Universality of linear in temperature and linear in field Planckian scattering rate in high temperature cuprate superconductors

This paper proposes a unified quantum-critical origin for the simultaneous linear-in-temperature and linear-in-field Planckian scattering rates observed in cuprate superconductors, supported by experimental observations in LSCO and a theoretical model based on spin-driven charge fluctuations.

The Gist

The Mystery of the "Perfectly Frictionless" Metal: A Simple Guide

Imagine you are driving a car on a highway. Usually, if you press the gas pedal harder, you go faster, but you also face more wind resistance and friction. If the weather gets hotter, your engine might struggle more. In a normal metal (like the copper in your house wires), electricity flows like a car on a well-paved road: there is predictable friction (resistance) caused by electrons bumping into things.

But in certain "super-materials" called high-$T_c$ cuprates (special ceramics that can conduct electricity with almost zero resistance at high temperatures), something very strange happens. The "car" (the electricity) behaves as if it is driving through a chaotic, invisible storm that follows a very strict, universal rule.

This paper, written by a team of international physicists, finally cracks the code on why this "storm" behaves the way it does.

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1. The "Planckian" Speed Limit

In these strange materials, the electricity doesn't just bump into impurities or heat; it hits a fundamental "speed limit" of nature. Scientists call this Planckian dissipation.

The Analogy: Imagine a crowded dance floor. In a normal metal, people (electrons) bump into furniture or occasional obstacles. But in a "Strange Metal," the dance floor is so packed and the music is so intense that every single person is constantly colliding with everyone else. The rate of these collisions isn't determined by how much furniture is on the floor, but solely by the intensity of the music (Temperature).

The paper shows that this "collision rate" is universal. No matter what the material is made of, if you turn up the "music" (Temperature), the friction increases in a perfectly straight line.

2. The Magnetic Twist (The $B/T$ Scaling)

The researchers discovered something even more mind-blowing. Not only does the friction change with Temperature ($T$), but it also changes perfectly with a Magnetic Field ($B$).

The Analogy: Imagine that instead of just turning up the music, you also start spinning the entire dance floor. This spinning is the magnetic field. The researchers found that the "chaos" of the dancers depends on a specific ratio: how fast the floor is spinning compared to how loud the music is ($B/T$).

If you double the music volume, you must double the spinning speed to keep the "chaos" exactly the same. This is what they call $B/T$ scaling. It’s like finding out that a hurricane’s intensity is determined by a perfect mathematical balance between wind speed and air pressure.

3. The "Kondo" Secret: What’s causing the chaos?

For years, scientists argued about why this happens. Is it the shape of the electrons? Is it random dirt in the material?

The authors propose a new theory: The Spin-Based Mechanism. They suggest that the electrons are actually "split" into different parts (a concept called fractionalization). One part carries the charge, and another part carries the "spin" (the tiny magnetic personality of the electron).

The Analogy: Think of the electrons not as solid billiard balls, but as spinning tops attached to rubber bands. As they move through the material, the "spinning" part of the electron gets caught in a tug-of-war with the magnetic field. This tug-of-war creates the perfect, universal friction they observed.

Why does this matter?

We are looking for the "Holy Grail" of energy: Room-Temperature Superconductivity. If we can make materials that conduct electricity with zero friction at normal temperatures, we could have:

• Trains that float on magnets (Maglev) with almost no energy cost.
• Batteries that never lose charge.
• Computers that never get hot.

By understanding the "rules of the storm" in these strange metals, this paper provides a roadmap for scientists to design new materials that could eventually change the world.

Technical Summary

This paper, titled "Universality of T–linear and B–linear Planckian scattering rate in high-$T_c$ cuprate superconductors," presents a theoretical and experimental unification of two hallmark transport properties of the "strange metal" phase in cuprates: linear-in-temperature ($T$-linear) and linear-in-magnetic-field ($B$-linear) resistivity.

1. The Problem: The Mystery of the Strange Metal

In conventional metals, electrical resistivity is governed by quasiparticle scattering and is limited by the Mott-Ioffe-Regel (MIR) limit. However, high-$T_c$ cuprates exhibit "Planckian dissipation," where the scattering rate ($1/\tau$) is determined solely by fundamental constants and temperature: $1/\tau \approx \alpha_T k_B T / \hbar$.

While $T$-linear resistivity is well-documented, recent experiments have observed a simultaneous $B$-linear resistivity at high magnetic fields. This manifests as a universal field-to-temperature ($B/T$) scaling in magnetoresistance. Previously, there was no coherent microscopic theory to explain why these two behaviors coexist or how they are linked to the underlying quantum criticality.

2. Methodology

The authors employ a dual approach combining high-field experimental analysis with advanced many-body theoretical modeling:

• Experimental Analysis: The authors analyze existing magneto-transport data for underdoped $\text{La}_{2-x}\text{Sr}_x\text{CuO}_4$ (LSCO) near optimal doping ($p \approx 0.19$). They use a decomposition method to separate the resistivity into a $T$-linear component and a universal $B/T$-scaling function.
• Theoretical Framework: They propose a microscopic mechanism based on a heavy-fermion formulated slave-boson $t$-$J$ model.
  • The model treats the electron as fractionalized into a fermionic spinon and a bosonic holon.
  • They utilize a Renormalization Group (RG) approach to identify a local quantum critical point (QCP) arising from the competition between the pseudogap phase (Heisenberg $J$ term) and the Fermi liquid phase (hopping $t$ term).
  • Crucially, they incorporate a Zeeman term to account for the magnetic field, treating the Zeeman energy ($\mu_B B$) as an external energy scale analogous to frequency ($\hbar\omega$) or temperature ($k_B T$).

3. Key Contributions

• Unified Scaling Law: The authors derive an analytical expression for the total field-dependent magneto-scattering rate that naturally produces both $T$-linear and $B$-linear limits.
• Zeeman-Driven Planckian Dissipation: They demonstrate that the $B$-linear behavior is not due to orbital cyclotron motion (which violates Kohler’s rule) but is driven by the Zeeman splitting of the fermionic bands near a local QCP.
• Coefficient Correlation: They establish a rigorous mathematical relationship between the $T$-linear Planckian coefficient ($\alpha_T$) and the $B$-linear coefficient ($\alpha_B$), predicting $\alpha_T \approx 2\alpha_B$.

4. Results

• Excellent Data Fit: The theoretical model provides an unprecedented match to the experimental magnetoresistance data for LSCO, successfully fitting the $B/T$-scaling function and the slope of the magnetoresistance ($\partial\rho/\partial B$).
• Verification of Coefficients:
  • The theory predicts $\alpha_T = 8/\pi \approx 2.54$ and $\alpha_B = 4/\pi \approx 1.27$.
  • Experimental extractions from LSCO data (using plasma frequency and specific heat estimates) show remarkable agreement with these values, confirming the universality of the Planckian coefficients across different doping levels.
• Failure of MFL Models: The authors show that the standard Marginal Fermi Liquid (MFL) model fails to account for the coexistence of $T$-linear and $B$-linear regimes, whereas their quantum-critical model succeeds.

5. Significance

This work is highly significant for condensed matter physics as it provides a unified quantum-critical origin for Planckian transport in cuprates. By showing that the magnetic field acts as a tunable energy scale in the same way temperature does, the paper reinforces the idea that the strange metal is a distinct phase of matter governed by a hidden quantum critical point. This provides a roadmap for understanding other strongly correlated materials where universal dissipation is observed.