Author Archives: innavishik

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).

Josephson junction schematic

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

IV curve josephson

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.

Bi2212 intrinsic Josephson junctions

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.

BSCCO mesa

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

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]


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.


[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)

Staying cool this summer

Many green energy solutions originate as condensed matter physics problems. Prominent examples include electricity production via solar cells, brighter and more efficient lighting via LEDs, and thermoelectric materials for converting waste heat into electricity.  Another promising but less well-known approach is using metamaterials for passive—no power input required– daytime radiative cooling.  This may one day supplement or replace air conditioners or be incorporated in clothing.  Just what we need with summer upon us.

A recent Science paper illustrated how a species of ants in the Sahara Desert uses special triangular hairs on the top part of its body to cool themselves in the middle of the day in temperatures up to 158° F [1].  This work was also highlighted in a New York Times article.

Left: SEMS image of Sahara silver ant head. Right: SEM image of ant hairs.  Notice that they are corrugated on the top surfaces, have a triangular cross-section, and are of different sizes.  From Ref. [1].

Left: SEM image of Sahara silver ant head.
Right: SEM image of ant hairs. Notice that they are corrugated on the top surfaces, have a triangular cross-section, and are of different sizes. From Ref. [1].

The engineering requirements for daytime radiative cooling are high reflectivity at visible wavelengths, where the solar spectrum is peaked, and high-emissivity (corresponding to low reflectivity, aka high absorptivity) at mid-infrared wavelengths, where the blackbody spectrum of a human or a hot building are peaked (~9 microns).  This originates from Kirchhoff’s law of thermal radiation, which states that the absorptivity (\alpha_\lambda) and emissivity (\epsilon_\lambda) must be equal at a given wavelength (\lambda ) in order to maintain equilibrium.  However, the overall absorption and emission is weighted by the solar spectrum (I_{\lambda,sun} ) and the blackbody spectrum of the hot body (I_{\lambda,body}), respectively.

Total absorptivity: \alpha =\frac{ \int^\infty_0 \alpha_{\lambda,body}I_{\lambda,sun} \mathrm{d}\lambda}{\int^\infty_0 I_{\lambda,sun}\mathrm{d}\lambda}

Total emissivity: \epsilon = \frac{\int^\infty_0 \epsilon_{\lambda,body}I_{\lambda,body} \mathrm{d}\lambda}{\int^\infty_0I_{\lambda,body} \mathrm{d}\lambda}

The values above might not be equal, even though emissivity and absorptivity must be equal at a given wavelength.  An object which is highly reflective at visible wavelengths is not effectively heated up by absorbing energy from the sun.  Meanwhile, an object which has high emissivity (aka high absorptivity aka low reflectivity) at mid-IR wavelengths can effectively radiate heat, provided the atmosphere has sufficient transparency, which it does for radiation with wavelengths between 8 and 13 microns.  An example of the latter is a plant leaf: their high emissivity at mid-IR wavelengths allows them to cool below ambient temperature at night, which is why you find dew condensed on the grass in the morning.  If a single material or structure has high reflectivity at visible wavelengths and high emissivity at mid-IR wavelengths, there is the possibility of passively cooling below ambient temperature in the middle of the day.

These engineering requirements are generally hard to achieve in bulk materials, and this is where metamaterials—composites or structures engineered to have properties not found in bulk materials– come in.  Recently, passive daytime radiative cooling has been predicted [2] and achieved [3] in engineered photonic structures.

Returning to the desert ants, their hairs are an example of a natural photonic metamaterial which passively cools them in the middle of the day so they can venture out for a snack while their predators are hiding from the heat.  The hairs’ shape, size, and surface all conspire to reflect visible light.  The triangular cross-section permits total internal reflection for a range of incidence angles (see figure below).  The cross-sectional size of the hairs is comparable to the wavelength of visible light, which allows for the trapping and re-radiation of light via a process called Mie scattering.  A given cross-sectional area will give enhanced reflection at a single wavelength, but the polydisperse distribution of hair sizes allows for broadband coverage.  Finally, surface roughness allows for diffuse scattering of visible light at the surface of the hair.  As for mid-IR absorption, the paper says that the hairs act as an antireflective coating at these wavelengths, though they do not specify the mechanism.  Most likely, the sub-wavelength size of the hairs present an effective medium with an effective index of refraction to incoming mid-IR light, and the triangular shape helps produce a gradient of the refractive index which minimizes reflection due to index mismatch with air.  Another factor might be that the size of the hairs (and they appear to grow in a single layer) is roughly comparable to ¼ of the wavelength of mid-IR light, and quarter-wave-thick layers are frequently used in antireflective coatings.   And it really works.  Both in vacuum and in air, the ant is able to stay 10° C cooler with the hairs than without.

Total internal reflection happens for a range of incidence angles, and is one mechanism by which the ants' triangular hairs reflect visible light.

Total internal reflection happens for a range of incidence angles, and is one mechanism by which the ants’ triangular hairs reflect visible light.

It sounds too good to be true—cooling a body or an object passively in full sunlight—but the Sahara Desert ants (Ref. [1]) and the experiments in Ref. [3] show that it is really possible to achieve this feat by manipulating the optical properties of materials.

Thermal images of the ant head show that radiative cooling works both in vacuum and in air, and that the hairs are the source of this phenomenon

Thermal images of the ant head show that radiative cooling works both in vacuum and in air, and that the hairs are the source of this phenomenon.


[1] N. N. Shi et al. Science (2015), Advance online publication

[2] E. Rephaeli et al. Nano Lett.,  13 (4), pp 1457–1461 (2013)

[3] A. Raman et al. Nature515 pp 540–544 (2014)