Charge density fluctuations shed light on the enigmatic strange metal phase of cuprates

The normal state of cuprate superconductors exhibits a “strange metal phase” characterised by highly unconventional properties, including a linear dependence of the resistivity with temperature, and anomalous features in the optical conductivity, magnetoresistance and spin relaxation rate [1]. This phase has captivated physicists for decades. It has been observed in a variety of superconducting quantum materials, from pnictides to heavy fermions and, more recently, in magic-angle, double-layer graphene. This ubiquitous behaviour raises the question of what underlies the universality of the strange metal phase. The observation that superconductivity intensifies when the strange metal phase is more robust excites scientists, as it holds the promise of revealing the fundamental mechanisms driving superconductivity in cuprate superconductors.

This enigmatic phase of matter is believed to arise from the presence of a quantum critical point (QCP) at zero temperature [2]. A QCP is a singularity at a temperature of 0 K (−273.15°C), signalling a quantum phase transition between different states of matter. Reaching the absolute zero to directly observe the QCP is practically impossible. Nevertheless, when one gets closer to a quantum critical point, quantum fluctuations emerge. The detection of these fluctuations, which have remained elusive until now, is crucial to confirm if the physics of a strange metal is ruled by a QCP scenario and, in the affirmative case, to determine its true nature.

Charge density fluctuations (CDF) [3] could be the hypothetical quantum fluctuations ruling the physics close to a QCP. CDF are ripples of electric charge generated by patterns of electrons in the material lattice, recently observed in several cuprate families, and pervading the whole strange metal region above and below the pseudogap temperature T* [4]. Due to their characteristics – being present in a broad range of doping in the phase diagram, having finite energy and short correlation length that implies a broad, almost isotropic q-space distribution – these fluctuations were immediately connected by various theories to the strange metal phase of the cuprates [5].

In this work, CDF were investigated using resonant inelastic X-ray scattering (RIXS) measurements (Figure 1), at beamline ID32 and at Diamond Light Source (UK). To determine precisely the location of the quantum critical point in the phase diagram, extensive studies of CDF were conducted in two families of cuprate superconductors across a broad range of doping levels and temperatures.

Click image to enlarge

Fig. 1: High-resolution (ΔE=38 meV) RIXS map along the (H,0) direction taken at a temperature T=20 K for a strongly underdoped (p=0.06) YBa₂Cu₃O_7-δ sample. The map is presented after subtracting the fit of the pure elastic peak from the raw spectra. In addition to lattice (phonons) and magnetic (paramagnons) excitations, charge density fluctuations emerge at a finite energy, with a broad intensity peak at a momentum q=qCDF=(0.35,0).

The experiments reveal a crucial finding: as the temperature approaches absolute zero, at a specific critical doping level of p* ≈ 0.19, the putative QCP, the intensity of CDF reaches its maximum, while the characteristic energy of these fluctuations is minimal (Figure 2). This phenomenon creates a unique wedge-shaped region in the phase diagram as a function of doping, providing strong evidence of quantum critical behaviour.

Click image to enlarge

Fig. 2: The CDF energy Δ, directly measured at q=qCDF in the high-resolution RIXS spectra and at low temperature, is plotted as a function of the doping level p. It is lowest at p=p*= 0.19, while it increases at all dopings. The values of Δ, converted into kelvin, define a characteristic wedge with a minimum at p*, lining up with the border of the strange metal phase as determined by transport.

These results unveil the connection between the strange metal phase and quantum criticality, and support the crucial role of charge order in driving this unconventional phenomenon. Ultimately, these interconnections introduce new insights into our understanding of high critical-temperature superconductivity.

Principal publication and authors
Signature of quantum criticality in cuprates by charge density fluctuations, R. Arpaia (a), L. Martinelli (b), M. Moretti Sala (b), S. Caprara (c), A. Nag (d), N.B. Brookes (e), P. Camisa (b), Q. Li (f), Q. Gao (f), X. Zhou (f), M. Garcia-Fernandez (d), K.-J. Zhou (d), E. Schierle (g), T. Bauch (a), Y.Y. Peng (f), C. Di Castro (c), M. Grilli (c), F. Lombardi (a), L. Braicovich (b,e), G. Ghiringhelli (b,h), Nat. Commun. 14, 7198 (2023); https://doi.org/10.1038/s41467-023-42961-5
(a) Chalmers University, Göteborg (Sweden)
(b) Politecnico di Milano, Milan (Italy)
(c) Università La Sapienza, Rome (Italy)
(d) Diamond Light Source, Didcot (UK)
(e) ESRF
(f) Peking University, Beijing (China)
(g) BESSY II, Berlin (Germany)
(h) CNR-SPIN, Milan (Italy)

References
[1] P. W. Phillips et al., Science 377, eabh4273 (2022).
[2] S. Sachdev, Phys. Status Solidi (b) 247, 537 (2010).
[3] R. Arpaia et al., Science 365, 906 (2019).
[4] R. Arpaia, G. Ghiringhelli, Phys. Soc. Jpn. 90, 111005 (2021).
[5] G. Seibold et al., Commun. Phys. 4, 7 (2021).