🔬 mesoscale physics

Supercurrent effect in a charge density wave intertwined superconductor

This study demonstrates that in superconducting NbSe2, Meissner currents induced by an in-plane magnetic field selectively Doppler-shift Bogoliubov quasiparticle spectra at charge density wave vectors, thereby driving a symmetry-breaking transition in CDW modulations and enabling momentum-space engineering of intertwined electronic phases.

Original authors: Zhen Zhu, Wei Cheng, Dang Liu, Pengyu Hu, Yi Yang, Qiaoyan Yu, Shasha Xue, Ruijun Xi, Xingsen Chen, Jice Sun, Dandan Guan, Yaoyi Li, Shiyong Wang, Canhua Liu, Zhuan Xu, Xin Liu, Hao Zheng, Jinfeng Jia

Published 2026-07-24

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CC BY 4.0

Original authors: Zhen Zhu, Wei Cheng, Dang Liu, Pengyu Hu, Yi Yang, Qiaoyan Yu, Shasha Xue, Ruijun Xi, Xingsen Chen, Jice Sun, Dandan Guan, Yaoyi Li, Shiyong Wang, Canhua Liu, Zhuan Xu, Xin Liu, Hao Zheng, Jinfeng Jia

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 the world of electrons inside a solid material as a bustling, invisible city. In this city, electrons don't just sit still; they zip around, creating waves of energy that define how the material behaves. Sometimes, these electrons decide to dance in perfect unison, forming a superconductor where electricity flows with zero resistance. Other times, they arrange themselves into a rigid, repeating pattern called a charge density wave (CDW), like a traffic jam that freezes into a grid. Scientists have long known that if you push a superconductor with a current, the energy of its electrons shifts, much like the pitch of a siren changes as an ambulance zooms past you (a phenomenon called the Doppler effect). But what happens when you have a material where these two electron dances—the superconducting flow and the rigid CDW grid—happen at the same time? Does the "siren" effect of the current mess up the traffic jam, or do they ignore each other? Understanding this is like trying to figure out how a spinning ice skater changes their spin when they suddenly put on a heavy, patterned coat. It's a fundamental question about how quantum materials work, and solving it could help us design better electronics or even new types of quantum computers.

In this study, researchers took a closer look at a specific material called 2H-NbSe2, which is famous for hosting both superconductivity and a charge density wave. They wanted to see if they could use a magnetic field to "push" the electrons and watch how the two dances interacted. By placing the material in a super-cold environment (40 millikelvin, which is just a hair above absolute zero) and applying a magnetic field parallel to its surface, they generated a special "shielding current" on the surface of the material. This current acts like a gentle wind blowing across the electron city.

The team used a super-powerful microscope called a scanning tunneling microscope (STM) to take pictures of the electrons' energy and arrangement. They found that when they blew this "wind" (the current) in a specific direction, the rigid CDW pattern didn't just stay the same; it changed its shape and symmetry. Normally, the CDW pattern looks like a perfect triangle with three equal sides (a symmetry called C3v). However, when the current was applied, the pattern broke its symmetry, becoming more like a rectangle with two long sides and two short sides (a symmetry called Cs). Specifically, the "ripples" in the electron density became much stronger in the direction the wind was blowing and weaker in the other directions.

The researchers suggest that this happens because the current changes the energy landscape for the electrons, a process known as a Doppler shift. Imagine the electrons as runners on a track; the current gives some runners a boost and slows others down, depending on which way they are running. This reshapes the "constant energy lines" where the electrons can exist. Because the CDW pattern is built on top of these electron waves, when the waves get reshaped by the current, the CDW pattern gets distorted too. The team confirmed this idea by running computer simulations that matched their experimental pictures almost perfectly. They also checked that this effect wasn't caused by tiny magnetic whirlpools (vortices) that usually appear in such materials, as they measured areas far away from those whirlpools.

In short, the paper shows that by simply changing the direction of a magnetic field, scientists can "tune" the electronic patterns in this material, making the charge density wave stronger in one direction and weaker in another. This proves that the supercurrent effect can be used as a tool to engineer and control quantum phases in materials where different electronic orders are intertwined. It's like having a remote control that can reshape the very fabric of an electron city just by changing the direction of a magnetic breeze.

Technical Summary: Supercurrent Effect in a Charge Density Wave Intertwined Superconductor

Problem Statement
The energy-momentum ( $E$ - $k$ ) dispersion of quasiparticles is a foundational concept in condensed matter physics. In superconductors, the flow of supercurrent induces a Doppler shift in the Bogoliubov quasiparticle spectrum, a phenomenon known to manipulate emergent quantum properties such as Fermi surface segmentation and the Josephson diode effect. However, the specific impact of supercurrents on superconductors that are intertwined with charge orders, such as Charge Density Waves (CDW), remains poorly understood. While CDW and superconductivity are known to compete or coexist in materials like 2H-NbSe $_2$ , the mechanism by which supercurrents alter the interplay between these orders, particularly regarding the symmetry and momentum-space distribution of CDW modulations, has not been experimentally elucidated.

Methodology
The authors employed a combination of low-temperature scanning tunneling microscopy/spectroscopy (STM/STS) and theoretical modeling to investigate 2H-NbSe $_2$ , a canonical system exhibiting both $s$ -wave superconductivity ( $T_c \approx 7.2$ K) and a $3\times3$ CDW transition ( $T_{CDW} \approx 33$ K).

Experimental Setup: Measurements were conducted in a dilution refrigerator at a base temperature of 40 mK. An in-plane magnetic field (up to 400 mT) was applied to generate Meissner screening currents on the sample surface. Spectroscopic imaging was performed by acquiring $dI/dV$ maps across a range of energies, from the superconducting gap edge to the normal state.
Data Analysis: Fast Fourier Transforms (FFT) of the real-space $dI/dV$ maps were used to visualize CDW vectors in momentum space. The intensity of CDW peaks, denoted as $P(\pm \mathbf{d}_i)$ , was analyzed as a function of magnetic field strength and orientation.
Theoretical Modeling: A real-space tight-binding model was constructed for NbSe $_2$ , incorporating Ising spin-orbit coupling, a triple-Q CDW potential, and $s$ -wave superconductivity. The supercurrent effect was simulated using the Peierls substitution ( $\mathbf{p} \to \mathbf{p} + e\mathbf{A}$ ), where the vector potential $\mathbf{A}$ was derived from the London gauge. The Kernel Polynomial Method (KPM) was utilized to calculate the local density of states (LDOS) for large system sizes, allowing for the simulation of constant-energy contours and real-space patterns under various field orientations.

Key Results

Supercurrent-Induced Doppler Shift: The application of an in-plane magnetic field caused the superconducting coherence peaks to shift to higher energies and the gap edge to move, confirming the presence of a Doppler shift induced by surface screening currents.
Symmetry Breaking of CDW Modulations: In the absence of a magnetic field, the CDW modulation exhibits $C_{3v}$ $C_{3 v}$ symmetry, characterized by three equivalent wavevectors ( $\mathbf{d}_1, \mathbf{d}_2, \mathbf{d}_3$ $d_{1}, d_{2}, d_{3}$ ) with equal intensities. Upon applying an in-plane field, this symmetry is broken, transitioning to $C_s$ $C_{s}$ symmetry.
- When the field is aligned along the $\Gamma$ - $M$ direction, the CDW peak parallel to the field ( $P(\mathbf{d}_1)$ ) is significantly enhanced, while the other two peaks ( $P(\mathbf{d}_2), P(\mathbf{d}_3)$ ) are suppressed.
- Rotating the field to the $\Gamma$ - $K$ direction reverses this effect, enhancing the peaks nearest to the new field direction.
Energy Dependence: This anisotropic enhancement is strictly confined to the energy window within the superconducting gap ($0.2 - 0.6$ meV), where Bogoliubov quasiparticles exist. At energies above the gap ( $>0.6$ meV) or in the normal state, the CDW peaks retain equal intensity and $C_{3v}$ symmetry, indicating the effect is specific to the superconducting state.
Momentum-Space Reconstruction: Theoretical calculations demonstrate that the Doppler shift selectively modifies the $E$ - $k$ dispersion of Bogoliubov quasiparticles. For energies within the gap ( $E_D < E < \Delta$ ), the constant-energy contours lose their $C_{3v}$ symmetry, becoming mirror-symmetric ( $C_s$ ). This reconstruction alters the scattering phase space, leading to the selective enhancement of specific CDW peaks based on the field orientation.

Significance and Claims
The paper claims to demonstrate a novel mechanism for controlling emergent electronic phases through momentum-space engineering. The primary contribution is the experimental observation that supercurrents, generated via the Meissner effect, can tailor Bogoliubov quasiparticle excitations at precursor CDW vectors. This results in a field-driven, on-demand tuning of CDW anisotropy.

The authors assert that this work provides fundamental momentum-space evidence of the Doppler shift acting on Bogoliubov quasiparticles in a CDW-intertwined superconductor. By visualizing how the supercurrent reshapes the constant-energy contours and subsequently modulates the CDW pattern, the study establishes a direct link between supercurrent-induced symmetry breaking and the manipulation of charge order. The findings suggest a pathway for controlling quantum phases in superconductors intertwined with other orders using engineered supercurrents and magnetic fields, without invoking vortex-core effects as the primary driver (as measurements were taken away from visible vortices, though bulk vortices are acknowledged as a potential secondary factor).

Technical Summary: Supercurrent Effect in a Charge Density Wave Intertwined Superconductor

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