Nonreciprocal superconducting critical currents with normal state field trainability in kagome superconductor CsV3Sb5

This study demonstrates that the kagome superconductor CsV3Sb5 exhibits spontaneous time-reversal symmetry breaking in both its charge density wave and superconducting states, evidenced by nonreciprocal critical currents that can be deterministically trained by an external magnetic field.

The Gist

The Big Picture: A One-Way Street for Electricity

Imagine a superconductor as a magical highway where electricity flows without any friction or resistance. Usually, this highway is perfectly symmetrical: cars (electrons) can drive just as fast and easily in the North direction as they can in the South direction.

However, the scientists in this paper discovered that in a specific material called CsV₃Sb₅ (a "kagome superconductor"), this highway has a hidden traffic rule. In this material, electricity flows much more easily in one direction than the other, even when there is no external magnet pushing it. This is called the Superconducting Diode Effect (SDE). It's like a one-way street for super-powerful electricity.

The Material: A Special "Kagome" Pattern

The material they studied, CsV₃Sb₅, is special because its atoms are arranged in a pattern called a "kagome" lattice (named after a Japanese woven basket pattern). Think of this pattern as a complex, geometric dance floor. On this dance floor, the electrons don't just sit still; they form complex patterns called Charge Density Waves (CDW) before they even become superconductors.

The Mystery: Why Does the Traffic Flow One Way?

In physics, there is a rule called Time-Reversal Symmetry (TRS). In simple terms, if you played a movie of electrons moving backward in time, the laws of physics should look the same as the movie playing forward.

The researchers found that in CsV₃Sb₅, this symmetry is broken. The electrons are spontaneously forming tiny, invisible loops of current (like microscopic whirlpools) that create a preferred direction. This breaks the "mirror" of time, making the material behave differently depending on which way the electricity tries to flow.

The Experiment: The "Field Training" Trick

The most exciting part of the paper is how they proved where this one-way behavior comes from. They used a clever trick called "Field Training."

1. The Setup: They took the material and heated it up to room temperature (where it acts like a normal metal, not a superconductor).
2. The Training: They applied a magnetic field (pointing either "Up" or "Down") while the material was warm.
3. The Cooling: They cooled the material down to near absolute zero while keeping that magnetic field on, and then carefully turned the field off before the material became a superconductor.
4. The Result:
   • If they trained it with an Up field, the electricity preferred to flow Right.
   • If they trained it with a Down field, the electricity preferred to flow Left.

The Analogy: Imagine a field of tall grass. If you walk through it in a specific direction (the magnetic field) while the grass is soft and flexible (the normal state), you flatten the grass in that direction. Even after you stop walking and the grass hardens (becomes a superconductor), the path remains flattened. The "memory" of your walk dictates which way the grass bends.

The Key Discovery: The Memory is in the "Normal" State

The researchers found that this "training" only worked if they applied the magnetic field above a certain temperature (the CDW transition temperature).

• If they applied the field below that temperature (in the CDW state), it still worked.
• If they applied the field above that temperature (in the normal metal state) and then removed it before the CDW state formed, the training didn't work.

What this means: The "one-way street" rule isn't created when the material becomes a superconductor. Instead, the rule is written into the material's DNA before it becomes a superconductor, during the "Charge Density Wave" phase. The superconducting state simply inherits this memory.

The "Flip" Test: Proving It's Not a Glitch

To make sure they weren't just seeing a leftover magnetic field from their equipment, they did a "flip test."

• They measured the one-way effect.
• Then, they physically flipped the device upside down.
• If the effect was caused by a stray magnet in the room, flipping the device would reverse the effect.
• Result: The effect stayed exactly the same. This proved the "one-way" behavior is an intrinsic property of the material itself, not a trick of the equipment.

The "Thermal Cycling" Surprise

When they warmed the material up to room temperature and cooled it back down without any magnetic field, the direction of the one-way street would change randomly. Sometimes it went Right, sometimes Left.

• Analogy: Imagine a room full of people (domains) who can choose to face North or South. Without a leader (magnetic field), they randomly pick a side. If you reset the room (thermal cycle), they pick a new random side.
• However, if you give them a leader (the magnetic field training), they all line up in the direction you tell them, and they stay that way.

Summary

This paper shows that in the kagome superconductor CsV₃Sb₅:

1. Electricity flows easier in one direction than the other (a superconducting diode).
2. This happens without any external magnets.
3. The "memory" of which direction to flow is established in the material's normal state (before it becomes a superconductor) and is carried over into the superconducting state.
4. Scientists can "train" this memory using a magnetic field, effectively programming the material to act as a one-way valve for electricity.

Technical Summary

Technical Summary: Nonreciprocal Superconducting Critical Currents with Normal State Field Trainability in Kagome Superconductor CsV3Sb5

Problem Statement
Determining the nature of time-reversal symmetry (TRS) and chirality in the superconducting state of kagome superconductors, specifically CsV3Sb5, and establishing their relationship to the normal-state symmetry and topology remains a central challenge in condensed matter physics. While various quantum phenomena, including charge density waves (CDW), nematic order, and indications of TRS breaking, have been observed in CsV3Sb5, contradictory results have left the question of whether TRS is genuinely broken in both the high-temperature CDW order and the superconducting state unresolved. Furthermore, a direct experimental link connecting the CDW order to the superconducting state has been lacking.

Methodology
The authors fabricated seven thin-flake devices (f1–f7) and two micro-bridge devices (s1, s2) from bulk CsV3Sb5 single crystals grown via the self-flux method. To ensure rigorous zero-field conditions, the team employed multiple protocols: oscillating magnetic fields to zero at room temperature, warming superconducting magnets to release trapped flux, using high-precision Hall sensors for calibration, and performing in-situ device flipping to rule out residual field effects.

Transport measurements were conducted using standard four-terminal methods. The study focused on:

1. Zero-field Critical Currents: Measuring voltage-current (V-I) characteristics to detect nonreciprocal critical currents ($I_c^+$ vs. $|I_c^-|$).
2. Thermal Cycling: Repeatedly warming samples to 300 K (above the CDW transition, $T_{CDW}$) and cooling them back to the superconducting state to observe the stability and stochastic reversal of the superconducting diode effect (SDE) polarity.
3. Field Training: Applying magnetic fields ($\pm 100$ Oe or $\pm 10$ T) at room temperature, cooling the sample to specific temperatures (5 K, 50 K, or 150 K) while under the field, removing the field, and then cooling to the superconducting state to test if the SDE polarity could be "trained" by the normal-state field.
4. Control Experiments: Comparing training protocols where the field was removed below $T_{CDW}$ versus above $T_{CDW}$ (150 K) to determine the origin of the symmetry breaking.

Key Results

• Zero-Field Superconducting Diode Effect (SDE): The authors observed unambiguous nonreciprocal critical currents in zero magnetic field across all devices. The critical current for positive flow ($I_c^+$) differed from that of negative flow ($|I_c^-|$), with diode efficiencies reaching up to 22% in flakes and 40% in specific thermal cycles. This indicates spontaneous breaking of both TRS and inversion symmetry.
• Thermal History Dependence: In zero-field thermal cycles, the polarity of the SDE reversed randomly upon cooling from 300 K. This stochastic behavior suggests the existence of domains with opposite chirality that form stochastically below a TRS-breaking onset temperature.
• Field Trainability: When a magnetic field was applied in the normal state and removed at temperatures below $T_{CDW}$ (e.g., 5 K or 50 K), the polarity of the SDE in the superconducting state consistently followed the direction of the applied training field. This "training" effect was robust and reproducible across multiple cycles and devices.
• Origin of Trainability: Crucially, when the training field was removed at 150 K (well above $T_{CDW}$), the SDE polarity became stochastic and independent of the field direction. This demonstrates that the TRS-breaking order parameter is established in the CDW state and serves as a template for the superconducting state.
• Micro-bridge Stability: In micro-bridge devices with smaller widths, the SDE polarity remained stable against thermal cycling and did not exhibit the random reversal seen in larger flakes, suggesting geometric confinement stabilizes the TRS-breaking domains.

Significance and Claims
The paper claims to provide macroscopic evidence for TRS breaking in CsV3Sb5, settling debated issues regarding the nature of the superconducting state. The primary significance lies in demonstrating that the TRS breaking is not merely a feature of the superconducting phase but originates in the normal-state CDW order.

By showing that the polarity of the superconducting diode effect can be trained by a magnetic field applied in the normal state (specifically within the CDW phase), the authors establish an intertwined relationship between the CDW state and the superconducting state. This supports the theoretical model of a "loop-current" CDW state that breaks TRS, which subsequently induces a chiral topological superconducting state. The results provide evidence that the CDW state in CsV3Sb5 is a macroscopic, trainable TRS-breaking state that persists into the superconducting phase, offering a new platform for studying spontaneous TRS breaking and novel superconductivity in kagome metals.