Quasiparticles-mediated thermal diode effect in Weyl Josephson junctions

This paper theoretically demonstrates a tunable quasiparticle-mediated thermal diode effect in inversion symmetry-broken Weyl Josephson junctions, where an external Zeeman field induces asymmetric thermal currents that can be controlled by the superconducting phase difference and junction length to enable functional thermal switching.

The Gist

Imagine you have a one-way street for cars. In the world of electricity, we call this a diode. It lets current flow easily in one direction but blocks it in the other. This is the backbone of all modern electronics, from your phone to your computer.

But what if you could build a similar one-way street for heat? That's the goal of this paper. The authors, Pritam Chatterjee and Paramita Dutta, propose a theoretical device called a Thermal Diode. Instead of blocking electricity, it blocks heat in one direction while letting it flow freely in the other.

Here is the simple breakdown of how they plan to do it, using some creative analogies.

1. The Setting: A "Magic" Bridge

Imagine a bridge connecting two islands.

• The Islands: These are made of a special superconducting material (a material that conducts electricity with zero resistance). Let's call them the "Super Islands."
• The Bridge: The middle part of the bridge is made of a "Weyl Semimetal." Think of this as a magical, high-tech highway where particles (quasiparticles) behave like massless ghosts. They move incredibly fast and have a property called "chirality" (like being left-handed or right-handed).

2. The Problem: Heat Usually Flows Both Ways

Normally, if you put a hot cup of coffee on one side of a bridge and a cold one on the other, heat will flow from hot to cold. If you swap them, heat flows the other way. It's symmetrical. You can't make a "one-way heat valve" easily because heat usually just follows the temperature difference.

3. The Solution: The "Magnetic Wind" and the "Phase Switch"

The authors propose two secret ingredients to break this symmetry and create a one-way street for heat:

A. The Magnetic Wind (Zeeman Field)
Imagine blowing a strong wind across the bridge. In their experiment, this "wind" is a magnetic field applied perpendicular to the bridge.

• The Effect: This wind pushes the "left-handed" particles one way and the "right-handed" particles the other way. It shifts the lanes of traffic.
• The Result: Now, the path for heat to go from Left-to-Right is different than the path for Right-to-Left. It's like having a highway where the lanes are shifted depending on which way you are driving.

B. The Phase Switch (Superconducting Phase)
This is the most unique part. The two "Super Islands" have a secret handshake called a "phase difference."

• The Analogy: Imagine the two islands are dancers. They can be in sync (holding hands perfectly) or out of sync (stepping on each other's toes). By changing how they are synchronized (using an external knob), the authors can change the "shape" of the bridge.
• The Magic: By turning this knob, they can actually flip the direction of the one-way street.
  • Scenario A: Heat flows easily Left-to-Right, but is blocked Right-to-Left.
  • Scenario B (after turning the knob): Heat flows easily Right-to-Left, but is blocked Left-to-Right.

4. The Length Matters

The size of the bridge matters too.

• Short Bridge: If the bridge is short, the "wind" and the "dancers" work together perfectly to create a strong one-way effect. The heat flow is very efficient.
• Long Bridge: If the bridge is too long, the effect gets messy and weak, like trying to blow a strong wind through a mile-long tunnel; the wind just dissipates.

5. Why This is a Big Deal

The authors show that this device can be 90% efficient. That means it acts almost like a perfect one-way valve.

• Tunability: Unlike old diodes that are fixed in stone, this one is like a smart home thermostat. You can use a magnetic field or a phase switch to turn the "heat valve" on, off, or even reverse its direction.
• Applications: This could lead to new types of "thermal circuits." Imagine computer chips that can actively cool themselves by directing heat away from hot spots, or devices that harvest waste heat and turn it into useful energy more efficiently.

Summary

Think of this paper as a blueprint for a smart heat valve.

1. They built a bridge using exotic quantum materials.
2. They used a magnetic field to shift the traffic lanes.
3. They used a "phase switch" to control the traffic flow.
4. The result is a device that lets heat flow in one direction but not the other, and you can flip the direction at will.

It's a theoretical concept right now (a recipe for a cake that hasn't been baked yet), but it opens the door to a future where we can control heat with the same precision we currently control electricity.

Technical Summary

1. Problem Statement

The paper addresses the challenge of creating efficient, tunable thermal diodes (devices that allow heat flow in one direction but block it in the reverse) using superconducting systems. While the Superconducting Diode Effect (SDE) and Josephson Diode Effect (JDE) for charge currents are well-studied, the Thermal Diode Effect (TDE) in superconducting junctions remains under-explored.

• Specific Gap: Existing thermal diodes often rely on 1D lattices or normal metal interfaces. There is a lack of theoretical proposals for TDE in 3D Weyl Josephson Junctions (WJJ) where the rectification can be externally controlled by both magnetic fields and superconducting phases.
• Goal: To theoretically demonstrate a quasiparticle-driven TDE in an inversion-symmetry-broken (ISB) Weyl semimetal (WSM) sandwiched between two Weyl superconductors (WSC), and to show that the rectification is highly tunable.

2. Methodology

The authors employ a theoretical framework combining Bogoliubov–de Gennes (BdG) Hamiltonians with scattering matrix formalism.

• System Model:

  • A junction consisting of two Weyl Superconductors (WSC) separated by an Inversion Symmetry-Broken (ISB) Weyl Semimetal (WSM) of length $L$.
  • Hamiltonian: The ISB WSM is described by a specific 4-band Hamiltonian (Eq. 1) featuring four Weyl nodes with opposite chiralities.
  • Symmetry Breaking: Time-reversal symmetry is broken by applying an external Zeeman field ($h_x$) perpendicular to the junction interface. This field shifts the Weyl nodes of opposite chiralities in opposite directions along the $k_z$ axis.
  • Thermal Bias: A temperature gradient is applied across the junction ($T_L \neq T_R$), creating a thermal current carried by quasiparticles with energy $\epsilon > \Delta_0$ (above the superconducting gap).

• Calculation Approach:

  • Transmission Probabilities: The authors calculate the forward ($T_F$) and reverse ($T_R$) transmission probabilities for quasiparticles using the scattering matrix method. They match wavefunctions at the WSC-WSM interfaces.
  • Thermal Conductance: The thermal current is derived by integrating the transmission probabilities over energy and incident angles, weighted by the derivative of the Fermi-Dirac distribution.
  • Rectification Coefficient ($R$): Defined as $R = \frac{|\kappa_F| - |\kappa_R|}{|\kappa_F|}$, where $\kappa$ is the thermal conductance.

3. Key Contributions

1. Mechanism Identification: The paper identifies that the Zeeman-field-induced shift of Weyl nodes creates an asymmetry in quasiparticle transmission probabilities ($T_F \neq T_R$) between forward and reverse directions, driving the TDE.
2. Analytical Expressions: The authors derive analytical formulas for transmission probabilities in both the short junction limit ($L \ll \xi$) and long junction limit ($L \gg \xi$), explicitly showing the dependence on the Zeeman field and superconducting phase difference ($\phi$).
3. Dual Tunability: A major contribution is demonstrating that the TDE is not only driven by the magnetic field but is also highly sensitive to the superconducting phase difference ($\phi$), allowing for external control of both the magnitude and the sign of the rectification.

4. Key Results

• Asymmetry and Diode Effect:
  • In the absence of a Zeeman field, forward and reverse thermal conductances are equal ($\kappa_F = \kappa_R$).
  • With a Zeeman field, a significant asymmetry arises ($\kappa_F \neq \kappa_R$), confirming the TDE.
• Junction Length Dependence:
  • Short Junction ($L < \xi$): The diode effect is most efficient. The rectification coefficient can reach up to 90%, approaching ideal diode behavior.
  • Long Junction ($L > \xi$): The rectification is suppressed due to the dominance of the chemical potential term over the magnetic field term in the transmission probability.
• Phase and Field Tunability:
  • The sign of the rectification coefficient ($R$) can be flipped from positive to negative (and vice versa) by tuning the superconducting phase difference $\phi$.
  • The magnitude of $R$ is maximized when $|h_x L| \approx \pi/4$.
  • Notably, a finite phase difference is not strictly required for TDE (it exists at $\phi=0$), but a finite Zeeman field is essential.
• Sign Changing Behavior: The ability to switch the direction of preferred heat flow (sign of $R$) by simply adjusting the phase or magnetic field makes the device a functional thermal switch.

5. Significance and Implications

• Functional Thermal Switching: The ability to tune the rectification sign and magnitude externally (via magnetic field and phase) positions this WJJ as a promising component for caloritronics and thermal circuits, acting as a thermal transistor or switch.
• Topological Origin: The study highlights the unique role of topological materials (Weyl semimetals) in thermal transport. The breaking of inversion and time-reversal symmetries in Weyl materials provides a robust mechanism for non-reciprocal heat transport that is distinct from traditional resistive diodes.
• Ideal Diode Potential: Achieving a 90% rectification coefficient in the short junction limit suggests that these devices could approach the performance of ideal thermal diodes, which is a significant milestone for thermal management in quantum devices.
• Future Applications: The work opens avenues for designing thermal devices based on superconducting junctions, potentially leading to advanced thermal isolation, cooling systems, and energy harvesting technologies in the quantum regime.

In summary, the paper provides a robust theoretical proposal for a highly tunable thermal diode in a 3D Weyl Josephson junction, leveraging the unique properties of Weyl nodes and quasiparticle transport to achieve efficient, externally controllable heat rectification.