At last, physicists report finding the ‘fourth sign’ of superconductivity

A schematic illustration of an ARPES setup. On the left is the head-on view of the manipulator holding the sample and at the centre is the side-on view. On the right is an electron energy analyser.
A schematic illustration of an ARPES setup. On the left is the head-on view of the manipulator holding the sample and at the centre is the side-on view. On the right is an electron energy analyser. Credit: Ponor/Wikimedia Commons, CC BY-SA 4.0

Using an advanced investigative technique, researchers at Stanford University have found that cuprate superconductors – which become superconducting at higher temperatures than their better-known conventional counterparts – transition into this exotic state in a different way. The discovery provides new insights into the way cuprate superconductors work and eases the path to discovering a room-temperature superconductor one day.

A superconductor is a material that can transport an electric current with zero resistance. The most well-known and also better understood superconductors are certain metallic alloys. They transition from their ‘normal’ resistive state to the superconducting state when their temperature is brought to a very low value, typically a few degrees above absolute zero.

The theory that explains the microscopic changes that occur as the material transitions is called Bardeen-Cooper-Schrieffer (BCS) theory. As the material crosses its threshold temperature, called the critical temperature, BCS theory predicts four signatures of superconductivity. If these four signatures occur, we can be sure that the material has become superconducting.

First, the material’s resistivity collapses and its electrons begin to flow without any resistance through the bulk – the electronic effect.

Second, the material expels all magnetic fields within its bulk – the magnetic (a.k.a. Meissner) effect.

A magnet levitating above a high-temperature superconductor, thanks to the Meissner effect. Credit: Mai-Linh Doan/Wikimedia Commons, CC BY-SA 3.0

Third, the amount of heat required to excite electrons to an arbitrarily higher energy is called the electronic specific heat. This number is lower for superconducting electrons than for non-superconducting electrons – but it increases as the material is warmed, only to drop abruptly to the non-superconducting value at the critical temperature. This is the effect on the material’s thermodynamic behaviour.

Fourth, while the energies of the electrons in the non-superconducting state have a variety of values, in the superconducting state some energy levels become unattainable. This shows up as a gap in a chart mapping the energy values. This is the spectroscopic effect. (The prefix ‘spectro-‘ refers to anything that can assume a continuous series of values, on a spectrum.)

Conventional superconductors are called so simply because scientists discovered them first and they defined the convention: among other things, they transition from their non-superconducting to superconducting states at very low temperature. Their unconventional counterparts are the high-temperature superconductors, which were discovered in the late 1980s and which transition at temperatures greater than 77 K. And when they do, physicists have thus far observed the corresponding electronic, magnetic and thermodynamic effects – but not the spectroscopic one.

A new study, published on January 26, 2022, has offered to complete this record. And in so doing, the researchers have uncovered new information about how these materials transition into their superconducting states: it is not the way low-temperature superconductors do.

The research team, at Stanford, reportedly did this by studying the thermodynamic effect and connecting it to the material’s spectroscopic effect.

The deeper problem with zeroing in on the spectroscopic effect in high-temperature superconductors is that an electron energy gap shows up before the transition, when the material is not yet a superconductor, and persists into the superconducting phase.

First, recall that at the critical temperature, the electronic specific heat stops increasing and drops suddenly to the non-superconducting value. The specific heat is directly related to the amount of entropy in the system (energy in the system that can’t be harnessed to perform work). The entropy is in turn related to the spectral function – an equation that dictates which energy states the electrons can and can’t occupy. So by studying changes in the specific heat, the researchers can understand the spectroscopic effect.

Second, to study the specific heat, the researchers used a technique called angle-resolved photo-emission spectroscopy (ARPES). These are big words but they have a simple meaning. Photo-emission spectroscopy refers to a technique in which energy-loaded photons are shot into a target material, where they knock out those electrons that they have the energy for. Based on the energies of the electrons knocked out, their position and their momenta, scientists can piece together the properties of the electrons inside the material.

ARPES takes this a step further by also recording the angle at which the electrons are knocked out of the material. This provides an insight into another property of the superconductor. Specifically, another way in which cuprates differ from conventional superconductors is the way in which the electrons pair up. In the latter, the pairs break rotational symmetry, such that the energy required to break up the pair is not equal in all directions.

This affects the way the thermodynamic and spectral effects look in the data. For example, photons fired at certain angles will knock out more electrons from the material than photons incoming at other angles.

The angle-specific measurements of the specific-heat coefficient (y-axis) versus the temperature (x-axis). Credit: https://doi.org/10.1038/s41586-021-04251-2

Taking all this into account, the researchers reported that a cuprate superconductor called Bi-2212 (bismuth strontium calcium copper oxide) transitions to becoming a superconductor in two steps – unlike the single-step transition of low-temperature superconductors.

According to BCS theory, the electrons in a conventional superconductor are encouraged to overcome their mutual repulsion and bind to each other in pairs when two conditions are met: the material’s lattice – the grid of atomic nuclei – has a vibrational energy of a certain frequency and the material’s temperature is lowered. These electron pairs then move around the material like a fluid of zero viscosity, thus giving rise to superconductivity.

The Stanford team found that in Bi-2212, the electrons pair up with each other at around 120 K, but condense into the fluid-like state only at around 77 K. The former gives rise to an energy gap – i.e. the spectroscopic effect – even as the superconducting behaviour itself arises only at the 77-K mark, when the pairs condense.

A small sample of Bi-2212 The side is 1 mm long. Credit: James Slezak, Cornell Laboratory of Atomic and Solid State Physics, CC BY-SA 3.0

There are two distinct feats here: finding the spectroscopic effect and finding the two-step transition. Both – but the first more so – were the product of technological advancements. The researchers obtained their Bi-2212 samples, created with specific chemical compositions so as to help analyse the ARPES data, from their collaborators in Japan, and then studied it with two instruments capable of performing ARPES studies at Stanford: an ultraviolet laser and the Synchrotron Radiation Lightsource.

Makoto Hashimoto, a physicist at Stanford and one of the study’s authors, said in a press statement: “Recent improvements in the overall performance of those instruments were an important factor in obtaining these high-quality results. They allowed us to measure the energy of the ejected electrons with more precision, stability and consistency.”

The second finding, of the two-step transition, is important foremost because it is new knowledge of the way cuprate superconductors ‘work’ and because it tells physicists that they will have to achieve two things – instead of just one, as in the case of conventional, low-temperature superconductors – if they want to recreate the same effects in a different material.

As Zhi-Xun Shen, the researcher who led the study at Stanford, told Physics World, “This knowledge will ultimately help us make better superconductors in the future.”

Featured image: A schematic illustration of an ARPES setup. On the left is the head-on view of the manipulator holding the sample and at the centre is the side-on view. On the right is an electron energy analyser. Credit: Ponor/Wikimedia Commons, CC BY-SA 4.0.