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This paper is dedicated to the memory of Professor K. Alex Mueller. I present a few remarks about my interactions with Alex over the years. Then I present a very brief summary of recent transport studies of the strange metal normal state in the high-temperature copper oxide superconductors, a subject of great interest to Alex. 

An understanding of the high-temperature copper oxide (cuprate) superconductors has eluded the physics community for over thirty years and represents one of the greatest unsolved problems in condensed matter physics. Particularly enigmatic is the normal state from which superconductivity emerges, so much so that this phase has been dubbed a “strange metal.” In this article, we review recent research into this strange metallic state as realized in the electron-doped cuprates with a focus on their transport properties. The electron-doped compounds differ in several ways from their more thoroughly studied hole-doped counterparts, and understanding these asymmetries of the phase diagram may prove crucial to developing a final theory of the cuprates. Most of the experimental results discussed in this review have yet to be explained and remain an outstanding challenge for theory. 

In the physics of condensed matter, quantum critical phenomena and unconventional superconductivity are two major themes. In electron-doped cuprates, the low critical field (H C2 ) allows one to study the putative quantum critical point (QCP) at low temperature and to understand its connection to the long-standing problem of the origin of the high- T C superconductivity. Here we present measurements of the low-temperature normal-state thermopower ( S ) of the electron-doped cuprate superconductor La 2− x Ce x CuO 4 (LCCO) from x = 0.11–0.19. We observe quantum critical S / T versus l n ( 1 / T ) behavior over an unexpectedly wide doping range x = 0.15–0.17 above the QCP ( x = 0.14), with a slope that scales monotonically with the superconducting transition temperature ( T C with H = 0). The presence of quantum criticality over a wide doping range provides a window on the criticality. The thermopower behavior also suggests that the critical fluctuations are linked with T C . Above the superconductivity dome, at x = 0.19, a conventional Fermi-liquid S ∝ T behavior is found for T ≤ 40 K. 

According to conventional wisdom, the extraordinary properties of the cuprate high-temperature superconductors arise from doping a strongly correlated antiferromagnetic insulator. The highly overdoped cuprates—whose doping lies beyond the dome of superconductivity—are considered to be conventional Fermi liquid metals. We report the emergence of itinerant ferromagnetic order below 4 kelvin for doping beyond the superconducting dome in thin films of electron-doped La 2– x Ce x CuO 4 (LCCO). The existence of this ferromagnetic order is evidenced by negative, anisotropic, and hysteretic magnetoresistance, hysteretic magnetization, and the polar Kerr effect, all of which are standard signatures of itinerant ferromagnetism in metals. This surprising result suggests that the overdoped cuprates are strongly influenced by electron correlations.