Observation of a two-mode resonant state in a $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ mesa device for terahertz emission

Using low-temperature scanning laser microscopy (LTSLM), we have studied the cavity resonance behavior of a rectangular $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ mesa THz device containing $N=640$ stacked intrinsic Josephson junctions. Our results show that this microscopy technique is an effective means of mapping electromagnetic resonances in this type of device, and we present a detailed analysis of the mechanisms underlying contrast formation in scanning laser microscopy. The LTSLM images reveal that the THz excitation of the stacked junctions contains more than one mode with components along both the long and short axes of the mesa. Thermoluminescent mapping of the same device shows that the mesa temperature is uniform demonstrating that the features seen in LTSLM are electromagnetic in origin, not thermal. Our results also imply that for the purposes of maximizing the THz emission power from $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ mesas, it is important to design devices that are capable of being excited in a single, purely transverse mode.

Figure 1

Schematic of the Bi-2212 mesa imaged here and of possible $c$-axis mode profiles.

Figure 2

(a) (Main) Resistance versus temperature plotted for the mesa studied in this experiment. Red curve was measured directly with 10 μA bias current, while blue squares for data points below $T_c$ were obtained from the tangent to downward-sweep I-V curves (black line in inset) as described in Ref. [26]. (Inset) I-V characteristic for mesa at 75 K showing hysteretic switching of IJJs. THz emission occurs on downward sweep. (b) Enlargement of region enclosed in dotted red box in (a). Vertical axis shows mesa bias current, while voltage and total radiated THz power are plotted on horizontal axes. (c) Maps of position-dependent scanning laser signal, showing signed root mean square (RMS) perturbation to mesa voltages at a range of bias currents, and a bath temperature of 75 K. Red dashed lines show cross sections plotted in Figs. 3 and 4. (d) Conventional optical image of mesa at top (with 500-nm Au current electrode on right) and direct thermoluminescent images of mesa under same conditions as measured in (c).

Figure 3

(a) Longitudinal cross sections of scanning laser signal data plotted in Fig. 2 along centerline of mesa [red dashed line in Fig. 2] showing strong positive and negative oscillations at bias currents for which the mesa's cavity resonance is excited, and $T_{\mathrm{bath}}=75\mathrm{K}$. (b) Equivalent cross sections for thermoluminescent data, indicating absence of corresponding oscillations in the mesa temperature itself. Vertical dashed lines show locations of thermal imaging artifacts due to reflection of light from the sidewalls of the mesa and its 500-nm-thick Au current electrode. Note that the temperature rise observed here is not very large compared with the noise floor of this technique. The steep rise in the temperature profiles starting near 450 µm is caused by Joule heating in the contact. At this point the gold film transitions onto an epoxy ramp leading to contact pads further out. Due to the reduced thermal conductivity of the epoxy the temperature rises rapidly.

Figure 4

(a) Longitudinal cross sections of scanning laser image for $T_{\mathrm{bath}}=75\mathrm{K}$, $I=15.25\mathrm{mA}$, taken at increasing distance from the centerline of the mesa. The amplitude of the oscillations strongly decreases as the edge of the mesa is approached, indicating that the cavity mode being excited has a significant transversal component. (b) Transverse cross sections of the LTSLM image for $T_{\mathrm{bath}}=75\mathrm{K}$ taken at increasing bias current. These cross sections were taken through the minimum of the LTSLM pattern which occurs at $x=130\mu \mathrm{m}$, indicated by the arrow in Fig. 4.

Figure 5

Typical spatial patterns corresponding to the $c$-axis (${\sigma }_c$ and $j_J$) and in-plane response channels for three different modes. We note that all of these patterns have maxima / minima at the edges of the sample, in contrast with what we observe experimentally.

Figure 6

(a) I-V characteristic for a second mesa patterned on the same chip as the mesa presented in Fig. 2, at 75 K showing hysteretic switching of IJJs. THz emission occurs on downward sweep. (b) Enlargement of region enclosed in dotted red box in (a). Vertical axis shows mesa bias current, while voltage and total radiated THz power are plotted on horizontal axes. (c) Maps of position-dependent scanning laser signal, showing signed RMS perturbation to mesa voltages at a range of bias currents, and a bath temperature of 75 K. The signal magnitude is slightly larger than it is for the data in Fig. 2, due to the higher ratio of laser-heated spot volume to mesa volume for this mesa. The top panel shows an optical image of the mesa (with 500-nm Au current electrode on right).

Figure 7

(Top) Section of the experimental LTSLM pattern seen at $T_{\mathrm{bath}}=75\mathrm{K}$, $I=15.25\mathrm{mA}$, as compared with the function $\mathrm{si}{\mathrm{n}}^2\left(\pi x\right)\mathrm{co}{\mathrm{s}}^2\left(\pi y\right)+\mathrm{co}{\mathrm{s}}^2\left(\pi x\right)\mathrm{si}{\mathrm{n}}^2\left(\pi y\right)-1.2\mathrm{si}{\mathrm{n}}^2\left(\pi y\right)$ (Bottom). This function approximates the sum of the two theoretical in-plane response patterns for perturbations of the $in$-plane parameters, corresponding to the cavity modes (0, $m$) and (1, $m$).

Figure 8

Fourier transform infrared spectra emitted by the mesa at its highest achievable THz power output, which occurred at $T_{\mathrm{bath}}=75\mathrm{K}$, $I=15.00\mathrm{mA}$, and also at the closest local maximum of emitted power with respect to bias current, which occurred at 15.75 mA. The total emitted power (radiated over all angles) at 15.00 mA is approximately 1.4 μW, while the center frequency is 396 GHz. The observed linewidth at 15.00 mA is limited by the spectrometer resolution at $0.75\mathrm{c}{\mathrm{m}}^{-1}$, or 2.25 GHz. At 15.75 mA, the emission linewidth becomes broader, and possibly multipeaked. The satellite peaks, however, are difficult to definitively distinguish from background noise. (Two spectra taken at 15.75 mA are plotted as an indication of the level of reproducibility of these spectra).

Figure 9

(a) Current-voltage characteristic and THz emission data at $T_{\mathrm{bath}}=65\mathrm{K}$, for the same mesa as shown in Fig. 2 in the main text. Vertical axis shows mesa bias current, while voltage and total radiated THz power are plotted on horizontal axes. (b) Maps of position-dependent scanning laser signal, showing signed RMS perturbation to mesa voltages at a range of bias currents, and a bath temperature of 65 K. (c) Conventional optical image of mesa at top (with 500 nm Au current electrode on right) and direct thermoluminescent images of mesa under same conditions as measured in (b).

Figure 10

Detail of downward-sweep current-voltage characteristics in the regions at which THz emission occurred at $T_{\mathrm{bath}}=75\mathrm{K}$. Current-voltage characteristics show good agreement between the three cryostat systems in which the devices were measured, with only minor shifts due to small variations in thermometer calibration. Curves measured in the scanning laser imaging system (purple solid lines) are plotted for the time-averaged DC voltage while the sample is illuminated by the laser beam. Note that these curves show a slightly higher retrapping current as compared to the other systems, due to laser-spot induced heating causing an increased probability of Josephson retrapping.