasiparticle interference wavevector with arc-like pattern starts to emerge even at zero bias, and its intensity grows with increasing doping level. Its energy dispersion is incompatible with the octet model for d-wave superconductivity, but is highly consistent with the scattering interference of gapless normal carriers. The gapless quasiparticles are mainly located near the antinodes and are independent of temperature, consistent with the disorder scattering mechanism. We propose that a branch of normal fluid emerges from the pair-breaking scattering between flat antinodal bands in the quantum ground state, which is the primary cause for the reduction of superfluid density and suppression of superconductivity in overdoped cuprates.

Momentum-dependent scaling exponents of nodal self-energies measured in strange metal cuprates and modelled using semi-holography

The anomalous strange metal phase found in high-Tc cuprates does not follow the conventional condensed-matter principles enshrined in the Fermi liquid and presents a great challenge for theory. Highly precise experimental determination of the electronic self-energy can provide a test bed for theoretical models of strange metals, and angle-resolved photoemission can provide this as a function of frequency, momentum, temperature and doping. Here we show that constant energy cuts through the nodal spectral function in (Pb,Bi)2Sr2-xLaxCuO6+δ have a non-Lorentzian lineshape, consistent with a self-energy that is k dependent. This provides a new test for aspiring theories. Here we show that the experimental data are captured remarkably well by a power law with a k-dependent scaling exponent smoothly evolving with doping, a description that emerges naturally from anti-de Sitter/conformal-field-theory based semi-holography. This puts a spotlight on holographic methods for the quantitative modelling of strongly interacting quantum materials like the cuprate strange metals.

The Wiedemann-Franz law in doped Mott insulators without quasiparticles

Many metallic quantum materials display anomalous transport phenomena that defy a Fermi liquid description. Here, we use numerical methods to calculate thermal and charge transport in the doped Hubbard model and observe a crossover separating high- and low-temperature behaviors. Distinct from the behavior at high temperatures, the Lorenz number [Formula: see text] becomes weakly doping dependent and less sensitive to parameters at low temperatures. At the lowest numerically accessible temperatures, [Formula: see text] roughly approaches the Wiedemann-Franz constant [Formula: see text], even in a doped Mott insulator that lacks well-defined quasiparticles. Decomposing the energy current operator indicates a compensation between kinetic and potential contributions, which may help to clarify the interpretation of transport experiments beyond Boltzmann theory in strongly correlated metals.

Shot noise in a strange metal

Strange-metal behavior has been observed in materials ranging from high-temperature superconductors to heavy fermion metals. In conventional metals, current is carried by quasiparticles; although it has been suggested that quasiparticles are absent in strange metals, direct experimental evidence is lacking. We measured shot noise to probe the granularity of the current-carrying excitations in nanowires of the heavy fermion strange metal YbRh2Si2. When compared with conventional metals, shot noise in these nanowires is strongly suppressed. This suppression cannot be attributed to either electron-phonon or electron-electron interactions in a Fermi liquid, which suggests that the current is not carried by well-defined quasiparticles in the strange-metal regime that we probed. Our work sets the stage for similar studies of other strange metals.

Signature of quantum criticality in cuprates by charge density fluctuations

The universality of the strange metal phase in many quantum materials is often attributed to the presence of a quantum critical point (QCP), a zero-temperature phase transition ruled by quantum fluctuations. In cuprates, where superconductivity hinders direct QCP observation, indirect evidence comes from the identification of fluctuations compatible with the strange metal phase. Here we show that the recently discovered charge density fluctuations (CDF) possess the right properties to be associated to a quantum phase transition. Using resonant x-ray scattering, we studied the CDF in two families of cuprate superconductors across a wide doping range (up to p = 0.22). At p* ≈ 0.19, the putative QCP, the CDF intensity peaks, and the characteristic energy Δ is minimum, marking a wedge-shaped region in the phase diagram indicative of a quantum critical behavior, albeit with anomalies. These findings strengthen the role of charge order in explaining strange metal phenomenology and provide insights into high-temperature superconductivity.

Ferromagnetic Fluctuations in the Heavily Overdoped Regime of Single-Layer High-Tc Cuprate Superconductors

To investigate proposed ferromagnetic fluctuations in the so-called single-layer Bi-2201 and La-214 high-Tc cuprates, we performed magnetization and electrical resistivity measurements using single-layer Tl-2201 cuprates Tl2Ba2CuO6+δ and La-214 La2-xSrxCuO4 in the heavily overdoped regime. Magnetization of Tl2Ba2CuO6+δ and La2-xSrxCuO4 exhibited the tendency to be saturated in high magnetic fields at low temperatures, suggesting the precursor behavior toward the formation of a ferromagnetic order. It was found that the power of temperature n obtained from the temperature dependence of the electrical resistivity is ~4/3 and ~5/3 for Bi-2201 and La2-xSrxCuO4, respectively, and is ~4/3 at high temperatures and ~5/3 at low temperatures in Tl2Ba2CuO6+δ. These results suggest that two- and three-dimensional ferromagnetic fluctuations exist in Bi-2201 and La2-xSrxCuO4, respectively. In Tl2Ba2CuO6+δ, it is suggested that the dimension of ferromagnetic fluctuations is two at high temperatures and three at low temperatures, respectively. The dimensionality of ferromagnetic fluctuations is understood in terms of the dimensionality of the crystal structure and the bonding of atoms in the blocking layer.

Transport properties and doping evolution of the Fermi surface in cuprates

Measured transport properties of three representative cuprates are reproduced within the paradigm of two electron subsystems, itinerant and localized. The localized subsystem evolves continuously from the Cu 3d[Formula: see text] hole at half-filling and corresponds to the (pseudo)gapped parts of the Fermi surface. The itinerant subsystem is observed as a pure Fermi liquid (FL) with material-independent universal mobility across the doping/temperature phase diagram. The localized subsystem affects the itinerant one in our transport calculations solely by truncating the textbook FL integrals to the observed (doping- and temperature-dependent) Fermi arcs. With this extremely simple picture, we obtain the measured evolution of the resistivity and Hall coefficients in all three cases considered, including LSCO which undergoes a Lifshitz transition in the relevant doping range, a complication which turns out to be superficial. Our results imply that prior to evoking polaronic, quantum critical point, quantum dissipation, or even more exotic scenarios for the evolution of transport properties in cuprates, Fermi-surface properties must be addressed in realistic detail.

Puddle formation and persistent gaps across the non-mean-field breakdown of superconductivity in overdoped (Pb,Bi)2Sr2CuO6+δ

The cuprate high-temperature superconductors exhibit many unexplained electronic phases, but the superconductivity at high doping is often believed to be governed by conventional mean-field Bardeen-Cooper-Schrieffer theory¹. However, it was shown that the superfluid density vanishes when the transition temperature goes to zero^2,3, in contradiction to expectations from Bardeen-Cooper-Schrieffer theory. Our scanning tunnelling spectroscopy measurements in the overdoped regime of the (Pb,Bi)₂Sr₂CuO_6+δ high-temperature superconductor show that this is due to the emergence of nanoscale superconducting puddles in a metallic matrix^4,5. Our measurements further reveal that this puddling is driven by gap filling instead of gap closing. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory.

The breakdown of both strange metal and superconducting states at a pressure-induced quantum critical point in iron-pnictide superconductors

Here we report the first observation of the concurrent breakdown of the strange metal (SM) normal state and superconductivity at a pressure-induced quantum critical point in Ca₁₀(Pt₄As₈)((Fe_0.97Pt_0.03)₂As₂)₅ superconductor. We find that, upon suppressing the superconducting state, the power exponent (α) changes from 1 to 2, and the slope of the temperature-linear resistivity per FeAs layer (A^□) gradually diminishes. At a critical pressure, A^□ and superconducting transition temperature (T_c) go to zero concurrently, where a quantum phase transition from a superconducting state with a SM normal state to a non-superconducting Fermi liquid state occurs. Scaling analysis reveals that the change of A^□ with T_c obeys the relation of T_c ~ (A^□)^0.5, similar to what is seen in other chemically doped unconventional superconductors. These results suggest that there is a simple but powerful organizational principle of connecting the SM normal state with the high-T_c superconductivity.

Dissipative Quantum Criticality as a Source of Strange Metal Behavior

The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/T∼log(1/T), down to low temperatures.

Critical metallic phase in the overdoped random t-J model

We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev-Ye-Kitaev-like large-M limit with SU(M) spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom, t-J models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non-Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparameterization symmetry, akin to Sachdev-Ye-Kitaev (SYK) models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-T resistivity in a broad region. The critical metal also displays a strong particle-hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two-dimensional Hubbard model

SignificanceMost metals display an electron-scattering rate [Formula: see text] that follows [Formula: see text] at low temperatures, as prescribed by Fermi liquid theory. But there are important exceptions. One of the most prominent examples is the "strange" metal regime in overdoped cuprate supercondcutors, which exhibits a linear T dependence of the scattering rate [Formula: see text] that reaches a putative Planckian limit. Here, using cutting-edge computational approaches, we show that T-linear scattering rate can emerge from the overdoped Hubbard model at low temperatures. Our results agree with cuprate experiments in various aspects but challenge the Planckian limit. Finally, by identifying antiferromagnetic fluctuations as the physical origin of the T-linear scattering rate, we discover the microscopic mechanism of strange metallicity in cuprates.

High-T c Cuprates: a Story of Two Electronic Subsystems

A review of the phenomenology and microscopy of cuprate superconductors is presented, with particular attention to universal conductance features, which reveal the existence of two electronic subsystems. The overall electronic system consists of 1 + p charges, where p is the doping. At low dopings, exactly one hole is localized per planar copper-oxygen unit, while upon increasing doping and temperature, the hole is gradually delocalized and becomes itinerant. Remarkably, the itinerant holes exhibit identical Fermi liquid character across the cuprate phase diagram. This universality enables a simple count of carrier density and yields comprehensive understanding of the key features in the normal and superconducting state. A possible superconducting mechanism is presented, compatible with the key experimental facts. The base of this mechanism is the interaction of fast Fermi liquid carriers with localized holes. A change in the microscopic nature of chemical bonding in the copper oxide planes, from ionic to covalent, is invoked to explain the phase diagram of these fascinating compounds.

A mechanism for the strange metal phase in rare-earth intermetallic compounds

The elusive strange metal phase (ground state) was observed in a variety of quantum materials, notably in f-electron–based rare-earth intermetallic compounds. Its emergence has remained unclear. Here, we propose a generic mechanism for this phenomenon driven by the interplay of the gapless fermionic short-ranged antiferromagnetic spin correlation and critical bosonic charge fluctuations near a Kondo breakdown quantum phase transition. It is manifested as a fluctuating Kondo-scattering–stabilized critical (gapless) fermionic spin liquid. It shows ω/T scaling in dynamical electron scattering rate, a signature of quantum criticality. Our results on quasilinear-in-temperature scattering rate and logarithmic-in-temperature divergence in specific heat coefficient as temperature vanishes were recently seen in CePd1−xNi_xAl.

A major mystery in strongly interacting quantum systems is the microscopic origin of the “strange metal” phenomenology, with unconventional metallic behavior that defies Landau’s Fermi liquid framework for ordinary metals. This state is found across a wide range of quantum materials, notably in rare-earth intermetallic compounds at finite temperatures (T) near a magnetic quantum phase transition, and shows a quasilinear-in-temperature resistivity and a logarithmic-in-temperature specific heat coefficient. Recently, an even more enigmatic behavior pointing toward a stable strange metal ground state was observed in CePd1−xNi_xAl, a geometrically frustrated Kondo lattice compound. Here, we propose a mechanism for such phenomena driven by the interplay of the gapless fermionic short-ranged antiferromagnetic spin correlations (spinons) and critical bosonic charge (holons) fluctuations near a Kondo breakdown quantum phase transition. Within a dynamical large-N approach to the Kondo–Heisenberg lattice model, the strange metal phase is realized in transport and thermodynamical quantities. It is manifested as a fluctuating Kondo-scattering–stabilized critical (gapless) fermionic spin-liquid metal. It shows ω/T scaling in dynamical electron scattering rate, a signature of quantum criticality. Our results offer a qualitative understanding of the CePd1−xNi_xAl compound and suggest a possibility of realizing the quantum critical strange metal phase in correlated electron systems in general.

Scaling of the strange-metal scattering in unconventional superconductors

Marked evolution of properties with minute changes in the doping level is a hallmark of the complex chemistry that governs copper oxide superconductivity as manifested in the celebrated superconducting domes and quantum criticality taking place at precise compositions^1-4. The strange-metal state, in which the resistivity varies linearly with temperature, has emerged as a central feature in the normal state of copper oxide superconductors^5-9. The ubiquity of this behaviour signals an intimate link between the scattering mechanism and superconductivity^10-12. However, a clear quantitative picture of the correlation has been lacking. Here we report the observation of precise quantitative scaling laws among the superconducting transition temperature (T_c), the linear-in-T scattering coefficient (A₁) and the doping level (x) in electron-doped copper oxide La_2-xCe_xCuO₄ (LCCO). High-resolution characterization of epitaxial composition-spread films, which encompass the entire overdoped range of LCCO, has enabled us to systematically map its structural and transport properties with unprecedented accuracy and with increments of Δx = 0.0015. We have uncovered the relations T_c ~ (x_c - x)^0.5 ~ (A₁^□)^0.5, where x_c is the critical doping in which superconductivity disappears and A₁^□ is the coefficient of the linear resistivity per CuO₂ plane. The striking similarity of the T_c versus A₁^□ relation among copper oxides, iron-based and organic superconductors may be an indication of a common mechanism of the strange-metal behaviour and unconventional superconductivity in these systems.

Charge density waves and Fermi surface reconstruction in the clean overdoped cuprate superconductor Tl2Ba2CuO6+δ

Hall effect and quantum oscillation measurements on high temperature cuprate superconductors show that underdoped compositions have small Fermi surface pockets whereas when heavily overdoped, a single much larger pocket is found. The origin of this change in electronic structure has been unclear, but may be related to the high temperature superconductivity. Here we show that the clean overdoped single-layer cuprate Tl₂Ba₂CuO_6+δ (Tl2201) displays CDW order with a remarkably long correlation length ξ ≈ 200 Å which disappears above a hole doping of p_CDW ≈ 0.265. We show that the evolution of the electronic properties of Tl2201 as the doping is lowered may be explained by a Fermi surface reconstruction which accompanies the emergence of the CDW below p_CDW. Our results demonstrate importance of CDW correlations in understanding the electronic properties of overdoped cuprates.

The origin of the Fermi surface reconstruction that occurs in cuprate superconductors as hole doping increases remains unclear. Here, the authors observe long range charge density wave (CDW) order in the overdoped single-layer cuprate Tl₂Ba₂CuO_6+δ, which then disappears above a hole concentration 0.265, suggesting a correlation between Fermi surface reconstruction and the emergence of the CDW.

Signatures of a strange metal in a bosonic system

Fermi liquid theory forms the basis for our understanding of the majority of metals: their resistivity arises from the scattering of well defined quasiparticles at a rate where, in the low-temperature limit, the inverse of the characteristic time scale is proportional to the square of the temperature. However, various quantum materials^1-15-notably high-temperature superconductors^1-10-exhibit strange-metallic behaviour with a linear scattering rate in temperature, deviating from this central paradigm. Here we show the unexpected signatures of strange metallicity in a bosonic system for which the quasiparticle concept does not apply. Our nanopatterned YBa₂Cu₃O_7-δ (YBCO) film arrays reveal linear-in-temperature and linear-in-magnetic field resistance over extended temperature and magnetic field ranges. Notably, below the onset temperature at which Cooper pairs form, the low-field magnetoresistance oscillates with a period dictated by the superconducting flux quantum, h/2e (e, electron charge; h, Planck's constant). Simultaneously, the Hall coefficient drops and vanishes within the measurement resolution with decreasing temperature, indicating that Cooper pairs instead of single electrons dominate the transport process. Moreover, the characteristic time scale τ in this bosonic system follows a scale-invariant relation without an intrinsic energy scale: ħ/τ ≈ a(k_BT + γμ_BB), where ħ is the reduced Planck's constant, a is of order unity^7,8,11,12, k_B is Boltzmann's constant, T is temperature, μ_B is the Bohr magneton and γ ≈ 2. By extending the reach of strange-metal phenomenology to a bosonic system, our results suggest that there is a fundamental principle governing their transport that transcends particle statistics.