Strange Metal Research Articles

Incoherent transport in a model for the strange metal phase: Memory-matrix formalism

Incoherent transport in a model for the strange metal phase: Memory-matrix formalism

Plethora of many body ground states in magic angle twisted bilayer graphene

The discovery of magic angle twisted bilayer graphene (MATBG), in which two sheets of monolayer graphene are precisely stacked at a specific angle, has opened up a plethora of grand new opportunities in the field of topology, superconductivity, strange metal, and other strongly correlated effects. This review will focus on the various forms of quantum phases in MATBG revealed through quantum transport measurements. The goal is to highlight the uniqueness and current understanding of the various phases, especially how electronic interaction plays a role in them, as well as open questions in regard to the phase diagram.

Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model.

Accurate simulations of the two-dimensional (2D) Hubbard model constitute one of the most challenging problems in condensed matter and quantum physics. Here we develop a tangent space tensor renormalization group (tanTRG) approach for the calculations of the 2D Hubbard model at finite temperature. An optimal evolution of the density operator is achieved in tanTRG with a mild O(D^{3}) complexity, where the bond dimension D controls the accuracy. With the tanTRG approach we boost the low-temperature calculations of large-scale 2D Hubbard systems on up to a width-8 cylinder and 10×10 square lattice. For the half-filled Hubbard model, the obtained results are in excellent agreement with those of determinant quantum MonteCarlo (DQMC). Moreover, tanTRG can be used to explore the low-temperature, finite-doping regime inaccessible for DQMC. The calculated charge compressibility and Matsubara Green's function are found to reflect the strange metal and pseudogap behaviors, respectively. The superconductive pairing susceptibility is computed down to a low temperature of approximately 1/24 of the hopping energy, where we find d-wave pairing responses are most significant near the optimal doping. Equipped with the tangent-space technique, tanTRG constitutes a well-controlled, highly efficient and accurate tensor network method for strongly correlated 2D lattice models at finite temperature.

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)((Fe0.97Pt0.03)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 (Tc) 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 Tc obeys the relation of Tc ~ (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-Tc superconductivity.

A New Card up Graphene’s Sleeve

Graphene is found to exhibit a magnetoresistance dwarfing that of all known materials at room temperature—a behavior that may lead to new magnetic sensors and help decipher the physics of strange metals.

Collective density fluctuations of strange metals with critical Fermi surfaces

Recent spectroscopic measurements in a number of strongly correlated metals that exhibit non-Fermi liquid like properties have observed evidence of anomalous frequency and momentum-dependent charge-density fluctuations. Specifically, in the strange metallic regime of the cuprate superconductors, there is a featureless particle-hole continuum exhibiting unusual power-laws, and experiments suggest that the plasmon mode decays into this continuum in a manner that is distinct from the expectations of conventional Fermi liquid theory. Inspired by these new experimental developments, we address the nature of low-energy collective modes and the particle-hole continua for different "solvable" lattice models of non-Fermi liquids that host a critical Fermi surface -- a sharp electronic Fermi surface without any low-energy electronic quasiparticles. We scrutinize theoretically the possible existence of a long-lived zero-sound mode, which is renormalized to the plasma frequency in the presence of long-ranged coulomb interactions, and its decay into the continuum over a wide range of frequencies and momenta. Quite remarkably, some of the models analyzed here can account for certain aspects of the universal experimental observations, that clearly lie beyond the purview of standard Fermi liquid theory.

FL* Interpretation of a Dichotomy in the Spin Susceptibility of the Cuprates

We propose that some dichotomic Fermi liquid versus non-Fermi liquid behaviours of physical quantities in hole-doped cuprates can be explained in terms of the FL* fractionalized Fermi liquid concept, introduced some years ago, even beyond the region of underdoping. The particle excitations of this FL* system are the holon carrying charge, the spinon carrying spin 1/2, gauge fluctuations coupling them and the hole as a spinon–holon bound state or resonance due to gauge binding. In our proposal, physical responses have a Fermi-liquid-type behaviour if they are dominated by the hole resonance, whereas a non-Fermi liquid behaviour appears if they are dominated by spinon–spinon (and possibly also holon–holon) gauge interactions. The specific case of spin susceptibility in the so-called "strange metal phase" is discussed. The uniform susceptibility turns out to be hole-dominated, the spin-lattice relaxation rate in the Cu sites is spinon-dominated.

Role of chemical potential in strange metal behavior

Role of chemical potential in strange metal behavior

Observation of a critical charge mode in a strange metal.

Understanding the strange metallic behavior that develops at the brink of localization in quantum materials requires probing the underlying electronic charge dynamics. Using synchrotron radiation-based Mössbauer spectroscopy, we studied the charge fluctuations of the strange metal phase of β-YbAlB4 as a function of temperature and pressure. We found that the usual single absorption peak in the Fermi-liquid regime splits into two peaks upon entering the critical regime. We interpret this spectrum as a single nuclear transition, modulated by nearby electronic valence fluctuations whose long time scales are further enhanced by the formation of charged polarons. These critical charge fluctuations may prove to be a distinct signature of strange metals.

Probes to entropy flow in strange metals

Probes to entropy flow in strange metals

Superconductivity nearby quantum critical region in hole-doped organic strange metal κ-(ET)4Hg3-δBr8, δ=11%

The hole-doped organic superconductor κ-(ET)4Hg3-δBr8, (κ-HgBr), where δ=11% and ET=bis(ethylenedithio)tetrathiafulvalene, has been the key to bridge the knowledge gap between half-filled organics and doped cuprate systems. Nonetheless, the isotropic triangular lattice of ET dimers of κ-HgBr is responsible for the magnetic susceptibility and its superconductivity. We have measured zero-field (ZF) muon spin relaxation-rotation (µ+SR) in κ-HgBr showing the ZF-µ+SR relaxation rate from temperature around 10 K down to 0.3 K is temperature-independent. This is consistent with a superconducting state that preserved time-reversal symmetry. There was almost no change in the maximally 100 Oe of transverse-field-µ+SR time spectra, at 0.3 K and above superconducting temperature, T c~4.6(3) K. This suggests that the in-plane London penetration depth, λbc, is longer than a μm order, while we estimate the lower limit of the lower critical field, H c1, to be 30 Oe, although, however, the measurement using another geometric setup is necessary to determine the absolute value of λbc. These could be an indication of a strong-coupling superconductor. A possible mechanism of preserved time-reversal Cooper pairing formation from strong-coupling non-FL metal with geometrical frustration is discussed.

Unified intermediate coupling description of pseudogap and strange metal phases of cuprates

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 coupling is large compared to the effective tight binding scale and a different method is required. This scenario provides an alternative to the paradigm that the coupling should be strong, say $U/t>6$, in order to describe the strange metal. We argue that to obtain phenomenologically acceptable underdoped normal state characteristics like $T^{\ast }$, pseudogap values, and spectral weight distribution, a large value of $U$ is detrimental. Surprisingly the resistivity in the above temperature range is linear $\rho =\rho_{0}+\alpha \frac{m^{\ast }}{e^{2}n\hbar }T$ with the "Planckian" coefficient $\alpha $ of order one.

Resistivity of various metals described in a wide temperature range with a universal theoretical equation

A generic conductivity equation, developed in our previous work without any restrictions to specific materials, is borrowed to evaluate how conductivity/resistivity changes with temperatures in a very wide temperature range from almost zero to several hundreds of Kelvins. Two scenarios are investigated, the parameters A and B in the conductivity equation are both dependent and independent of temperature. Derived equations show that conductivity/resistivity has a Taylor expansion relationship with temperature. They can fit resistivity data very well at both low and high temperature regions with an adequate volume-temperature expansion relationship. The predictions are in line with experimental observations and better than the latest empirical equations. Our findings provide a unified theoretical description of normal, bad, and strange metals.

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.

Fluctuating intertwined stripes in the strange metal regime of the Hubbard model

Strongly correlated electron systems host a variety of poorly understood correlations in their high-temperature normal state. Unlike ordered phases defined by order parameters, regions of the normal state are often defined through unconventional properties such as strange metallic transport or spectroscopic pseudogaps. Characterizing the microscopic correlations in the normal state is necessary to elucidate mechanisms that lead to these properties and their connection to ground-state orders. Here we establish the presence of intertwined charge and spin stripes in the strange metal normal state of the Hubbard model using determinant quantum Monte Carlo calculations. The charge and spin density waves constituting the stripes are fluctuating and short ranged; yet they obey a mutual commensurability relation and remain microscopically interlocked, as evidenced through measurements of three-point spin-spin-hole correlation functions. Our findings demonstrate the ability of many-body numerical simulations to unravel the microscopic correlations that define quantum states of matter.

Is the optical conductivity of heavy fermion strange metals Planckian?

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 kBT/ℏ, leads to the linear temperature dependence of the (dc) electrical resistivity, which is a hallmark of strange metal behavior. Here we extend a previously introduced analysis scheme based on the Drude description of the dc resistivity to optical conductivity data. When they are well described by a simple (ac) Drude model, the scattering rate can be directly extracted. This avoids the need to determine the ratio of charge carrier concentration to effective mass, which has complicated previous analyses based on the dc resistivity. However, we point out that strange metals typically exhibit strong deviations from Drude behavior, as exemplified by the “extreme” strange metal YbRh2Si2. This calls for alternative approaches, and we point to the power of strange metal dynamical (energy-over-temperature) scaling analyses for the inelastic part of the optical conductivity. If such scaling extends to the low-frequency limit, a strange metal relaxation rate can be estimated, and may ultimately be used to test whether strange metals relax in a Planckian manner.

Strange Metallicity and Magnetic Order in the CoNi(Cr/V) Medium-Entropy Alloy System.

CoNiCr is a prototypical example of topical multi-principle element alloys with superior cryogenic and high-temperature mechanical strength, corrosion, oxidation resistance, and yet-to-be-explored magnetic and electronic functionalities. The remarkable properties of this transition metal ternary system are not only due to atomic radii, electronic configurational mismatch, and atomic volume misfit but are also dependent on the debated magnetically driven chemical short-range order. The current study focuses on the electric and magnetic properties of the single-phase face-centered cubic CoNi(Cr/V) system in which V is introduced to the system at the expense of Cr to fine-tune the volume misfit in the system. All the samples exhibited ultra-small magnetic moments due to the complex magnetic interactions of the constituent elements. The electric transport measurements revealed a strange metallicity evidenced through the observation of the linear temperature dependence of the resistivity. Our findings support the recent theoretical studies on the magnetically driven chemical short-range order of the CoNiCr system.

Anomalous enhancement of the Nernst effect at the crossover between a Fermi liquid and a strange metal

A strange-metal state appears in many strongly correlated materials, so understanding its nature is a crucial problem in condensed matter physics. This knowledge could provide important insight into high-temperature superconductivity and quantum criticality, but standard Fermi-liquid theory fails in strange metals. Establishing an alternative theory has been a long-standing challenge and fundamental aspects of strange metals—including the nature of their charge carriers—remain elusive. Here we report the observation of a large Nernst response in the strange-metal state in a two-dimensional superconductor 2M-WS2. Specifically, when the system enters the strange-metal state from the Fermi-liquid state, the Nernst coefficient increases to be comparable to the vortex Nernst signal in superconducting cuprates, and it is highly sensitive to carrier mobility. The temperature and magnetic field dependence of the Nernst peak rule out the relevance of both Landau quasiparticles and superconductivity. Instead, the Nernst peak at the crossover indicates a change in carrier entropy when entering the strange-metal state. The presence of such an anomalous Nernst response is further confirmed in other iconic strange metals, suggesting its universality and places experimental constraints on the mechanism of strange metals. The transport behaviour of strange metals is distinct from weakly interacting Fermi liquids. Now, a large thermoelectric response has been shown at the transition between those two states.

Higher-order oscillatory planar Hall effect in topological kagome metal

Exploration of exotic transport behavior for quantum materials is of great interest and importance for revealing exotic orders to bring new physics. In this work, we report the observation of unconventional prominent planar Hall effect (PHE) and planar anisotropic magnetoresistivity (PAMR) in strange kagome metal KV3Sb5. The PHE and PAMR, which are driven by an in-plane magnetic field and display sharp difference from other Hall effects driven by an out-of-plane magnetic field or magnetization, exhibit exotic higher-order oscillations in sharp contrast to those following empirical rule only allowing two-fold symmetrical oscillations. These higher-order oscillations exhibit strong field and temperature dependence and vanish around charge density wave (CDW) transition. The unique transport properties suggest a significant interplay of the lattice, magnetic and electronic structure in KV3Sb5. This interplay can couple the hidden anisotropy and transport electrons leading to the unconventional PHE and PAMR in contrast to other materials.

Colloquium : Hydrodynamics and holography of charge density wave phases

Hydrodynamics is an old example of an effective description of complex matter, which describes the system's behavior at large length and timescales and lumps microscopic details into transport coefficients. A combination of hydrodynamics and the gauge-gravity duality, which was first explored in the context of string theory, has proven promising for a description of strongly correlated electron fluids. This Colloquium explains how to apply these techniques to strongly correlated materials where the electron fluid crystallizes, and in particular to the strange metal phase of high-temperature superconductors.