# Let there be (THz) light

The applications of scientific discoveries is sometimes not what you would expect, and high temperature superconductivity is no different.  When high-temperature superconductivity was discovered in copper-oxides (cuprates) in 1986, the envisioned applications were power lines, electromagnets, and maglev trains, all cooled by cheap-as-milk liquid nitrogen.  While applications involving high-temperature superconductors’ dissipationless and diamagnetic properties are slowly coming online, there are other potential technologies which most people are less aware of.  The one I want to discuss here is using the layered structure of cuprate high temperature superconductors to produce coherent THz emitters.  Creating light sources and detectors for the THz portion of the electromagnetic spectrum—the notorious THz gap—has been a pressing challenge for decades.

The Josephson effect

The Josephson effect underlies many important applications of superconductors, such as sensitive magnetometers, qubits for quantum computing, and the SI definition of the volt.  The starting point for the Josephson effect is a superconductors’ complex order parameter, $\Psi=\Psi_0 e^{\imath\varphi}$.  The amplitude, $\Psi_0$, is related to some measure of the robustness of the superconducting state–either the superfluid density or the superconducting gap.  The phase, $\varphi$, reflects that a superconductor is a phase-coherent state–a condensate.  At $T_c$, a superconductor chooses an arbitrary phase, and a current in a superconductor (a supercurrent) corresponds to a gradient in this phase.  A Josephson junction, sketched below, consists of two superconductors separated by a non-superconducting barrier.  Because each superconductor chooses an arbitrary phase and the superconducting wavefunctions can penetrate into the barrier, a phase gradient develops in the barrier region, and a supercurrent can flow.  This supercurrent is given by $I_s=I_c\sin(\delta\varphi)$, where  $I_c$ is the critical current which causes the Josephson junction to become resistive (different from the critical current which makes the superconductor resistive) and  $\delta\varphi$ is the phase difference between the two superconductors.  This is the DC Josephson effect.  In the resistive regime ($I>I_c$), one encounters the AC Josephson effect, in which the Josephson junction supports an oscillating current with AC Josephson frequency $\omega=\frac{2\pi V}{\Phi_0}$, where V is the voltage across the junction and $\Phi_0$ is the magnetic flux quantum.  The current in this regime is given by: $I(t)=I_c\sin(\delta\varphi + \frac{2\pi V}{\Phi_0}t)$

Thus, a Josephson junction can convert a DC voltage to an AC current (and vis versa).

Schematic of a Josephson junction, consisting of two superconductors with a barrier in between. The barrier may be an insulator, a metal, or a constricted piece of superconductor. Each superconducting slab has a complex wavefunction with an arbitrarily chosen phase, $\varphi_{1,2}$. Supercurrent through a Josephson junction depends on the phase difference, $\delta\varphi=\varphi_1-\varphi_2$

Schematic of IV curve of Josephson junction (solid line), from Ref [1]. For sufficiently small bias currents, a supercurrent flows through the junction and no voltage is sustained–the regime of the DC Josephson effect. At currents exceeding $I_c$, the junction becomes resistive and is able to sustain a voltage across it, even though each superconducting slab remains superconducting. This is where the AC josephson effect is realized. The dashed line is an ohmic resistance, which a Josephson junction approaches in the limit of high bias voltage.

More is better

While a Josephson junction in its resistive regime is a perfect DC to AC converter with frequency proportional to voltage, the amount of power it can output is limited by the fact that device performance (and eventually superconductivity) degrade if you crank the voltage up too high.  However, it turns out that if you have multiple Josephson junctions in series, the available power scales with the number of junctions, and if all of these junctions oscillate in phase, they can form a coherent radiation source.  This is where high temperature superconductors come in.

Calling all cuprates

The crystal structure of cuprate high temperature superconductors consists of $CuO_2$ sheet where superconductivity originates, separated by insulating layers.  While the $CuO_2$ sheets are coupled with each other, the coupling can be weak in some cuprates, such that the material behaves like an array of intrinsic Josephson junctions in series.  Thus, a structure which has to be specially manufactured for other superconductors, the cuprates give for free.

Crystal structure of the high temperature superconductor, $Bi_2Sr_2CaCu_2O_{8+\delta}$ (BSCCO) which is most commonly used to make THz emitters. The layered structure of cuprates—superconducting $CuO_2$ layers separated by insulating intervening layers– permits the material itself to be a series of Josephson junctions. Adapted from Ref. [2].

The first step to making a cuprate superconductor into an emitter of coherent THz radiation is to pattern a single crystal into a smaller structure called a mesa. The mesa behaves as a resonant cavity such that a half-integer number of wavelengths ($\lambda/2$) of radiation fit into the width, w, of the device.  The lowest-order resonance condition is met when the AC Josephson frequency is equal to the frequency of a cavity mode, $\omega_c=\frac{\pi c_0}{n w}$, where $c_0/n$ is the mode propagation velocity in the medium and n is the far-infrared refractive index.  For a given mesa width, the resonance condition is met for a specific value of applied voltage for each Josephson junction, $V_{jj}=\frac{c_0 \Phi_0}{2 w n}$.  For a stack of Josephson junctions in series, the applied voltage scales with the number of junctions (N): $V=NV_{jj}$

A schematic of such a device is shown below.  The mesa, produced by ion milling, is 1-2 microns high (corresponding to ~1000 intrinsic Josephson junctions), 40-100 microns wide (setting the resonance emission frequencies), and several hundred microns in length.  A voltage is applied along the height of the stack and THz radiation is emitted out the side of the stack.  Devices have been fabricated with emissions at frequencies between 250 GHz and 1THz.  Linewidths of ~10MHz have been achieved as have radiation powers of 80 microwatts, though it is predicted that the latter figure can be pushed to 1mW [2,3].  The emission frequency can be tuned either by fabricating a new device with a different width, or by fabricating a device shaped like a trapezoid or a stepped pyramid and varying the bias voltage [4].  The latter corresponds to different numbers of Josephson junctions in the stack oscillating coherently.

THz emitter made out of high-temperature superconducting cuprates. A ‘mesa’ is ion-milled from a single crystal of BSCCO with a restricted width dimension, w. THz radiation is emitted out of the side, with frequency depending on the width of the mesa and the applied voltage. From Refs [2-3].

Emission spectra of three devices with different widths,w, made out of high temperature superconductors operated at T~25K. Inset shows linear relationship between frequency and 1/w. From Ref [3]

Implications

Successful fabrication of coherent THz emittors out of high temperature superconductors is a relatively new achievement and there is additional progress to be made, particularly towards increasing the emitted power.  This technology is promising for filling in a portion of the THz gap outside the capabilities of quantum cascade lasers, whose lowest emission frequency is presently 1.6THz.  In the future, one can imagine a light source consisting of an array of BSCCO mesas of different dimensions producing a narrow-bandwidth lightsource which is tuneable between 250GHz and 1.5THz for security and research applications.

References

[1] J. Annett. Superconductivity, Superfluids, and Condensates, Oxford University Press (2003)

[2] U. Welp et alNature Photonics 7 702 (2013)

[3] L. Ozyuzer et al, Science 318 1291 (2007)

[4] T. M. Benseman et al, Phys. Rev. B 84 064523 (2011)