Rotational symmetry breaking in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ probed by polarized femtosecond spectroscopy

The quasiparticle (QP) dynamics with different symmetry is investigated in the superconducting (SC) and normal state of the high-temperature superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) using optical pump-probe experiments with different light polarizations at different doping levels. The observation of distinct selection rules for SC excitations present in $A_{1g}$ and $B_{1g}$ symmetries, and for the pseudogap (PG) excitations present in $A_{1g}$ and $B_{2g}$ symmetries by the probe, and absence of any dependence on the pump beam polarization leads to the unequivocal conclusion of the existence of a spontaneous spatial symmetry breaking in the PG state not limited to the sample surface.

Figure 1

(a) A schematic illustration of the two-color pump-probe setup for polarization-resolved measurements. The probe $({\lambda }_{\mathrm{pr}}=800$ nm) was variably polarized by a half-wave plate (HWP) and was combined with the pump $({\lambda }_{\mathrm{pu}}=400$ nm) by a dichroic mirror (DM). The angle $\theta$ is measured relative to the Cu-O bond axes. (b) The $k$-space selectivity of the probe according to the Raman-like process is indicated [15].

Figure 2

(a)–(c) and (g)–(i) $\Delta R\left(\theta \right)/R$ transients at typical temperatures for OD and UD samples, respectively. (d)–(f) and (j)–(l) Polar plots of the maximum values of $\Delta R\left(\theta \right)/R$ $\left(\times {10}^4\right)$. The solid lines indicate fits using Eq. (1). $\Delta R\left(\theta \right)/\Delta R$ at delay time of 10 ps is also shown (open circles with dashed fitting line) in (d) and (j). Note that the Cu-O bonds directions are drawn horizontal and vertical, while the crystalline axes are along the Bi-O bonds, and are rotated nearly ${45}^{\circ }$ from the Cu-O bonds.

Figure 3

$T$ dependencies of the $B_{1g},B_{2g}$, and $A_{1g}$ components of $\Delta R$ corresponding to SC, PG, and metallic state relaxation, respectively, for OD (top) and UD (bottom) samples. The values of the color bars indicate $\Delta R/R\times {10}^4$.

Figure 4

$T$ dependencies of the $A_{1g},B_{1g}$, and $B_{2g}$ component amplitudes for UD and OD samples. Note that both $B$ components begin to show an increase of the amplitude below $T^{*}$. $T^{*}\text{s}$ obtained from tunneling [30] are within the region indicated by the shaded area. In the case of the $A_{1g}$ symmetry the PG contribution is superimposed on top of the nearly temperature-independent signal, and has a negative sign. The solid and dashed lines are fits using Mattis-Bardeen [31] and Kabanov [32] models, respectively.

Figure 5

(a) The reduction of symmetries consistent with the observed polarization anisotropy. The ${\mathrm{CuO}}_2$ layers are shown. Using the centrosymmetric refinement [39], the highest possible symmetry below $T^{*}$ is $C_{2h}$. The relevant irreducible representations are given in each case. (b) Schematic representations corresponding to nematic ordering, (c) short stripe ordering [41, 42, 43, 44, 45, 46], and (d) local polaronic order [47].