Quantum interference in a twisted high-Tc SQUID senses emergent interfacial order

By fabricating SQUIDs from twisted $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ interfaces, researchers detected a $\pi$ phase shift and time-reversal symmetry breaking indicative of chiral superconducting order, while also demonstrating high-temperature flux sensing capabilities that open new avenues for studying unconventional superconductivity.

The Gist

Imagine you have two sheets of a very special, super-thin material called a "superconductor." When these sheets are cooled down, electricity flows through them with zero resistance, like a car driving on a perfectly frictionless highway.

Now, imagine taking one of these sheets, tearing it in half, and then stacking the two halves back on top of each other. But here's the twist: you rotate one half slightly before stacking it. This rotation is called a "twist."

This paper is about what happens when you twist these superconductor sheets at a very specific angle (around 45 degrees) and then build a tiny, ultra-sensitive magnetic sensor called a SQUID (Superconducting Quantum Interference Device) out of them.

Here is the story of their discovery, broken down into simple concepts:

1. The "Twisted" Dance Floor

Think of the superconductor sheets as dance floors where pairs of electrons (called Cooper pairs) dance in perfect sync. In normal superconductors, everyone dances in the same direction.

But in this high-tech material (called BSCCO), the "dance steps" are complex. When the researchers twisted the two layers by 45 degrees, they created a weird, new kind of dance floor at the interface where the two sheets meet.

• The Problem: At this specific angle, the usual dance steps get cancelled out. The electrons can't easily jump from one layer to the other. It's like trying to dance with someone who is facing the exact opposite direction; you can't hold hands easily.
• The Surprise: Even though the main dance stopped, a new, stranger dance emerged. The electrons found a way to "co-tunnel" (jumping in pairs of pairs) and started dancing in a chiral way. "Chiral" means they have a handedness—they dance either clockwise or counter-clockwise.

2. The SQUID: The Quantum Interference Sensor

To see this new dance, the scientists built a SQUID.

• The Analogy: Imagine a race track with two lanes (two paths for the electricity). If you send runners (electrons) down both lanes, they will eventually meet at the finish line.
• The Interference: If the runners are perfectly in sync, they arrive together and create a big wave (high current). If one runner is slightly out of step, they cancel each other out (low current).
• The Magic: By changing the magnetic field around the track, the scientists can make the runners speed up or slow down, creating a pattern of "beats" (interference). This pattern tells them exactly how the electrons are behaving.

3. The "Ghost" Phase Shift

This is the most exciting part of the paper.

• The Expectation: Since both lanes of the race track were cut from the same twisted piece of material, the scientists expected the runners in both lanes to be in the exact same state. They expected the "phase" (the timing of the dance) to be identical.
• The Discovery: When they applied a magnetic field, they found something weird. The runners in one lane were dancing clockwise, while the runners in the other lane were dancing counter-clockwise.
• The Result: This created a $\pi$ (pi) phase shift. In the language of waves, it's like one runner is at the top of a wave while the other is at the bottom. They are perfectly out of sync.

Why does this matter?
This proves that the twisted interface created a new type of superconductivity that breaks "time-reversal symmetry."

• Simple Analogy: Imagine watching a movie of the dancers. If you played the movie backward, the dancers would look different. In normal physics, playing a movie backward usually looks the same. But here, the "handedness" of the dance makes the past and future look different. This is a hallmark of chiral superconductivity, a state of matter that scientists have been hunting for decades.

4. Why This is a Big Deal

• A New Tool: They built the first-ever SQUID using this "twisted" high-temperature superconductor. It works even at 60 Kelvin (about -350°F), which is much warmer than the near-absolute-zero temperatures usually required for these sensors.
• Sensitivity: This new sensor is incredibly sensitive. It can detect tiny magnetic fields, making it a "state-of-the-art" tool for measuring magnetic noise.
• The Future: This opens the door to understanding why high-temperature superconductors work. If we can understand these twisted interfaces, we might one day build superconductors that work at room temperature, which would revolutionize power grids, MRI machines, and quantum computers.

Summary

The researchers took a high-tech superconductor, twisted it like a pretzel, and built a tiny magnetic sensor. They discovered that this twist forces the electrons to split into two groups: one dancing clockwise and one counter-clockwise. This "split personality" creates a new, exotic state of matter that breaks the rules of time symmetry, offering a glimpse into the future of quantum technology.

Technical Summary

Here is a detailed technical summary of the paper "Quantum interference in a twisted high-Tc SQUID senses emergent interfacial order."

1. Problem Statement

High-temperature superconductors (HTSC), particularly cuprates like $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_{8+\delta}$ (Bi-2212), possess an anisotropic $d$-wave order parameter. When two such superconductors are twisted relative to each other, the interfacial order parameter can exhibit exotic behaviors, such as the emergence of chiral superconductivity ($d \pm id$) and time-reversal symmetry (TRS) breaking.

• The Challenge: In a 45° twisted interface, single Cooper-pair tunneling is theoretically suppressed due to the orthogonality of the $d$-wave lobes. While previous studies observed signatures of co-tunneling (tunneling of two Cooper pairs) and TRS breaking in single Josephson junctions (JJs), these devices could not directly measure the anomalous phase difference between the two arms of a superconducting loop.
• The Gap: A single JJ cannot distinguish between a global phase shift and an intrinsic phase difference arising from distinct chiral states in the junctions. A Superconducting Quantum Interference Device (SQUID) is required to probe the relative phase between two junctions, but fabricating a high-quality, c-axis SQUID with precise twist angles in fragile van der Waals (vdW) cuprates has been a significant fabrication hurdle.

2. Methodology

The authors developed a novel fabrication and measurement protocol to create asymmetric SQUIDs from twisted Bi-2212 flakes.

• Fabrication:

  • Cryogenic Exfoliation: Utilizing a PDMS-assisted dry cryogenic exfoliation technique, they cleaved a single Bi-2212 flake into two "daughter" flakes at cryogenic temperatures to preserve oxygen stoichiometry.
  • Twist Assembly: The daughter flakes were rotated to specific angles ($0^\circ, 40^\circ, 42^\circ, 44^\circ, 45^\circ$) and stacked to form an artificial Josephson junction (AJJ) at the interface.
  • SQUID Geometry: Using a sharp fiber scalpel (approx. 1 $\mu$m tip), the authors made an asymmetric cut across the twisted overlap region to create a SQUID loop with two distinct JJ arms (one small, one large).
  • Contacts: Gold contacts were deposited using a SiN stencil mask, with Cr/Au extensions, ensuring Cr did not contact the Bi-2212 to prevent degradation.

• Measurement Techniques:

  • Transport: Four-probe DC transport measurements ($I-V$ characteristics) and switching current ($I_s$) measurements in a closed-cycle cryostat with a cryoperm shield.
  • Magnetic Field Control: Both out-of-plane (perpendicular) and in-plane magnetic fields were applied using a vector electromagnet to modulate the interference and probe symmetry breaking.
  • Phase Extraction: Differential resistance ($dV/dI$) measurements were performed at various bias currents to extract the phase minima. By extrapolating the phase minima to zero current ($I \to 0$), the authors isolated the intrinsic anomalous phase difference ($\phi_{12}$) from geometric inductance effects.
  • Noise Characterization: Flux noise sensitivity was measured using a spectrum analyzer to evaluate the device's performance as a sensor.

3. Key Contributions

1. First c-axis Twisted SQUID: The successful fabrication of the first SQUID utilizing the twisted interface of high-$T_c$ cuprates, overcoming the difficulty of creating overlapping, precisely twisted layers.
2. Direct Observation of Chiral Order: The first direct measurement of an anomalous phase difference ($\phi_{12} \approx \pi$) between two JJs in a twisted loop, providing definitive evidence for the coexistence of opposite chiral superconducting orders ($d+id$ and $d-id$) in the two arms.
3. Decoupling Geometric and Intrinsic Effects: The development of a theoretical framework (modifying the phase sum rule) to extract the intrinsic phase difference even in the presence of significant geometric inductance ($\beta \sim 1$).
4. High-Temperature Sensor: Demonstration that these exotic devices function as state-of-the-art flux sensors at liquid nitrogen temperatures (77 K range).

4. Key Results

• Quantum Interference & Phase Anomaly:

  • The SQUID exhibited clear magnetic field modulation of the switching current.
  • Critical Finding: When the in-plane magnetic field was set to 0 $\mu$T, the extrapolated phase difference between the two arms was $\pi$ (modulo $2\pi$). This indicates that the two junctions spontaneously settled into opposite chiral ground states ($\alpha = \pi/2$and$\alpha = -\pi/2$).
  • When an in-plane field was applied (e.g., 10 $\mu$T), the phase difference shifted to 0, indicating the field forced both junctions into the same chiral state. This tunability confirms the existence of degenerate chiral minima in the free energy landscape.

• Time-Reversal Symmetry (TRS) Breaking:

  • The devices exhibited a superconducting diode effect (non-reciprocal transport) where the positive switching current ($I_s^+$) differed from the negative switching current ($|I_s^-|$) even at zero magnetic field.
  • The diode efficiency ($\eta$) was finite at $B=0$ (approx. 4-8%), confirming intrinsic TRS breaking, a hallmark of chiral superconductivity.

• Co-tunneling and Higher Harmonics:

  • The critical current density for 45° devices was significantly suppressed compared to untwisted junctions, consistent with the suppression of single Cooper-pair tunneling.
  • Analysis of the switching current oscillations and Fast Fourier Transforms (FFT) revealed a prominent second-harmonic component ($\sin(2\phi)$) in the Current-Phase Relation (CPR). This confirms that co-tunneling (tunneling of two Cooper pairs, or $4e$ transport) is the dominant charge transport mechanism in these twisted interfaces.

• Device Performance:

  • The SQUID operated effectively at 60 K and near 77 K.
  • It achieved a flux noise sensitivity of $\sim 1.5 \, \mu\Phi_0/\sqrt{\text{Hz}}$ at 60 K, comparable to state-of-the-art low-$T_c$ SQUIDs and superior to many previous high-$T_c$ implementations.

5. Significance

• Fundamental Physics: This work provides the "smoking gun" evidence for emergent chiral superconductivity in twisted cuprates. It resolves the ambiguity of previous single-JJ studies by directly measuring the relative phase between two junctions, confirming the theoretical prediction that twisted interfaces can host degenerate $d \pm id$ states.
• Mechanism of Transport: It validates the role of co-tunneling ($4e$) in high-angle twisted junctions, offering a new perspective on charge transport in nodal superconductors.
• Technological Impact: The demonstration of a high-$T_c$ SQUID with low noise at 77 K opens the door for practical quantum sensors and magnetometers that do not require expensive liquid helium cooling.
• Platform for Twistronics: The fabrication technique establishes a robust platform for exploring other emergent phenomena in twisted van der Waals heterostructures beyond cuprates, potentially leading to new topological quantum devices.

In summary, the paper successfully bridges the gap between theoretical predictions of chiral superconductivity in twisted cuprates and experimental verification, utilizing a novel SQUID architecture to reveal the microscopic nature of interfacial superconducting order.