Effect of a magnetic field on the electron-boson spectral function of cuprate superconductors

We have performed magneto-optical measurements on a series of $\mathrm{high}\text{−}{T}_c$ superconductors with magnetic field up to $18\mathrm{T}$. Similar to previous reports in smaller fields, the results reveal that the optical constants, both in the normal and superconducting state, of several families of $\mathrm{high}\text{−}{T}_c$ cuprates are completely insensitive to the application of external magnetic field. These magneto-optical results seem to indicate that either the bosonic mode responsible for pairing is not magnetic in origin, or the charge carriers are not very strongly coupled to it. We discuss the results within the existing theoretical models.

Figure 1

(Color online) Optical constants of ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ (LBCO) with $T_c=2.4\mathrm{K}$ in zero magnetic field. (a) Reflectance $R\left(\omega \right)$ at 300 and $10\mathrm{K}$. (b) The scattering rate $1∕\tau \left(\omega \right)$ at 300 and $10\mathrm{K}$. (c) Calculated electron-boson spectral function ${\alpha }^{2}F\left(\omega \right)$ at $10\mathrm{K}$ (full blue line) and the same function with the main peak suppressed (dash-dot-dot green line) and enhanced (dash-dot magenta line) by 40%. These modifications of ${\alpha }^{2}F\left(\omega \right)$ are intended to simulate the effect of external magnetic field. (d) Calculated reflectance ratio $R(\omega ,B)∕R(\omega ,0\mathrm{T})$ with the intensity of the main peak suppressed (dash-dot-dot green) or enhanced (dash-dot magenta) by 40% [panel (c)]. The vertical dashed line indicates the position of the peak in ${\alpha }^{2}F\left(\omega \right)$ and the “kink” in $1∕\tau \left(\omega \right)$. Note that below the peak calculated changes of reflectance are small, but are expected to grow monotonically above the peak.

Figure 2

(Color online) The magneto-optical results at $4.2\mathrm{K}$ for optimally doped YBCO $1.6\mathrm{\mu }\mathrm{m}$ thick film with $T_c=92\mathrm{K}$ and at several different magnetic field values between 0 and $18\mathrm{T}$. The top panel displays a 100% line, which is commonly used to quantify the signal-to-noise ratio and temporal drift in the measurement system.[20] The other four panels show reflectance ratios $R(\omega ,B)∕R(\omega ,0\mathrm{T})$, with $B=7$, 10, 14 and $18\mathrm{T}$. The vertical dashed line indicates the approximate position of the peak in ${\alpha }^{2}F\left(\omega \right)$ in zero field. The biggest changes in reflectance are expected above the frequency of the peak, but within the error bars there are no field-induced changes. Thin black lines are expected changes for each field value, based on the calculations described in the text.

Figure 3

(Color online) Magneto-optical ratios $R(\omega ,B=18\mathrm{T})∕R(\omega ,0\mathrm{T})$ at $4.2\mathrm{K}$ for YBCO film (Fig. 2), $\mathrm{Bi}2212$ single crystal, LBCO single crystal with $T_c=2.4\mathrm{K}$ and NCCO single crystal with $T_c=23\mathrm{K}$. The biggest field-induced changes of reflectance are expected in the mid-IR part of the spectrum, however, within the error bars of this experiment, no changes are detected in either of the samples.