Quantum critical metals and loss of quasiparticles Haoyu Hu12 Lei Chen1 Qimiao Si1 1Department ofPhysics andAstronomy Extreme Quantum Materials Alliance

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Quantum critical metals and loss of quasiparticles

Haoyu Hu1,2,∗, Lei Chen1,∗, Qimiao Si1,∗

1Department of Physics and Astronomy, Extreme Quantum Materials Alliance,

Smalley-Curl Institute, Rice University, Houston, TX 77005, USA

2Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San

Sebastian, Spain

Strange metals develop near quantum critical points in a variety of strongly

correlated systems. Some of the issues that are central to the ﬁeld include how

the quantum-critical state loses quasiparticles, how it drives superconductivity,

and to what extent the strange-metal physics in diﬀerent classes of correlated

systems are interconnected. In this Review, we survey some of these issues

from the vantage point of heavy fermion metals. We will describe the notion of

Kondo destruction and how it leads to several crucial eﬀects. These include a

transformation of the Fermi surface from large to small when the system is tuned

across the quantum-critical point, a loss of quasiparticles everywhere on the

Fermi surface when it is perched at the quantum-critical point, and a dynamical

Planckian scaling in various physical properties including charge responses. We

close with a discussion about the connections between the strange-metal physics

in heavy fermion metals and its counterparts in the cuprates and other correlated

materials.

E-mail: huhaoyu314@gmail.com; lc73@rice.edu; qmsi@rice.edu

arXiv:2210.14183v3 [cond-mat.str-el] 12 Mar 2025

I. INTRODUCTION

Large classes of quantum materials host strongly correlated electrons [1, 2] and many of

them feature unconventional superconductivity. One connection among the strongly corre-

lated systems is illustrated in Fig. 1(a), which shows the superconducting transition temper-

ature Tcand the eﬀective Fermi temperature T0, the temperature for Fermi degeneracy, for

various strongly-correlated superconductors. The ratio of Tc/T0is several percent, with each

temperature scale spanning about three decades. This qualiﬁes these systems as high-Tcsu-

perconductors, given that this ratio is about two orders of magnitude smaller in conventional

superconductors. Another connection lies in their normal states at temperatures above the

superconducting transition temperature (so, when T > Tc), which are often strange metals

that have an electrical resistivity that is linear in temperature, and a slew of other exotic

properties.

The link between the strange-metal normal state and unconventional superconductivity

in heavy fermion systems, which are characterized by electronic excitations whose eﬀective

masses are orders of magnitude larger than the free electron mass, is particularly striking.

Indeed, heavy fermion metals represent a prototype setting in which quantum critical metal-

licity has been elucidated [3], in part because Tcis relatively small in absolute magnitude in

these materials, so it opens up a large window of temperature over which the strange-metal

properties can be explored. These systems often possess antiferromagnetic (AF) correlations.

The existence of heavy fermion superconductors is a venerable topic, and this material fam-

ily has now grown to about 50 members. In contrast, the strange-metal behavior and its

association with quantum criticality have only been the focus relatively recently.

It is natural for quantum criticality to drive unusual properties [4]. Indeed, as a system

is tuned towards its quantum-critical regime at a given low (but nonzero) temperature,

the entropy is expected to be maximized [5, 6]. The behavior has been demonstrated in

Fig. 1(b) [7], which presents the experimental observations in CeCu6−xAuxacross multiple

tuning parameters. Tuning the system in the directions that are orthogonal to the gradient of

entropy, the distance to the QCP remains unchanged. The gradient of the entropy vanishes

precisely at the QCP, which indicates the accumulation of entropy in the quantum critical

regime. In this sense, quantum critical systems are particularly soft and are prone to the

formation of unusual excitations and exotic phases.

That strange metals develop via quantum criticality is clearly demonstrated in heavy

fermion metals. We illustrate the point in YbRh2Si2and CeRhIn5, via their respective

phase diagrams shown in Fig. 1(c,d). The colour coding of γin the ﬁgure represents the

exponent of the resistivity’s dependence on temperature, so regions where γ≃1 represent

the strange metal regime. Both exhibit an AF order at ambient conditions. In YbRh2Si2, a

magnetic ﬁeld applied perpendicular to its tetragonal plane of about 0.7 T (or one applied

within the plane of about 66 mT) tunes the system to its quantum critical point (QCP)

[8], where a T-linear resistivity [9] occurs over more than three decades in temperature [10].

In CeRhIn5, a quantum critical fan develops near a pressure of 2.3 GPa [11, 12] with a

nearly-T-linear resistivity [13].

Theories of metallic QCPs have two general types. One class of theory is based on the

ﬂuctuations of Landau’s order parameter, as described by the Hertz-Millis-Moriya approach

[14, 15]. Typically, this order parameter corresponds to a spin-density-wave (SDW) order

at an AF wavevector Q. In this case, the nonzero ordering wavevector Qlinks narrow

hot regions of the Fermi surface to each other. The order parameter ﬂuctuations couple

to electrons from a small portion (hot region) of the Fermi surface, as shown in Fig. 2.

Meanwhile, the majority of the Fermi surface remains cold in the sense that the order

parameter ﬂuctuation connects one point on the cold region of the Fermi surface to another

point in the Brillouin zone where the energy level lies substantially away from the Fermi

energy. Correspondingly, for the electronic states in the cold region of the Fermi surface,

the quantum critical ﬂuctuations have a minimal eﬀect and the quasiparticles retain their

integrity [16–18]. The electrical transport will not show the strange-metal behavior given

that the quasiparticles, being long-lived, will short-circuit the electrical transport.

To realize the strange-metal behavior, it is necessary to destroy the quasiparticles on the

entire Fermi surface. This takes place in the second type of theory for metallic quantum

criticality, which goes beyond the Landau framework [19–21].

Here, we survey the beyond-Landau quantum criticality. We start by considering how

quasiparticles can be critically destroyed. The central theme here is that, for bad metals such

as heavy fermion systems, the quasiparticles are fragile to begin with and their formation

takes place through a process that is non-perturbative in electron correlations, and yet well-

understood. This understanding sets the stage for confronting the central challenge, which

is how the quasiparticles are lost. For heavy fermion metals, the Kondo eﬀect underlies the

formation of heavy quasiparticles, whereas the Kondo destruction leads to their suppression.

We suggest that these understandings are relevant to the loss of quasiparticles in a variety

of strongly correlated systems, including the doped cuprates, the iron chalcogenides and

certain organic superconductors. In addition to surveying the theoretical issues, we will

describe some of the salient experimental developments [22–28].

II. QUANTUM CRITICAL METALS – HOW TO DESTROY QUASIPARTICLES

To see how the quasiparticles can be lost everywhere on the Fermi surface, we start from

their formation away from the QCP.

A. Quasiparticles: the robust and the fragile

For quantum many-body systems, the physics at low energies is analyzed in terms of

building blocks and their symmetry-allowed interactions [2]. Traditionally, one takes bare

electrons as the building blocks and treat the electron-electron interactions order by order in

perturbation theory [29]. The notion of quasiparticles survives up to inﬁnite order of the per-

turbation series. In that sense, quasiparticles are rather robust. For a long time, the validity

of Fermi liquid theory was largely unquestioned for systems in dimensions higher than one;

indeed, Fermi liquid was considered to be the only ﬁxed point of the renormalization-group

(RG) ﬂow in such dimensions [30, 31]. A quasiparticle corresponds to a sharp peak in the

electron spectral function as a function of energy for a ﬁxed wavevector. The wavevectors

of zero energy excitations form a Fermi surface; the volume enclosed by the Fermi surface,

according to Luttinger’s theorem, is proportional to the number of the underlying electrons

even in the presence of interactions [32]. The quasiparticle has the physical meaning of a

dressed electron; its quantum numbers are exactly those of a bare electron or hole, namely

charge ±eand spin ℏ

2. Their Fermi statistics dictates a decay rate that goes as (kBT)2,

or as E2as the energy measured from the Fermi energy, E, goes to zero. In the language

of Green’s functions, the self-energy Σ(k, ω) retains the Fermi liquid form up to inﬁnite

orders of the perturbative expansion [29]. This turns out to ensure a nonzero value for the

quasiparticle weight, Zk.

Suﬃciently strong electron correlations can lead to other forms of the building blocks for

the low-energy physics. For example, heavy fermion systems involve local f-electron-derived

moments and itinerant spd-electron bands as the starting point for the description of their

low-energy properties [2, 3, 33–35]. In that case, quasiparticles are fragile, with a weight

that is exponentially small.

Consider the Kondo lattice Hamiltonian, which is described in Box 1. We start from the

parameter regime when the Kondo interaction between the local moments and the itinerant

electrons succeeds in driving the formation of a Kondo singlet, which can be pictured as a

bound state between a local moment and a triplet particle-hole combination of the conduc-

tion electrons. Breaking the bound state leads to not only bare conduction electrons, but

also a composite heavy fermion formed between the local moment and a conduction elec-

tron. The composite fermions have the same quantum numbers as bare electrons, and they

hybridize with the conduction electrons to form heavy quasiparticles. These quasiparticles

have a large eﬀective mass and a small quasiparticle weight Zthat is exponentially small

and, in practice, is of the order 10−3.

When the quasiparticles are this fragile, competing interactions can readily destroy them.

B. Quantum criticality from Kondo destruction

The notion of Kondo destruction quantum criticality invokes ﬂuctuations that go beyond

a Landau order parameter. For Kondo lattice systems, it captures the dynamical compe-

tition between the Kondo interaction described above and RKKY interactions, which are

interactions between the local moments mediated by the spins of the itinerent electrons as

described in Box 1. The corresponding QCP is illustrated in Fig. 3(a) [3, 19], in the space

of temperature and non-thermal control parameter, δ=T0

K/I, the ratio of the bare Kondo

temperature to the RKKY interaction I.

When δis suﬃciently large, the Kondo interaction dominates and a Kondo singlet is

formed in the ground state, as illustrated in Fig. 3(c). As the RKKY interaction is in-

creased, meaning when the parameter δis tuned downward, the RKKY interaction becomes

important and promotes correlations of a spin singlet between the local moments. This

process is detrimental to the formation of the Kondo singlet. When it suppresses the Kondo

singlet in the ground state, the composite heavy quasiparticles are lost.

Thus, both the formation and loss of quasiparticles can be considered by analyzing the

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QuantumcriticalmetalsandlossofquasiparticlesHaoyuHu1,2,∗,LeiChen1,∗,QimiaoSi1,∗1DepartmentofPhysicsandAstronomy,ExtremeQuantumMaterialsAlliance,Smalley-CurlInstitute,RiceUniversity,Houston,TX77005,USA2DonostiaInternationalPhysicsCenter,P.ManueldeLardizabal4,20018Donostia-SanSebastian,SpainStrangemet...

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Quantum critical metals and loss of quasiparticles Haoyu Hu12 Lei Chen1 Qimiao Si1 1Department ofPhysics andAstronomy Extreme Quantum Materials Alliance

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