YbSb2, a Type-I Superconductor, Shows Signs of Broken Time-Reversal Symmetry

A joint research team including the Indian Institute of Science Education and Research (IISER) Bhopal, the Indian Institute of Technology Kanpur, the University of Warwick in the UK, and the ISIS Neutron and Muon Source at the UK's Rutherford Appleton Laboratory has reported evidence that time-reversal symmetry is spontaneously broken in single crystals of ytterbium diantimonide ( $YbSb_{2}$ ) at the same moment the material becomes superconducting.

The results were published in the peer-reviewed journal Physical Review Letters (DOI: 10.1103/drzq-lfn5, preprint arXiv:2601.07460). According to Anshu Kataria and colleagues, this is the first observation of broken time-reversal symmetry in a type-I superconductor that can be confirmed in the literature.

The phrase "broken time-reversal symmetry" may bring time travel, or changes in the flow of time itself, to mind. That is not what is being described here.

In physics, one sometimes considers how a phenomenon would look if the direction of time were reversed in the equations. For example, the magnetic field produced by a moving charge points in the opposite direction when time is reversed. If the physical state is still the same after such a transformation, the system is said to have time-reversal symmetry.

In $YbSb_{2}$ , however, a very small internal magnetic field of about 0.44 gauss appeared when the material became superconducting, even though no external magnetic field was applied.

This indicates that the superconducting state has spontaneously chosen one "direction." Reversing time would also reverse the direction of the magnetic field, so the result would not be the same as the original state. This is what is meant here by broken time-reversal symmetry.

The important point is to separate what was confirmed experimentally from the theory proposed to explain it.

What the experiment supports fairly strongly is that $YbSb_{2}$ behaves as a type-I superconductor while generating a weak static or quasi-static magnetic field at the superconducting transition. By contrast, the specific electron-pairing state responsible, as well as any future link to Majorana states or quantum computing, remains at this stage only a theoretical candidate.

What makes the study interesting is that a more complex quantum state than expected has turned up in a material long regarded as a relatively simple superconductor.

A Type-I Superconductor Known for Years

$YbSb_{2}$ is not a newly discovered material.

Its crystal is orthorhombic with $D_{2 h}$ point-group symmetry. It is one of the $RSb_{2}$ ( $R = Ca, Yb$ ) family of compounds made of calcium or rare-earth elements and antimony, and its crystal contains a two-dimensional square net formed by antimony atoms.

In 2012, Liang L. Zhao and colleagues reported in detail in Physical Review B that $YbSb_{2}$ is a type-I superconductor (DOI: 10.1103/PhysRevB.85.214526).

The measurements at the time found:

Superconducting transition temperature $T_{c}$ : about 1.3 K
Critical field $H_{c}$ : about 55 Oe
Ginzburg–Landau parameter $κ$ : 0.05

$κ$ is an important value for distinguishing type-I from type-II superconductors. A value of 0.05, well below $1/ 2 \approx 0.707$ , made $YbSb_{2}$ look like a typical type-I superconductor.

The electron-phonon coupling constant $λ_{el-ph}$ was about 0.51, and the material was regarded as a weak-coupling superconductor that conventional BCS theory could explain fairly readily.

In other words, at least back then, it was considered a "fairly ordinary type-I superconductor."

The 2012 measurements did, however, reveal something slightly odd.

Near 0.41 K there were signs suggestive of a second superconducting transition, with a critical field reaching about 430 Oe. The authors could not give a clear explanation for this phenomenon.

In the new study, the researchers measured high-quality single crystals again.

They observed only a single superconducting transition, near $T_{c} = 0.95 (1) K$ . This is lower than the roughly 1.3 K reported in 2012, and the second transition near 0.41 K was not seen.

The team points to subtle differences in composition between samples, as well as defects and internal strain, as possible causes.

In Thin Films, It Becomes a Type-II Superconductor

More interestingly, the nature of the superconductivity in $YbSb_{2}$ changes depending on how the sample is made.

Epitaxial thin films reported in 2025 gave the following values:

$T_{c} \approx 1.025 K$
$H_{c ⊥} (0) \approx 83.85 Oe$
$κ \approx 2.04$

In thin films, greater crystal disorder shortens the "mean free path," the distance electrons can travel without colliding. As a result, $κ$ rises well above $1/ 2$ , and the film behaves as a weak type-II superconductor rather than a type-I one.

データを表で見る

	超伝導転移温度 Tc (K)
2012年単結晶（Liang L. Zhaoら）	1.3
2025年エピタキシャル薄膜	1.03
2026年単結晶（Anshu Katariaら）	0.95

YbSb2の試料形態による超伝導転移温度（Tc）の比較同じYbSb2でも、単結晶の作製条件や薄膜化に伴う結晶の乱れによって超伝導特性が変化する出典: 各研究論文データより作成

So this result is not about discovering a new superconducting material.

A closer look at a material long thought to be a typical type-I superconductor suggests that an unconventional superconducting state may be at work inside it.

Muons Detect an Internal Field of 0.44 Gauss

The most important part of the study is the measurement using muons.

In ordinary superconductors, electrons form pairs called Cooper pairs. Electrons normally repel each other, but at low temperatures they can effectively attract each other through mediators such as lattice vibrations (phonons).

In a typical s-wave BCS superconductor, the two electrons form a "spin singlet" with opposite spins.

In this state the two spins cancel, so the pair as a whole has no magnetic orientation. It is therefore not normally expected that the superconducting state itself would generate a magnetic field when no external field is present.

In $YbSb_{2}$ , however, a different result was obtained.

The research team used muon spin rotation, relaxation, and resonance spectroscopy ( $μ SR$ ).

The muon is an elementary particle with properties similar to the electron, but about 207 times heavier. By implanting spin-polarized muons into a sample and examining how their spins change over time, even extremely weak magnetic fields inside the sample can be detected.

Put differently, it is a measurement method that embeds tiny magnetic sensors inside the material.

The team first measured with the external magnetic field set to nearly zero.

At 1.5 K, above the superconducting transition temperature, the muon spins showed no major change. The slight relaxation observed can be explained mainly by the magnetism of nuclei such as antimony.

Below 0.95 K, however, the situation changed.

The muon spin relaxation rate $Λ$ began to increase sharply.

This means that a new magnetic-field component was added inside the sample at almost the same time as superconductivity set in.

The team calculated its magnitude as

B_{in} \approx 0.44 (3) G

This is about 0.044 millitesla.

It is very small compared with the Earth's surface magnetic field, which is roughly 0.3 to 0.5 G. What matters, though, is not the absolute size but the fact that in an environment with the external field removed, a new magnetic field appeared only when the material became superconducting.

Is the Field Really Static?

A disturbance in the muon spins does not immediately prove that "the superconductor generated a magnetic field itself."

A similar signal could also arise from slowly fluctuating magnetic impurities.

The team therefore performed "LF decoupling measurements," applying a longitudinal field of about 10 mT externally.

The spin relaxation observed earlier was strongly suppressed.

This supports the conclusion that the detected field is not rapidly fluctuating noise but a "static or quasi-static field" essentially fixed inside the sample.

And that field appears only below the superconducting transition temperature.

This combination is strong evidence that the superconducting state itself spontaneously breaks time-reversal symmetry.

It Was Still a Type-I Superconductor

Here a further puzzle arises.

Superconductors that break time-reversal symmetry have been reported before.

Examples include $Sr_{2} RuO_{4}$ , uranium-based heavy-fermion superconductors, and $LaNiGa_{2}$ .

But most of those cases were type-II superconductors.

$YbSb_{2}$ is different.

While showing signs of broken time-reversal symmetry, its macroscopic response to magnetic fields remained that of a type-I superconductor.

The difference between type I and type II becomes clear as the external field is increased.

In a type-II superconductor, above a certain field, magnetic flux begins to penetrate as thin "vortices."

A type-I superconductor, by contrast, essentially expels the field from its interior, and superconductivity is lost altogether once the critical field is exceeded.

In real samples of finite size, however, an "intermediate state" appears near the critical field in which superconducting and normal regions coexist.

There, flux pushed out of the superconducting regions concentrates in the normal regions. As a result, in places the field is stronger than the externally applied field.

The team confirmed this feature in transverse-field $μ SR$ measurements.

When a 40 G field was applied at 0.1 K, regions with a field of about 51 G, exceeding 40 G, appeared inside the sample.

This matches the behavior expected in the intermediate state of a type-I superconductor.

When the field was raised further to about 100 G, the superconducting state vanished and the entire sample became normal.

From these results, the thermodynamic critical field at 0.1 K was determined to be

H_{c} = 51 (1) G

In other words, even though an anomalous field appears locally, the material as a whole is indeed a type-I superconductor.

The Energy Gap Also Looked Ordinary at First Glance

Specific heat measurements also gave a surprising result.

In superconductors, the formation of Cooper pairs opens a "superconducting gap," the minimum energy needed to excite an electron.

In unconventional superconductors, this gap can vary strongly with direction, or have "nodes" where it vanishes in certain directions.

The specific heat data for $YbSb_{2}$ , however, agreed better with an isotropic s-wave model with a gap open over the whole Fermi surface than with such complex models.

Roughly summarized, the experimental results are:

It is a type-I superconductor
A gap is open over the entire Fermi surface
It shows thermodynamic properties close to weak-coupling BCS
Yet an internal field that breaks time-reversal symmetry is generated

This is a seemingly strange combination.

Item	2012 single-crystal study (Liang L. Zhao et al.)	2025 epitaxial thin-film study	2026 single-crystal study (Anshu Kataria et al.)
Sample form	Bulk single crystal	Epitaxial thin film, about 35 nm thick	Bulk single crystal
Superconducting transition temperature $T_{c}$	About 1.3 K (sign of a second transition at 0.41 K)	About 1.025 K	0.95(1) K (single transition)
Critical field	$H_{c} \approx 55 Oe$ (430 Oe for the 0.41 K phase)	$H_{c ⊥} (0) \approx 83.85 Oe$	$H_{c} = 51 (1) G$ (0.1 K)
Superconductor type	Type I ( $κ = 0.05$ )	Weak type II ( $κ \approx 2.04$ )	Type I (intermediate state observed)
Gap and other features	Weak-coupling, isotropic s-wave	Anisotropy parameter $γ \approx 1.54$	Isotropic full gap (consistent with s-wave model)
Time-reversal symmetry	Not measured	Not measured	Evidence of breaking observed ( $B_{in} \approx 0.44 G$ )

How can these seemingly contradictory features be explained? This is where the somewhat unusual electron pairing proposed in the study comes in.

Electrons May Be Forming an Unusual Kind of Pair

The team carried out first-principles calculations and symmetry analysis to examine which superconducting states could explain the experimental results.

From here on, what follows was not directly confirmed experimentally; it is a theoretical candidate for explaining the observations.

Electronic structure calculations show that multiple electron orbitals exist near the Fermi level in $YbSb_{2}$ .

This is the key point.

In the usual explanation, for the two electrons forming a Cooper pair, one mainly considers:

Their spatial arrangement
The direction of their spins

Electrons are fermions, so exchanging two of them must flip the sign of the total wave function.

In a typical s-wave superconductor, the spatial part is symmetric, so the spin part must be antisymmetric.

As a result, the pair becomes a spin singlet:

One electron has spin up
The other has spin down

In a material like $YbSb_{2}$ where multiple orbitals are involved, however, there is one more degree of freedom.

It is the question of which electron orbital each electron occupies.

Suppose, for example, that electrons in orbital A and orbital B form a pair.

In this case, the antisymmetry required for electron exchange can be built from a combination of three properties:

Space
Spin
Orbital

In other words, the role previously played by the spin part can be assigned to the orbital part.

Then, even if the spatial part remains symmetric as in an s-wave state, the two electrons can form a spin triplet.

This is the key point for understanding the present theory.

The INT State Could Explain Both Features at Once

The leading candidate proposed by the team is the

Internally Antisymmetric Non-unitary Triplet (INT) state.

The name is complicated, but it is easier to understand when split into two parts.

First, "internally antisymmetric" means the electron pair changes sign when the orbitals the electrons occupy are exchanged.

Because the orbital part carries the antisymmetry, the spin can form a triplet rather than the singlet of an ordinary s-wave superconductor.

Second, "non-unitary" refers to a spin-triplet state in which the up and down spins are not perfectly balanced.

A spin-triplet state can generally be described by a complex vector $d$ , and when

q = i (d \times d^{\*}) \neq = 0

it is called a non-unitary state.

Without following the details of the equation, it suffices here to think of it as meaning that

within a Cooper pair the spins do not cancel completely, leaving a slight magnetic orientation.

As a result, the superconducting state itself can generate a small magnetic field without any externally applied field.

In other words, the INT state can simultaneously:

Open a gap over the entire Fermi surface, as in s-wave
Still form a spin triplet
Carry a spontaneous magnetic moment
As a result, break time-reversal symmetry

This could explain the strange combination observed here: a material that looks like an ordinary s-wave superconductor yet has a spontaneous internal magnetic field.

A similar mechanism has also been theoretically proposed for $LaNiGa_{2}$ , and the team considers it a strong candidate for $YbSb_{2}$ as well.

Note, however, that the INT state itself has not been directly observed.

Why Does This Lead to Majorana Particles?

The team also performed calculations on the electronic structure of $YbSb_{2}$ .

The results suggest that the material may have properties of a $Z_{2}$ topological metal with Dirac nodal lines.

Combining this with the INT superconducting state described above, "Majorana surface states" could appear on the surface of the material.

This is why it has been reported that the work "may lead to quantum computers."

Majorana-type quasiparticles have the special property that particle and antiparticle cannot be distinguished. If such states can be controlled well, they could potentially be used for "topological qubits" that are resistant to external noise.

There is still a long way to go, however.

What has been confirmed here is

experimental evidence that time-reversal symmetry is broken in the superconducting state.

Meanwhile, the following have not yet been confirmed:

Whether the INT state is actually realized
Whether Majorana surface states exist
Whether they can be manipulated
Whether they can be used as qubits

It is therefore premature to understand this as "a new material usable for quantum computers has been found."

Additional Experiments Are Needed to Confirm Majorana States

The next step is to directly probe the electronic states on the material's surface.

Candidate methods are tunneling spectroscopy and point-contact spectroscopy at extremely low temperatures.

If Majorana states exist, characteristic signals such as a zero-bias conductance peak (ZBCP) may appear.

In addition, the following will also be needed:

Fermi surface measurements by angle-resolved photoemission spectroscopy (ARPES)
Surface electronic state measurements by scanning tunneling microscopy (STM)
Measurements sensitive to the phase of the superconducting order parameter

Without repeated experiments of this kind, it is impossible to judge whether the actual electron pairs are in the INT state or in some other unknown superconducting state.

Not a Superconductor Ready for Practical Use

Caution is also needed regarding applications.

The temperature at which $YbSb_{2}$ becomes superconducting is only

T_{c} \approx 0.95 K

Converted to Celsius, that is about −272.2 degrees, extremely close to absolute zero.

Its critical field is also very small, about 51 G, or about 0.005 tesla.

It is therefore not a promising practical superconducting material for uses requiring high magnetic fields, such as MRI, large electromagnets, or power transmission lines.

The value of this work lies at a more fundamental level.

Even "Simple" Superconductors Still Hold Mysteries

Type-I superconductivity has been one of the most fundamental subjects of superconductivity research ever since Heike Kamerlingh Onnes discovered superconductivity in mercury in 1911.

Weak-coupling, s-wave type-I superconductors in particular are considered relatively well understood through BCS theory.

$YbSb_{2}$ was long regarded as one such material.

Now, highly sensitive local magnetic measurements have revealed a side of it that differs from that simple picture.

Although it is a type-I superconductor that appears to have a gap over the whole Fermi surface, a spontaneous internal magnetic field appears when it becomes superconducting.

A special spin-triplet state that exploits multiple electron orbitals has been put forward as a candidate cause.

Going forward, replication by other research groups will also be important. It will be necessary to check whether the 0.44 G signal changes with impurities or internal strain in different samples, and whether similar phenomena occur in related materials such as $CaSb_{2}$ .

If the INT state and Majorana surface states are further confirmed experimentally, this could become an important example that broadens the conventional understanding of type-I superconductors.

The most important point at present is not that "a material usable for quantum computers has been found."

It is that even within a type-I superconductor thought to be relatively well understood, a complex quantum state that spontaneously breaks time-reversal symmetry may be hidden.

An internal magnetic field of just 0.44 gauss shows that even superconductivity, a phenomenon studied for more than a century, still has aspects that remain unexplained.