Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin copper oxide films

Abstract

A central issue in the physics of high temperature superconductors is to understand superconductivity within a single copper-oxide layer or bilayer, the fundamental structural unit in the cuprates, and how it is lost with underdoping.As mobile holes are removed from the CuO 2 planes, the transition temperature T C and superfluid density n S decrease in a surprisingly correlated fashion in crystals and thick films 1-4 . We seek to elucidate the intrinsic physics of bilayers in the strongly underdoped regime, near the critical doping level where superconductivity disappears. We report measurements of n S (T) in films of Y 1-x Ca x Ba 2 Cu 3 O 7-δ as thin as two copper-oxide bilayers with T C 's as low as 3 K. In addition to seeing the two-dimensional (2D) Kosterlitz-Thouless-Berezinski transition 5,6 at T C , we observe a remarkable scaling of T C with n S (0) that demonstrates that the disappearance of superconductivity with underdoping is due to quantum fluctuations near a T = 0 2D quantum critical point.Early measurements 1 of the suppression of superfluid density n S and T C for moderately underdoped cuprates prompted the suggestion that thermal fluctuations 7 of the phase of the superconducting order parameter were the primary cause. This 1

Algebraic charge liquids

“…We note that in the cuprates, there is a superconductor-insulator transition at a non-zero x = x c , and in its immediate vicinity distinct quantum critical behavior of ρ s is expected, as has been observed recently [25]. However, in characterizing different theories of the underdoped regime, it is useful to consider the behavior as x → 0 assuming the superconductivity survives until x = 0.…”

Doping dependence of the vortex-core energy in bilayer films of cuprates

“…͑2͒ with n = 1 is satisfied, which is certainly the case for totally uncoupled cells. The best situation to analyze this effect in real systems is provided by the finite-frequency sheet conductivity measurements of thin Y 1−x Ca x Ba 2 Cu 3 O 7−␦ ͑YBCO͒ films by Hetel et al 11 Indeed, in these two-unit-cell thick samples, the superfluid-density downturn is necessarily between T BKT n=1 and T BKT n=2 , and its exact form depends on the relative strength of J Ќ and vortex-core energy. As we shall see, this allows us to extract from the data of Ref.…”

“…Indeed, in this case, the transition is ultimately of Beresinkii-KosterlitzThouless ͑BKT͒ type, as it is signaled by the linear relation between T c and J s , and its persistence as doping is changed by the electric-field effect 9,10 or chemical doping. 11 To clarify the role played by the vortex-core energy, let us recall some basic features of the BKT physics in a SC film made of few unit cells. In Y-based cuprates, whose data we will analyze below, there are two strongly coupled CuO 2 layers within each cell, which will be considered in what follows as the basic two-dimensional ͑2D͒ unit of the layered system, of thickness d = 12 Å, corresponding to the unit-cell size in the c direction.…”

High-Tc superconductivity in ultrathin Bi2Sr2CaCu2O8+x down to half-unit-cell thickness by protection with graphene

“…T wo-dimensional (2D) superconductors provide insights into the mechanisms of superconductivity and their possible device applications [1][2][3][4][5][6][7][8][9][10][11] . Bi2212 is a quasi-2D cuprate in which thin superconducting sheets (CuO 2 ) alternate with insulating layers (SrO, BiO).…”