Superfluid stiffness allows a superconductor to establish phase coherence and to sustain a supercurrent. Phase coherence may occur at a lower temperature than Cooper pair formation when the superfluid stiffness is small, lowering the critical temperature Tc below its mean-field value [1,2]. Coexistence of d-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism [3] (AFM) or charge-density waves [4] (CDW), may enhance the phase fluctuations and hence lower Tc. Recent observations [5] have shown that in the underdoped region, electron-doped cuprates obey the same scaling relation between Tc and superfluid stiffness as hole-doped cuprates [6]. To understand this, the superfluid stiffness along all principal axes were computed for different values of the Hubbard interaction U and different sets of tight-binding parameters using Cellular Dynamical Mean-Field Theory. Computations were done using both Exact Diagonalisation [7] (ED) and Continuous-Time Quantum Monte Carlo [8] (CT-HYB) as impurity solvers for the cluster Anderson impurity model. Only coexistence has been found in zero temperature calculations using ED. We conclude that the AFM+dSC coexistence increases the order parameter phase fluctuations and accounts for the lowering of Tc when approaching half-filling in the e-doped cuprates.
[1] Nelson, David R. and Kosterlitz, J. M., PhysRevLett.39.1201, 1977
[2] Keimer, B. et al., nature14165, 2015
[3] Mandal, P. R. et al, PhysRevB.97.014522, 2018
[4] Cyr-Choinière, O. et al, PhysRevB.98.064513, 2018
[5] Li, Yangmu et al, arXiv:1810.04634 [cond-mat], 2018
[6] Uemura, Y. J. et al, Physical review letters 62(19), 1989
[7] Sénéchal, David, arXiv:0806.2690 [cond-mat], 2008
[8] Werner, Philipp et al, PhysRevLett.97.076405, 2006