Anomalous Low-temperature Magnetotransport in Kagome Metal CsCr$_3$Sb$_5$ under Pressure

This study investigates the anomalous low-temperature magnetotransport in the kagome metal CsCr$_3$Sb$_5$ under hydrostatic pressure, revealing complex signatures below 30 K that suggest the existence of an exotic electronic order potentially analogous to the charge-density-wave state in its sister compound CsV$_3$Sb$_5$.

The Gist

Imagine a city built on a very specific, repeating pattern of streets: triangles sharing corners. In the world of physics, this is called a Kagome lattice. It's a magical grid where electrons (the tiny particles that carry electricity) behave in strange, unpredictable ways.

For years, scientists have been studying a family of these "cities" made with Vanadium (called $AV_3Sb_5$). They found that when cooled down, these materials develop a "traffic jam" called a Charge Density Wave (CDW), where electrons line up in a pattern, and this often leads to superconductivity (electricity flowing with zero resistance).

Recently, scientists discovered a new, slightly different version of this city: $CsCr_3Sb_5$, but instead of Vanadium, it uses Chromium. This new city is special because its electrons are "heavier" and more "social" (strongly correlated), meaning they interact with each other much more intensely than in the Vanadium cities.

The Mystery: The "Hump" in the Road

In this new Chromium city, researchers noticed something weird happening in the traffic flow (electrical resistance) when the temperature dropped to about 30 Kelvin (which is incredibly cold, about -243°C).

Instead of the traffic flow smoothly slowing down or speeding up, it hit a bump or a hump. It was like driving down a smooth highway and suddenly hitting a speed bump that no one could explain. They called this mysterious event $T_3$.

For a long time, scientists weren't sure what this bump meant. Was it a new type of traffic jam? A hidden roadblock? Or just a glitch in the measurement?

The Experiment: Squeezing the City

To solve the mystery, the team from the Chinese University of Hong Kong and Beijing Institute of Technology decided to squeeze the city.

They put the material under high pressure (like squeezing a sponge) while keeping it cold and measuring how electricity flowed through it. They also turned on strong magnets to see how the electrons reacted to magnetic fields.

Think of it like this: If you squeeze a crowded room, people might start moving differently. Some might get stuck, while others might find a super-fast shortcut.

What They Found: The "Super-Hall" Effect

When they squeezed the material and looked closely at the traffic patterns, they found three amazing things happening right at that mysterious 30 K bump:

1. The Hall Switch: Usually, when you push electrons with a magnet, they drift to one side (like cars drifting in a turn). This is called the Hall effect. In this material, as they cooled down past the 30 K bump, the direction of this drift suddenly flipped. It was as if all the cars suddenly decided to drive on the opposite side of the road. This suggests that the "traffic" changed from being dominated by negative electrons to being dominated by positive "holes" (empty spots acting like positive particles).
2. The Non-Linear Twist: At normal pressures, the traffic drift was a bit predictable. But under high pressure, the drift became wildly unpredictable and curved sharply, especially near zero magnetic field. It looked like a rollercoaster loop.
3. The "Sister" Connection: This wild, curved behavior looked exactly like what happens in the older Vanadium cities when they form their famous Charge Density Waves.

The Big Picture: A New Kind of Order

The researchers realized that this mysterious "hump" at 30 K isn't just a glitch. It's the moment when the Chromium city wakes up and forms a new, exotic type of order.

• The Analogy: Imagine a crowd of people dancing. At first, they are just milling about. Then, at a specific temperature, they suddenly start dancing in a complex, synchronized pattern that no one saw before. This new pattern changes how they move through the room.
• The Pressure Effect: When they squeezed the material (increased pressure), this new dance pattern became even more energetic. The "high-speed" dancers (high-mobility carriers) appeared in huge numbers, making the electricity flow much more efficiently and creating that strange, curved magnetic signature.

Why Does This Matter?

This discovery is like finding a new continent on a map we thought we knew. It suggests that $CsCr_3Sb_5$ has a hidden layer of complexity that we haven't fully understood yet.

The "hump" at 30 K is likely the birth of a new electronic state—a unique way for electrons to organize themselves that is different from the known patterns. It might involve:

• Tiny pockets of electrons moving at super speeds.
• Magnetic loops forming inside the material.
• Or even time-reversal symmetry breaking (a fancy way of saying the material creates its own internal magnetic field without a magnet).

Conclusion

In simple terms: Scientists found a weird bump in the road of a new super-material. By squeezing it, they realized that bump is actually a gateway to a new, exotic world where electrons dance in a strange, synchronized way. This new world looks very similar to the famous "traffic jams" found in older materials, but with its own unique, high-speed twists.

This discovery opens the door to understanding how complex materials work, which could one day help us build better superconductors, faster computers, or new types of quantum sensors. The mystery of the "hump" is now a clue to a deeper, stranger reality.

Technical Summary

1. Problem Statement

The kagome metal CsCr$_3$Sb$_5$ is a newly discovered superconductor with strong electronic correlations, distinct from its sister compound CsV$_3$Sb$_5$ (where the Fermi energy lies near van Hove singularities). In CsCr$_3$Sb$_5$, the Fermi energy is located near a flat band, leading to unique properties like frustrated magnetism and non-Fermi liquid behavior.

While the material exhibits known phase transitions at $T_1$ ($\approx$58 K) and $T_2$ ($\approx$46 K), a third anomaly, $T_3 \approx$ 30 K, has been observed as a "hump" in electrical resistivity. However, the nature of this $T_3$ anomaly remains poorly understood due to a lack of supporting evidence from other experimental probes. The central problem is to determine whether $T_3$ signifies a new electronic order (such as a charge density wave or magnetic ordering) and to characterize the underlying charge transport mechanisms associated with it.

2. Methodology

The authors conducted systematic magnetotransport experiments under hydrostatic pressure to probe the nature of the $T_3$ anomaly.

• Samples: High-quality single crystals of CsCr$_3$Sb$_5$ were synthesized using a flux method. Two thin flakes (Sample K1 and K2) were mechanically cleaved.
• Pressure Conditions: Measurements were performed at 5 kbar (near-ambient) and 19 kbar using a device-integrated diamond anvil cell (DIDAC) with glycerin as the pressure-transmitting medium.
• Techniques:
  • Resistivity & Magnetoresistance (MR): Measured up to 14 T magnetic field ($B \parallel c$) down to 2 K.
  • Hall Effect: Measured to extract the Hall coefficient ($R_H$) and Hall resistivity ($\rho_{yx}$).
  • Data Analysis:
    • Extraction of effective carrier density using a one-band model at high temperatures.
    • Isolation of the non-linear Hall component ($\rho_{yx}^{NL}$) by subtracting the linear high-field term.
    • Mobility Spectrum Analysis (MSA): A model-independent technique used to deconvolve the contributions of carriers with different mobilities to the longitudinal ($\sigma_{xx}$) and transverse ($\sigma_{xy}$) conductivities.

3. Key Contributions

• Systematic Pressure Study: This is the first comprehensive study linking the $T_3$ resistivity anomaly to magnetotransport signatures under varying hydrostatic pressure.
• Discovery of Hall Anomaly: The authors identified a distinct, non-trivial temperature dependence in the Hall coefficient ($R_H$) that emerges precisely at $T_3$, which was not reported in initial studies.
• Identification of Multi-band/High-Mobility Carriers: Through MSA, the study provides evidence for the activation of high-mobility carriers below $T_3$, suggesting a multi-band transport regime.
• Analogy to CsV$_3$Sb$_5$: The paper establishes a strong phenomenological link between the $T_3$ state in CsCr$_3$Sb$_5$ and the Charge Density Wave (CDW) state in CsV$_3$Sb$_5$, characterized by an Anomalous Hall Effect-like (AHLE) response.

4. Key Results

A. Resistivity and Magnetoresistance (MR)

• At 5 kbar: A hump appears in $\rho(T)$ at $T_3 \approx$ 30 K. The MR is positive and sublinear, reaching 16% at 2 K.
• At 19 kbar: The $T_1$ transition shifts down to $\approx$50 K, and $T_2$ appears at $\approx$46 K. Crucially, $T_3$ remains stable at $\approx$30 K.
• Enhanced Transport: Below $T_3$ at 19 kbar, the resistivity drops dramatically ($\rho_0 = 0.06$ m$\Omega\cdot$cm), and the MR at 2 K skyrockets to 230% (14 times larger than at 5 kbar). This indicates a pressure-enhanced, exotic transport state.

B. Hall Effect and Carrier Dynamics

• Hall Coefficient ($R_H$) Upturn: At 5 kbar, $R_H$ (initially negative) shows a sharp positive upturn starting at $T_3 \approx$ 30 K, crossing zero at $\approx$15 K. This indicates a transition from electron-dominated to hole-dominated transport.
• Pressure Correlation: This upturn persists at 19 kbar at the same temperature ($T_3$) but becomes significantly more pronounced.
• Non-linear Hall Response: Below $T_3$, $\rho_{yx}(B)$ becomes non-linear at low fields ($|B| \le$ 5 T). This non-linearity is sharper and more abrupt at 19 kbar, resembling the Anomalous Hall Effect (AHE) seen in the CDW state of CsV$_3$Sb$_5$.

C. Mobility Spectrum Analysis (MSA)

• Multi-band Nature: MSA confirms the existence of multiple carrier types at both pressures.
• High-Mobility Carriers: At 19 kbar, the mobility spectrum broadens significantly, with a dominant contribution from high-mobility carriers ($> 5,000$ cm$^2$/Vs).
• Temperature Dependence: These high-mobility carriers fade out as temperature increases, correlating directly with the weakening of the non-linear Hall response. This suggests the AHLE-like feature is driven by these specific high-mobility carriers, likely associated with small Fermi pockets.

5. Significance and Conclusion

• Evidence for New Electronic Order: The coincidence of the resistivity hump ($T_3$), the sharp upturn in $R_H$, and the emergence of a strong non-linear Hall response strongly suggests the onset of an additional, exotic electronic order in CsCr$_3$Sb$_5$ below 30 K.
• Mechanism Implications: While the exact microscopic origin is not definitively proven, the results point toward possibilities such as:
  • A Charge Density Wave (CDW) or loop current order (similar to CsV$_3$Sb$_5$).
  • Altermagnetic order breaking time-reversal symmetry.
  • Topological effects involving Berry curvature or small Fermi pockets.
• Role of Pressure: Hydrostatic pressure suppresses competing orders ($T_1, T_2$) but enhances the transport signatures associated with $T_3$, making the anomalous features more distinct. This highlights the complex interplay and competition between multiple quantum orders in this kagome system.

Conclusion: The study successfully characterizes the $T_3$ anomaly as a critical point where unconventional, multi-band transport dominated by high-mobility carriers emerges. This provides a vital platform for exploring the interplay between strong correlations, topology, and superconductivity in kagome metals.