🔬 mesoscale physics

Magnetotransport of tomographic electrons in a Corbino disk

This paper demonstrates that tomographic electron transport in a Corbino disk generates a superballistic boundary layer that parametrically enhances quadratic magnetoresistance through electrode curvature, revealing three distinct magnetic field regimes (tomographic, hydrodynamic, and Ohmic) and offering a potential explanation for anomalous electron viscosity scaling observed in experiments.

Original authors: Nitay Ben-Shachar, Johannes Hofmann

Published 2026-07-08

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CC BY 4.0

Original authors: Nitay Ben-Shachar, Johannes Hofmann

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a crowded dance floor where thousands of people (electrons) are moving around. Usually, when people bump into each other, they scatter randomly, slowing down the flow of the crowd. This is like "traffic" in a normal wire.

However, in very clean materials at low temperatures, something weird happens. Because of a rule called the "Pauli exclusion principle" (which is like a rule saying two people can't stand in the exact same spot), most collisions don't actually change the direction of the crowd. The people just glide past each other without stopping. This creates a super-fluid-like flow where the crowd moves together very smoothly. Scientists call this hydrodynamic transport.

But this paper discovers a hidden layer to this story. It turns out that while the middle of the crowd flows smoothly, the behavior right at the edges (where the current enters and leaves the device) is very different. The authors call this "tomographic transport."

Here is the breakdown of their discovery using simple analogies:

1. The "Ghostly" Boundary Layer

Think of the device as a round, donut-shaped track (called a Corbino disk). The current enters through a small hole in the center and exits at the outer edge.

In a normal fluid (like water), if you pour it into a pipe, it sticks to the walls a bit (friction). But in this electron "super-fluid," the authors found that near the entry and exit points, the electrons form an extended, invisible "ghost layer."

The Analogy: Imagine a highway merging onto a circular track. Usually, cars merge smoothly. But here, the electrons near the merge point act like they are sliding on ice. They don't just stop or slow down; they "slip" sideways much more than expected.
The Result: This "slip" allows the electrons to move faster and more efficiently than standard physics predicts. It's like the electrons are finding a secret shortcut right at the entrance.

2. The Magnetic Field as a "Traffic Cop"

The researchers tested what happens when they turn on a magnetic field. They found that the behavior of the electrons changes in three distinct stages, depending on how strong the magnetic field is:

Stage 1: The "Tomographic" Zone (Weak Magnetic Field)
- What happens: The magnetic field is too weak to stop the "ghostly" slip at the edges. The electrons slide freely, creating a super-fast flow.
- The Catch: This flow is very sensitive to the shape of the track. If the inner circle is smaller, the "slip" effect is stronger. It's like a smaller turn forcing the cars to slide more dramatically.
- Why it matters: This explains why some experiments show strange patterns that don't fit the old "smooth fluid" theories. The "slip" at the edges is messing up the measurements.
Stage 2: The "Hydrodynamic" Zone (Medium Magnetic Field)
- What happens: As the magnetic field gets stronger, it starts to force the electrons into tight circles (like a spinning top). This stops the "ghostly" slip.
- The Result: The electrons finally behave like a normal, smooth fluid. The strange edge effects disappear, and the flow becomes predictable again.
Stage 3: The "Ohmic" Zone (Strong Magnetic Field)
- What happens: The magnetic field is now so strong that it forces the electrons to crash into each other constantly, breaking the smooth flow entirely.
- The Result: The electrons act like normal traffic again, bumping into each other and creating resistance. This is the "conventional" behavior we see in everyday electronics.

3. Why This Matters (According to the Paper)

The authors argue that many recent experiments trying to measure how "thick" or "sticky" the electron fluid is (viscosity) have been getting confused results.

The Problem: Scientists were measuring the "stickiness" at weak magnetic fields, not realizing that the "ghostly slip" at the edges was making the fluid look much more efficient (or "slippery") than it actually is.
The Solution: The paper suggests that if you look at the data at medium magnetic fields, you can ignore the "ghostly slip" and get a true measurement of the electron fluid's properties.

Summary

The paper reveals that electrons in a clean, donut-shaped device don't just flow like water; they have a "slippery" secret zone right at the entry and exit points. This "slip" is controlled by the shape of the device and the strength of the magnetic field. By understanding this, scientists can finally stop getting confused by weird experimental data and accurately measure how electrons flow together.

Technical Summary: Magnetotransport of Tomographic Electrons in a Corbino Disk

Problem Statement
In high-mobility electron gases at low-to-moderate temperatures, electron transport is often limited by electron-electron scattering, leading to hydrodynamic flow. However, experimental measurements of electron viscosity ( $\eta$ ) in these regimes frequently exhibit anomalous scaling with electron density ( $n$ ) and temperature ( $T$ ) that deviates from standard Fermi-liquid theory predictions ( $\eta \sim n^2/T^2$ ). A primary challenge in resolving these discrepancies is distinguishing hydrodynamic transport from disorder scattering and boundary effects. While the Corbino disk geometry has emerged as a promising tool to isolate hydrodynamic contributions by eliminating ambiguous boundary scattering (as all boundaries are current-injecting electrodes), recent measurements in this geometry still reveal anomalous viscosity scaling.

Theoretical work suggests that at low temperatures, Pauli blocking creates "odd-parity modes" of the Fermi surface that are anomalously long-lived. These modes give rise to "tomographic transport," a phenomenon not captured by standard hydrodynamic models. A comprehensive theory describing how these tomographic flows interact with electrode contacts in confined geometries like the Corbino disk has been largely missing.

Methodology
The authors derive a transport theory for tomographic flows in a Corbino disk by performing a matched asymptotic expansion of the underlying stationary Fermi-liquid kinetic equation.

Kinetic Framework: The study utilizes the linearized collision integral, distinguishing between momentum-conserving (MC) and momentum-relaxing (MR) collisions. The relaxation rates are parametrized to reflect the disparity between even-parity modes (short mean free path, $\ell_e$ ) and odd-parity modes (long mean free path, $\ell_o$ ), where $\ell_o \gg \ell_e$ .
Expansion Parameters: The solution is expanded in powers of the even-mode Knudsen number ( $k_e = \ell_e/L$ ), assuming $k_e \ll 1$ while the odd-mode Knudsen number ( $k_o = \ell_o/L$ ) and the Gurzhi number ( $G$ ) are of order unity.
Boundary Conditions: The authors impose microscopic boundary conditions at the electrodes (inner and outer radii) where quasiparticles are transmitted. They introduce "tomographic boundary layers" near the electrodes to satisfy these conditions, which decay over an anomalously large length scale $\sqrt{\ell_e \ell_o}$ rather than the standard mean free path.
Solution Strategy: The bulk equations are solved to leading order (hydrodynamic) and first order in $k_e$ (tomographic correction). These are matched with the boundary layer solutions to derive effective boundary conditions for the macroscopic variables (velocity and chemical potential).

Key Contributions and Results

Tomographic Boundary Layer and Slip Velocity: The analysis reveals an extended boundary layer near the electrodes where the system is far from local equilibrium. This layer induces a "tomographic slip condition" for the azimuthal velocity. Unlike conventional slip, this condition depends explicitly on the electrode curvature ( $1/r$ ) and the odd-mode mean free path.
Superballistic Injection and Conductance: The tomographic effect leads to superballistic current injection at the electrodes. The derived electrode conductance saturates an upper bound of twice the Sharvin conductance, a result consistent with microscopic scattering models involving retroreflected holes.
Three Distinct Magnetotransport Regimes: The paper identifies three regimes for the quadratic magnetoresistance coefficient ( $\alpha$ $α$ ) as a function of the magnetic field (parameterized by the dimensionless cyclotron radius $r_c$ $r_{c}$ ):
- Tomographic Regime (Weak Fields): Occurs when $r_c \gtrsim k_o$ . Here, the long-lived odd modes dominate, leading to enhanced slip velocity and a parametric enhancement of the magnetoresistance coefficient $\alpha$ .
- Hydrodynamic Regime (Intermediate Fields): Occurs when $k_e \lesssim r_c \lesssim k_o$ . As the cyclotron radius becomes comparable to the odd-mode mean free path, the tomographic slip is suppressed, and the system crosses over to standard hydrodynamic behavior.
- Ohmic Regime (Strong Fields): Occurs when $r_c \lesssim k_e$ . The cyclotron radius becomes comparable to the short even-mode mean free path, suppressing viscosity and leading to conventional Ohmic transport.
Non-Monotonic Behavior: The magnetoresistance coefficient $\alpha$ exhibits a non-monotonic dependence on the magnetic field: it decreases as the field increases from zero (transitioning from tomographic to hydrodynamic) and then increases at high fields (transitioning to the Ohmic regime).
Scaling Anomalies: The density and temperature dependence of the tomographic corrections to the magnetoresistance differ significantly from standard Fermi-liquid predictions. Specifically, the leading-order tomographic correction scales as $n^4/T^4$ , contrasting with the hydrodynamic $T^2/n$ scaling.

Significance and Claims
The paper claims that the derived tomographic corrections provide a mechanism to explain the anomalous temperature and density scaling of electron viscosity observed in recent Corbino disk experiments. By explicitly linking the magnetoresistance coefficient to the electrode curvature and the odd-mode mean free path, the theory offers a way to control and tune these effects via device geometry.

The authors suggest that the non-monotonic dependence of the magnetoresistance coefficient on the magnetic field serves as a signature of the tomographic effect. Furthermore, they propose that by measuring the magnetoresistance in the intermediate field regime (where the tomographic regime is suppressed), one can obtain a more robust extraction of the hydrodynamic electron viscosity and identify the odd-mode mean free path, resolving discrepancies between experimental data and standard Fermi-liquid theory.

1. The "Ghostly" Boundary Layer

2. The Magnetic Field as a "Traffic Cop"

3. Why This Matters (According to the Paper)

Summary

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