We numerically study a model of interacting spin-$1/2$ electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi liquid phase with a large Fermi surface volume and a low-doping phase with local moments ordering into a spin-glass. We show that this quantum critical point has non-Fermi liquid properties characterized by $T$-linear Planckian behavior, $ω/T$ scaling and slow spin dynamics of the Sachdev-Ye-Kitaev (SYK) type. The $ω/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a `skewed' non-Fermi liquid.
A purely Fermi-surface formula is proposed for the Ohmic "minimum metallic conductivity" tensor of clean metals with "Planckian limit" inelastic dissipation. This revises a recent proposal by Legros et al.
Perfect $T$-linear resistivity associated with universal scattering rate: $1/τ=αk_B T/\hbar$ with $α\sim 1$, so-called Planckian metal state, has been observed in the normal state of a variety of strongly correlated superconductors close to a quantum critical point. However, the microscopic origin of this intriguing phenomena and its link to quantum criticality still remains an outstanding open problem. In this work, we observe the quantum-critical $T/B$-scaling of the Planckian metal state in the resistivity and heat capacity of heavy-electron superconductor Ce$_{1-x}$Nd$_x$CoIn$_5$ in magnet…
Heavily oxygen deficient NdNiO$_3$ (NNO) films, which are insulating due to electron localization, contain pristine regions that undergo a hidden metal-insulator transition. Increasing oxygen content increases the connectivity of the metallic regions and the metal-insulator transition is first revealed, upon reaching the percolation threshold, by the presence of hysteresis. Only upon further oxygenation is the global metallic state (with a change in the resistivity slope) eventually achieved. It is shown that sufficient oxygenation leads to linear temperature dependence of resistivity in the m…
We discuss the recent extension of the Sachdev-Ye-Kitaev (SYK) microscopic model by Patel and Sachdev in arXiv:1906.03265, which demonstrates the characteristic features of the Khodel-Shaginyan fermion condensate -- the existence of the finite region of momenta, where the energy of electrons is exactly zero (the flat band). The microscopic derivation of the flat band in this interacting model supports the original idea of Khodel and Shaginyan based on the phenomenological approach. It also suggests that it is the flat band, which is responsible for the linear dependence of resistivity on tempe…
Strange metal behavior refers to a linear temperature dependence of the electrical resistivity at temperatures below the Mott-Ioffe-Regel limit. It is seen in numerous strongly correlated electron systems, from the heavy fermion compounds, via transition metal oxides and iron pnictides, to magic angle twisted bi-layer graphene, frequently in connection with unconventional or "high temperature" superconductivity. To achieve a unified understanding of these phenomena across the different materials classes is a central open problem in condensed matter physics. Tests whether the linear-in-temperat…
Strange metal behavior appears across a variety of condensed matter settings and beyond, and achieving a universal understanding is an exciting prospect. The beyond-Landau quantum criticality of Kondo destruction has had considerable success in describing the behavior of strange metal heavy fermion compounds, and there is some evidence that the associated partial localization-delocalization nature can be generalized to diverse materials classes. Other potential overarching principles at play are also being explored. An intriguing proposal is that Planckian scattering, with a rate of $k_{\rm B}…
We review the appearance of the Planckian time $τ_\text{Pl} = \hbar/(k_B T)$ in both conventional and unconventional metals. We give a pedagogical discussion of the various different timescales (quasiparticle, transport, many-body) that characterize metals, emphasizing conditions under which these times are the same or different. Throughout, we have attempted to clear up aspects of the problem that had been confusing us, in the hope that this helps the reader as well. We discuss the possibility of a Planckian bound on dissipation from both a quasiparticle and a many-body perspective. Planckian…
It has recently been conjectured that the transport relaxation rate in metals is bounded above by the temperature of the system. In this work, we discuss the transport phenomenology of overdoped electron-doped cuprates, which we show constitute an unambiguous counterexample to this putative "Planckian" bound, raising serious questions about the efficacy of the bound.
Materials with strongly-correlated electrons exhibit interesting phenomena such as metal-insulator transitions and high-temperature superconductivity. In stark contrast to ordinary metals, electron transport in these materials is thought to resemble the flow of viscous fluids. Despite their differences, it is predicted that transport in both, conventional and correlated materials, is fundamentally limited by the uncertainty principle applied to energy dissipation. Here we discover hydrodynamic electron flow in the Weyl-semimetal tungsten phosphide (WP2). Using thermal and magneto-electric tran…
We present a critical review of recent attempts to introduce the new quantum ("Planckian") limit for the temperature dependence of inelastic scattering rate of electrons in metals. We briefly discuss the main experimental facts and some simple theoretical models explaining the linear in temperature growth of resistivity (starting from very low temperatures) in superconducting cuprates and some similar systems. There is no commonly accepted theoretical explanation of such behavior up to now. We also discuss the known quantum limits for electrical conductivity (resistance). It is shown that the …
Universality of linear in temperature and linear in field Planckian scattering rate in high temperature cuprate superconductors
National Center for Theoretical Sciences（国家理论科学中心）；National Yang Ming Chiao Tung University（国立阳明交通大学）；Universidad de Los Andes（洛斯安第斯大学）；Universidad del Rosario（玫瑰大学）；National High Magnetic Field Laboratory（国家高磁场实验室）；Florida State University（佛罗里达州立大学）
We present a lattice model of fermions with $N$ flavors and random interactions which describes a Planckian metal at low temperatures, $T \rightarrow 0$, in the solvable limit of large $N$. We begin with quasiparticles around a Fermi surface with effective mass $m^\ast$, and then include random interactions which lead to fermion spectral functions with frequency scaling with $k_B T/\hbar$. The resistivity, $ρ$, obeys the Drude formula $ρ= m^\ast/(n e^2 τ_{\textrm{tr}})$, where $n$ is the density of fermions, and the transport scattering rate is $1/τ_{\textrm{tr}} = f \, k_B T/\hbar$; we find $…
In various "strange" metals, electrons undergo Planckian dissipation, a strong and anomalous scattering that grows linearly with temperature, in contrast to the quadratic temperature dependence expected from the standard theory of metals. In some cuprates and pnictides, a linear dependence of the resistivity on magnetic field has also been considered anomalous - possibly an additional facet of Planckian dissipation. Here we show that the resistivity of the cuprate strange metals Nd-LSCO and LSCO is quantitatively consistent with the standard Boltzmann theory of electron motion in a magnetic fi…
Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. In this paper we show that magic-angle bilayer graphene exhibits another hallmark of strongly correlated systems --- a broad regime of $T-$linear resistivity above a small, density dependent, crossover temperature--- for a range of fillings near the correlated insulator. We also extract a transport "scattering rate", which satisfies a near Planckian form that is universally related to the ratio of $(k_BT/\hbar)$. Our…
A variety of "strange metals" exhibit resistivity that decreases linearly with temperature as $T\rightarrow 0$, in contrast with conventional metals where resistivity decreases as $T^2$. This $T$-linear resistivity has been attributed to charge carriers scattering at a rate given by $\hbar/τ=αk_{\rm B} T$, where $α$ is a constant of order unity. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering---the "Planckian limit"---but little is known about the underlying origins of this l…
Metallic quantum criticality is a central theme in a variety of strongly correlated systems. Recent experiments have raised the fundamental question of how the charge response can be singular in cases where the Landau framework of quantum criticality allows singularity only in the spin channel. Motivated by this emerging issue, we study the particle-hole-asymmetric regime of a Bose-Fermi Anderson model with power-law forms for both the bosonic bath spectrum and the fermionic band density of states. We realize a particle-hole-asymmetric quantum-critical state where quasiparticles are lost due t…
We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems and conventional metals. We show that the observed scattering rate in strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors stems from phonon contribution that induce the linear temperature dependence of a resistivity. The above phonons are formed by the presence of flat band, resulting from the topological fermion condensation quantum phase transition (FCQPT).…
Efforts to understand metallic behaviour have led to important concepts such as those of strange metal, bad metal or Planckian metal. However, a unified description of metallic resistivity is still missing. An empirical analysis of a large variety of metals shows that the parallel resistor formalism used in the cuprates, which includes T-linear and T-quadratic dependence of the electron scattering rates, can be used to provide a phenomenological description of the electrical resistivity in all metals, where these two contributions are shown to correspond to the two first terms of a Taylor expa…
Could it be that the matter from the electrons in high Tc superconductors is of a radically new kind that may be called "many body entangled compressible quantum matter"? Much of this text is intended as an easy to read tutorial, explaining recent theoretical advances that have been unfolding at the cross roads of condensed matter- and string theory, black hole physics as well as quantum information theory. These developments suggest that the physics of such matter may be governed by surprisingly simple principles. My real objective is to present an experimental strategy to test critically whe…
By means of first principles schemes based on magnetically constrained density functional theory and on the band unfolding technique we study the effect of doping on the conducting behaviour of the Lifshitz magnetic insulator NaOsO3. Electron doping is treated realistically within a supercell approach by replacing sodium with magnesium at different concentrations. Our data indicate that by increasing carrier concentration the system is subjected to two types of transition: (i) insulator to bad metal at low doping and low temperature and (ii) bad metal to metal at high doping and/or high-temper…
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator…
P. W. Phillips, N. E. Hussey, P. Abbamonte (Review Article, 8 July 2022, eabh4273) consider heavy fermion (HF) metals and high-$T_c$ superconductors naming them strange metals. They analyze such features of strange metals as quantum criticality, Planckian dissipation and recently observed fundamental link between the high-$T_c$ superconductivity and strange metals, and conclude that these problems can be possibly resolved within the framework of theories based on gravity, etc. In this comment we discuss that this claim is not correct and the successful description of the quantum criticality, P…
Charge dynamics of (Ti1-xVx)2O3 with x=0-0.06 has been investigated by measurements of charge transport and optical conductivity spectra in a wide temperature range of 2-600K with the focus on the thermally and doping induced insulator-metal transitions (IMTs). The optical conductivity peaks for the interband transitions in the 3d t2g manifold are observed in the both insulating and metallic states, while their large variation (by ~0.4 eV) with change of temperature and doping level scales with that of the Ti-Ti dimer bond length, indicating the weakened singlet bond in the course of IMTs. The…
The insulator to metal transition in LaTiO_3 induced by La substitution via Sr is studied within multi-band exact diagonalization dynamical mean field theory at finite temperatures. It is shown that weak hole doping triggers a large interorbital charge transfer, with simultaneous electron and hole doping of t2g subbands. The transition is first-order and exhibits phase separation between insulator and metal. In the metallic phase, subband compressibilities become very large and have opposite signs. Electron doping gives rise to an interorbital charge flow in the same direction as hole doping. …
We study the doping-driven Mott metal-insulator transition for multi-orbital Hubbard models with Hund's exchange coupling at finite temperatures. As in the single-orbital Hubbard model, the transition is of first-order within dynamical mean field theory, with a coexistence region where two solutions can be stabilized. We find, that in the presence of finite Hund's coupling, the insulating phase is connected to a badly metallic phase, which extends to surprisingly large dopings. While fractional power-law behavior of the self-energies on the Matsubara axis is found on both sides of the transiti…
Filling-control metal-insulator transitions (MITs) and related electronic phase diagrams have been investigated for hole-doped vanadium oxides, Pr_{1-x}Ca_xVO_3, Nd_{1-x}Sr_xVO_3 and Y_{1-x}Ca_xVO_3, with perovskite structure. The increase of the doping level x causes the melting of the G-type (and C-type) orbital order, prior to or concomitantly with the MIT, due partly to the doped-hole motion and partly to the ramdom potential arising from the quenched disorder. In particular, the G-type spin- and C-type orbital-ordered phase present in Y_{1-x}Ca_xVO_3 disappears immediately upon hole dopin…
We show that by Ca-doping the Bi2Se3 topological insulator, the Fermi level can be fine tuned to fall inside the band gap and therefore suppress the bulk conductivity. Non-metallic Bi2Se3 crystals are obtained. On the other hand, the Bi2Se3 topological insulator can also be induced to become a bulk superconductor, with Tc ~ 3.8 K, by copper intercalation in the van der Waals gaps between the Bi2Se3 layers. Likewise, an as-grown crystal of metallic Bi2Te3 can be turned into a non-metallic crystal by slight variation of the Te content. The Bi2Te3 topological insulator shows small amounts of supe…
Transport properties of SrTiO$_3$-channel field-effect transistors with parylene organic gate insulator have been investigated. By applying gate voltage, the sheet resistance falls below $R_{\Box}$ $\sim$ 10 k$Ω$ at low temperatures, with carrier mobility exceeding 1000 cm$^2$/Vs. The temperature dependence of the sheet resistance taken under constant gate voltage exhibits metallic behavior ($dR$/$dT$ $>$ 0). Our results demonstrate an insulator to metal transition in SrTiO$_3$ driven by electrostatic carrier density control.
Hole-doping effects are investigated on the {\it t-J} ladder model with the linked-tetrahedra structure. We discuss how a metal-insulator transition occurs upon hole doping with particular emphasis on the effects of geometrical frustration. By computing the electron density and the spin correlation function by the density matrix renormalization group, we show that strong frustration triggers a first-order transition to a metallic phase, when holes are doped into the plaquette-singlet phase. By examining spin excitations in a metallic case in detail, we discuss whether the spin-gap phase persis…
We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $ξ_l$, in the insulating state. At finite values of $W$ we find results consistent with $ξ_l \sim | μ- μ_c|^{- 1/2} $ where $μ_c$ is the critical chemical potential. In contrast, $ξ_l \sim | μ- μ_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results i…
In this paper I discuss the electronic structure and properties of a specific, rather unconventional class of transition metal (TM) compounds, e.g. TM oxides, which formally have unusually high values of the oxidation state, or valence, of TM. In contrast to the typical situation, in this case the charge-transfer gap (excitation energy for the transfer of electrons from the ligands to the TM) is very small and may even become negative. As a result a profound modification of an electronic structure and of all the properties may take place: there appear holes in the oxygen p-bands (``self-doping…
We consider how electron-phonon interaction influences the insulator-metal transitions driven by doping in the strongly correlated system. Using the polaronic version of the generalized tight-binding method, we investigate a multiband two-dimensional model taking into account both Holstein and Su-Schrieffer-Heeger types of electron-lattice contributions. For adiabatic ratio of the hopping parameter and the phonon field energy, different types of band structure evolution are observed in a wide electron-phonon parameter range. We demonstrate the relationship between transition features and such …
Insulator-metal transition is investigated self-consistently on the frustrated Shastry-Sutherland lattice in the framework of Slave-Boson mean-field theory. Due to the presence of quasi-flat band structure characteristic, the system displays a spin-density-wave (SDW) insulating phase at the weak doping levels, which is robust against frustration, and it will be transited into an SDW metallic phase at high doping levels. As further increasing the doping, the temperature or the frustration on the diagonal linking bonds, the magnetic order $m$ will be monotonically suppressed, resulting in the ap…
"Bad metals" have a large linear resistivity at high-T that is universally seen in oxides close to the Mott-Hubbard insulating phase. They also have an universal thermopower alpha(T): (i) at very low doping (lightly doped) alpha(T) has a pronounced low-T peak that shifts to higher-T with doping; (ii) at moderate doping (underdoped) alpha(T) has a small low-T peak that shifts to lower-T with doping and has a high-T sign change; and (iii) at the highest doping (overdoped) alpha(T) is negative and depends monotonically on T. Here we show that the simplified Hubbard model provides an easy to under…
Strange metallicity encompasses high magnetic field-induced superconductivity in UTe2
Charles University, Faculty of Mathematics and Physics（查理大学数学物理学院）；Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿强磁场实验室（HLD-EMFL），德累斯顿罗森多夫亥姆霍兹中心）；Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）
We investigate the doping of AA-stacked graphene bilayers. Applying a mean field theory at zero temperature we find that, at half-filling, the bilayer is an antiferromagnetic insulator. Upon doping, the homogeneous phase becomes unstable with respect to phase separation. The separated phases are an undoped antiferromagnetic insulator and a metal with a non-zero concentration of charge carriers. At sufficiently high doping, the insulating areas shrink and disappear, and the system becomes a homogeneous metal. The conductivity changes drastically upon doping, so the bilayer may be used as a swit…
We have observed two spin density wave (SDW) phases in hole doped metallic V_{2-y}O_3, one evolves from the other as a function of doping, pressure or temperature. They differ in their response to an external magnetic field, which can also induce a transition between them. The phase boundary between these two states in the temperature-, doping-, and pressure-dependent phase diagram has been determined by magnetization and magnetotransport measurements. One phase exists at high doping level and has already been described in the literature. The second phase is found in a small parameter range cl…
Cluster dynamical mean field calculations based on 2, 4, 8 and 16 site clusters are used to analyze the doping-driven metal-insulator transition in the two dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole doped side than on the electron doped side. For particle-h…
We point out that there are two different chiral spin liquid states on the triangular lattice and discuss the conducting states that are expected on doping them. These states labeled CS1 and CS2 are associated with two distinct topological orders with different edge states, although they both spontaneously break time reversal symmetry and exhibit the same quantized spin Hall conductance. While CSL1 is related to the Kalmeyer-Laughlin state, CSL2 is the $ν=4$ member of Kitaev's 16 fold way classification. Both states are described within the Abrikosov fermion representation of spins, and the ef…
We construct the electron star solution to the model that was recently proposed by Kiritsis and Li in order to describe a holographic superconductor at finite doping. We do so by finding a map between the doped model and the standard undoped one. In this way, we are able to describe the holographic metallic phase at finite doping. In particular, we study the gauge field fluctuations and find the dependence of the electric conductivity on the doping parameter.
This paper has been withdrawn by the authors due to new theoretical evidence and experimental proof that the semiconducting bandgap reported in this paper and ascribed to a surface region is in fact a bulk property of divalent hexaborides. As reported in J. D. Denlinger et al., cond-mat/0107429, which supercedes this paper, bulk-sensitive boron K-edge soft x-ray emission provides a complementary confirmation of the X-point band gap identified by angle-resolved photoemission.
For some heavy-fermion compounds, it has been suggested that a Fermi-surface-changing Lifshitz transition, which can be driven, e.g., by varying an applied magnetic field, occurs inside the heavy- fermion regime. Here we discuss, based on microscopic calculations, how the location of such a transition can be influenced by carrier doping. Due to strong correlations, a heavy band does not shift rigidly with the chemical potential. Intriguingly, we find that the actual shift is determined by the interplay of heavy and additional light bands crossing the Fermi level: doped carriers tend to populat…
We present the carrier transport properties in the vicinity of a doping-driven Mott transition observed at a field-effect transistor (FET) channel using a single crystal of the typical two-dimensional organic Mott insulator $κ$-(BEDT-TTF)$_2$CuN(CN)$_2$Cl ($κ$-Cl).The FET shows a continuous metal$-$insulator transition (MIT) as electrostatic doping proceeds. The phase transition appears to involve two-step crossovers, one in Hall measurement and the other in conductivity measurement. The crossover in conductivity occurs around the conductance quantum $e^2/h$ , and hence is not associated with …
We establish that a doping-driven first-order metal-to-metal transition, from a pseudogap metal to Fermi Liquid, can occur in correlated quantum materials. Our result is based on the exact Dynamical Mean Field Theory solution of the Dimer Hubbard Model. This transition elucidates the origin of many exotic features in doped Mott materials, like the pseudogap in cuprates, incoherent bad metals, enhanced compressibility and orbital selective Mott transition. This phenomenon is suggestive to be at the roots of the many exotic phases appearing in the phase diagram of correlated materials.
The transition between a metallic and a pseudogap phase in high-$T_c$ cuprate superconductors is the subject of experimental investigations but has not been settled theoretically, even within the context of the Hubbard model. We apply the Cluster Dynamical Impurity Approximation (CDIA) to the anisotropic Hubbard model on the square lattice at zero temperature and finite doping. This approach can detect a first-order transition between two metallic states: a pseudogap state at low doping, with a depleted density of states at the Fermi level, and a correlated metal at higher doping. This transit…
High-$T_{\rm C}$ superconductors show anomalous transport properties in their normal states, such as the bad-metal and pseudogap behaviors. To discuss their origins, it is important to speculate whether these behaviors are material-dependent or universal phenomena in the proximity of the Mott transition, by investigating similar but different material systems. An organic Mott transistor is suitable for this purpose owing to the adjacency between the two-dimensional Mott insulating and superconducting states, simple electronic properties, and high doping/bandwidth tunability in the same sample.…
