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-temperature law might be dictated by Planckian dissipation - scattering with the rate $\sim k_{\rm B}T/\hbar$, are receiving considerable attention. Here we assess the situation for strange metal heavy fermion compounds. They allow to probe the regime of extreme correlation strength, with effective mass or Fermi velocity renormalizations in excess of three orders of magnitude. Adopting the same procedure as done in previous studies, i.e., assuming a simple Drude conductivity with the above scattering rate, we find that for these strongly renormalized quasiparticles, scattering is much weaker than Planckian, implying that the linear temperature dependence should be due to other effects. We discuss implications of this finding and point to directions for further work.
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}…
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…
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…
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…
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…
In this Letter, we explore dynamics in a three-dimensional strongly interacting liquid. In quantum liquids discussed below, thermodynamic properties such as pressure and thermal energies are fully characterized by $s(T)$, the entropy density of the liquid (that is also directly proportional to the hydrodynamic viscosity). We obtain a universal fermion spectral function $A(ω, {\bf k})$ that is distinctly specified by $\hbar / T$, a Planckian time scale. These phenomena can emerge in strongly interacting many-body states with a finite fermion density $ρ$ at temperatures $T^*$ where the chemical …
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…
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…
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).…
The mechanism of strange metal (SM) with unconventional charge transport near magnetic phase transitions has become an outstanding open problem in correlated electron systems. Recently, an exotic quantum critical SM phase was observed in paramagnetic frustrated heavy-fermion materials near Kondo breakdown. We establish a controlled theoretical framework to this issue via a dynamical large-N fermionic multichannel approach to the two-dimensional Kondo-Heisenberg lattice model, where KB transition separates a heavy-Fermi liquid from fermionic spin-liquid state. With Kondo fluctuations being full…
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 $…
Understanding electrical transport in strange metals, including the seeming universality of Planckian $T$-linear resistivity, remains a longstanding challenge in condensed matter physics. We propose that local imaging techniques, such as nitrogen vacancy center magnetometry, can locally identify signatures of quantum critical response which are invisible in measurements of a bulk electrical resistivity. As an illustrative example, we use a minimal holographic model for a strange metal in two spatial dimensions to predict how electrical current will flow in regimes dominated by quantum critical…
Fermi liquid theory forms the basis for our understanding of the majority of metals, which is manifested in the description of transport properties that the electrical resistivity goes as temperature squared in the limit of zero temperature. However, the observations of strange metal states in various quantum materials, notably high-temperature superconductors, bring this spectacularly successful theoretical framework into crisis. When electron scattering rate 1/τ hits its limit, kBT/{\hbar} where {\hbar} is the reduced Planck's constant, T represents absolute temperature and kB denotes Boltzm…
A one band Hubbard model with intermediate coupling is shown to describe the two most important unusual features of a normal state: linear resistivity strange metal and the pseudogap. Both the spectroscopic and transport properties of the cuprates are considered on the same footing by employing a relatively simple postgaussian approximation valid for the intermediate couplings $U/t=1.5-4$ in relevant temperatures $T>100{\rm K}.$ In the doping range $\ p=0.1-0.3$, the value of $U$ is smaller than that in the parent material. For a smaller doping, especially in the Mott insulator phase, the coup…
We consider non-Fermi liquids in which the inelastic scattering rate has an intrinsic particle-hole asymmetry and obeys $ω/T$ scaling. We show that, in contrast to Fermi liquids, this asymmetry influences the low-temperature behaviour of the thermopower even in the presence of impurity scattering. Implications for the unconventional sign and temperature dependence of the thermopower in cuprates in the strange metal (Planckian) regime are emphasized.
We introduce an effective theory for quantum critical points (QCPs) in heavy fermion systems, involving a change in carrier density without symmetry breaking. Our new theory captures a strongly coupled metallic QCP, leading to robust marginal Fermi liquid transport phenomenology, and associated linear in temperature ($T$) "strange metal" resistivity, all within a controlled large $N$ limit. In the parameter regime of strong damping of emergent bosonic excitations, the QCP also displays a near-universal "Planckian" transport lifetime, $τ_{\mathrm{tr}}\sim\hbar/(k_BT)$. This is contrasted with t…
The emergence of superconductivity in unconventional superconductors usually accompanies the normal-state phases of pseudogap, strange metal and Fermi liquid. It indicates these phases are strongly related to the superconducting state and should be dominated by yet unclear mechanism of superconductivity. Here, we propose a microscopic theory that, according to the coupling between localized and extended states, the pairing electrons which leap on and off a localized state result in superconducting instability. Two distinguishable pairing gaps are observed in these states, one dominates the sup…
Some of the highest-transition-temperature superconductors across various materials classes exhibit linear-in-temperature `strange metal' or `Planckian' electrical resistivities in their normal state. It is thus believed by many that this behavior holds the key to unlock the secrets of high-temperature superconductivity. However, these materials typically display complex phase diagrams governed by various competing energy scales, making an unambiguous identification of the physics at play difficult. Here we use electrical resistivity measurements into the micro-Kelvin regime to discover superc…
Strange-metal behavior in correlated molecular conductors
Universität Stuttgart（斯图加特大学）；Saitama University（埼玉大学）；RIKEN Nishina Center（理化学研究所西村研究中心）；Shibaura Institute of Technology（芝浦工业大学）；University of Tokyo（东京大学）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；Institut Néel - CNRS and Université Grenoble Alpes（内耳研究所-法国国家科学研究中心与格勒诺布尔阿尔卑斯大学）
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）
Strongly correlated Fermi systems are among the most intriguing, best experimentally studied and fundamental systems in physics. These are, however, in defiance of theoretical understanding. The ideas based on the concepts like Kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics. Alas, being suggested to describe one property, these approaches fail to explain the others. This means a real crisis in theory suggesting that there is a hidden fundamental law of nature, which remains to be recognized. A theory of fer…
Recent experiments on quantum criticality in the Ge-substituted heavy-electron material YbRh2Si2 under magnetic field have revealed a possible non-Fermi liquid (NFL) strange metal (SM) state over a finite range of fields at low temperatures, which still remains a puzzle. In the SM region, the zero-field antiferromagnetism is suppressed. Above a critical field, it gives way to a heavy Fermi liquid with Kondo correlation. The T (temperature)-linear resistivity and the T-logarithmic followed by a power-law singularity in the specific heat coefficient at low T, salient NFL behaviours in the SM reg…
Although the resistivity in traditional metals increases with temperature, its $T$ dependence vanishes at low or high temperature, albeit for different reasons. Here, we review a class of materials, known as \lq strange' metals, that can violate both principles. In materials exhibiting such behavior, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as $T \rightarrow 0$, can be imperceptible, suggesting complete continuity between the charge carriers at low and high $T$. Since particles cannot scatter at length scales shorter than the interatomic…
The breakdown of the celebrated Fermi liquid theory in the strange metal phase is the central enigma of correlated quantum matter. Motivated by recent experiments reporting short-lived carriers, along with the ubiquitous observations of modulated excitations in the phase diagram of cuprates, we propose a model for this phase. We introduce bosons emerging from the remnants of a pair density wave as additional current carriers in the strange metal phase. These bosonic excitations are finite momentum Cooper pairs and thus carry twice the electronic charge, and its net spin can either be zero or o…
Resistivity in the quantum-critical fluctuation region of several metallic compounds such as the cuprates, the heavy-fermions, Fe-chalogenides and pnictides, twisted bi-layer graphene and WSe$_2$, is linear in temperature $T$ as well as in a magnetic field $H$. Scattering of fermions by the excitations of a time-reversal odd polar vector field ${\bf Ω}$ characterizing loop-current fluctuations has been shown to give a linear in T resistivity and other anomalous properties in the cuprates. An extension of this theory to an applied magnetic field is presented. Magnetic field is shown to generate…
The flat bands of magic-angle twisted bilayer graphene (MATBG) host strongly-correlated electronic phases such as correlated insulators, superconductors and a strange-metal state. The latter state, believed to be key for understanding the electronic properties of MATBG, is obscured by various phase transitions and thus could not be unequivocally differentiated from a metal undergoing frequent electron-phonon collisions. Here, we report transport measurements in superconducting MATBG in which the correlated insulator states are suppressed by screening. The uninterrupted metallic ground state sh…
Strange metals possess highly unconventional transport characteristics, such as a linear-in-temperature ($T$) resistivity, an inverse Hall angle that varies as $T^2$ and a linear-in-field ($H$) magnetoresistance. Identifying the origin of these collective anomalies has proved profoundly challenging, even in materials such as the hole-doped cuprates that possess a simple band structure. The prevailing dogma is that strange metallicity in the cuprates is tied to a quantum critical point at a doping $p*$ inside the superconducting dome. Here, we study the high-field in-plane magnetoresistance of …
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…
The interplay of electronic correlations, multi-orbital excitations, and strong spin-orbit coupling is a fertile ground for new states of matter in quantum materials. Here, we report on a confocal Raman scattering study of momentum-resolved charge dynamics from a thin film of semimetallic perovskite $\mathbf{SrIrO_3}$. We demonstrate that the charge dynamics, characterized by a broad continuum, is well described in terms of the marginal Fermi liquid phenomenology. In addition, over a wide temperature regime, the inverse scattering time is for all momenta close to the Planckian limit $\mathbf{τ…
A fundamental challenge to our current understanding of metals is the frequent observation of qualitative departures from Fermi liquid behavior. The standard view attributes such non-Fermi liquid phenomena to the scattering of electrons off quantum critical fluctuations of an underlying order parameter. While the possibility of non-Fermi liquid behavior isolated from the border of magnetism has long been speculated, no experimental confirmation has been made. Here we report on the observation of a strange metal region in the absence of a magnetic instability in an ultrapure single crystal. In …
We discuss quantum phase transition by an exactly solvable model in the dual gravity setup. By considering the effect of the scalar condensation on the fermion spectrum near the quantum critical point(QCP), we find that there is a topologically protected fermion zero mode associated with the metal to insulator transition. We also show that the strange metal phase with T-linear resistivity emerges at high enough temperature as far as the gravity has a horizon. The phase boundaries are calculated according to the density of states, giving insights on structures of the phase diagram near the QCP.
`Strange metals' with resistivity depending linearly on temperature $T$ down to low-$T$ have been a long-standing puzzle in condensed matter physics. Here, we consider a model of itinerant spin-$1/2$ fermions interacting via on-site Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behaviour, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously es…
We study a dual flavor fermion model where each of the flavors form a Sachdev-Ye-Kitaev (SYK) system with arbitrary and possibly distinct $q$-body interactions. The crucial new element is an arbitrary all-to-all $r$-body interaction between the two flavors. At high temperatures the model shows a strange metal phase where both flavors are gapless, similar to the usual single flavor SYK model. Upon reducing temperature, the coupled system undergoes phase transitions to previously unseen phases - first, a strange half metal (SHM) phase where one flavor remains a strange metal while the other is g…
Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling b…
We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The only global symmetry of this theory is a U(1) associated with the conserved Dirac fermion number, and we study the theory at variable, non-zero densities. The high density limit is characterized by a deconfined Fermi surface state with Fermi wavevector equal to that of free gauge-charged fermions. Its low energy fluctuations are described by a coset conformal field theory with central charge c=(N^2-1)/3 and an emergent N=(2,2) supers…
It is presently unknown how strong lattice potentials influence the fermion spectral function of the holographic strange metals predicted by the AdS/CFT correspondence. This embodies a crucial test for the application of holography to condensed matter experiments. We show that for one particular momentum direction this spectrum can be computed for arbitrary strength of the effective translational symmetry breaking potential of the so-called Bianchi-VII geometry employing ordinary differential equations. Deep in the strange metal regime we find rather small changes to the single-fermion respons…
How to make a model of a non-Fermi-liquid metal with efficient current dissipation is a long-standing problem. Results from holographic duality suggest a framework where local critical fermionic degrees of freedom provide both a source of decoherence for the Landau quasiparticle, and a sink for its momentum. This leads us to study a Kondo lattice type model with SYK models in place of the spin impurities. We find evidence for a stable phase at intermediate couplings.
