Non-magnetic spin splitting driven by spin-valley-layer coupling in multilayer WSe2

This study demonstrates that an out-of-plane electric field can induce dominant spin splitting in the Q and Q' valleys of multilayer n-type WSe2 via spin-valley-layer coupling, offering a powerful non-magnetic alternative to magnetic fields for controlling spin states in low-power spintronic and quantum devices.

The Gist

Imagine a tiny, ultra-thin sheet of material called WSe₂ (Tungsten Diselenide). In the world of electronics, this material is special because it has a hidden "secret identity" for its electrons. Usually, electrons just flow like water in a pipe. But in this material, electrons also have a "spin" (like a tiny spinning top) and a "valley" (a specific location in their energy landscape).

In this paper, the researchers built a microscopic traffic jam—a Quantum Point Contact (QPC)—inside this material. Think of the QPC as a very narrow channel that forces electrons to line up single-file. In this narrow channel the electrons travel in a 'quasi-ballistic' way — most of them fly straight through without bouncing off anything, like a bullet shot through still air, rather than being scattered around like a ball bouncing through pinball pegs. By squeezing the electrons into this channel, the scientists could watch how they behave in extreme detail.

Here is the story of what they discovered, explained simply:

1. The Problem: How do we control electron spins without magnets?

In modern electronics, we often use magnets to control electron spins (which is how hard drives work). However, magnets are bulky and require a lot of energy. The scientists wanted to see if they could control these spins using only electricity (a voltage knob), without any magnets at all.

2. The Magic Ingredient: "Spin-Valley-Layer" Coupling

The material they used has a unique trick. In a stack of these thin sheets, the electrons' "spin" (up or down) is locked to two other things:

• The Valley: Which "valley" in the energy map they are in.
• The Layer: Which specific sheet in the stack they are sitting on.

This is called Spin-Valley-Layer (SVL) coupling. It's like a three-way handshake: if you know the electron is in the top layer, you know its spin and its valley. If you change the layer, the spin changes too.

3. The Experiment: Turning the "Electric Knob"

The researchers built a device with a "back gate" (a metal plate underneath the material) that acts like a volume knob for electricity.

• The Setup: They turned on a voltage on this back gate. This created an electric field pushing through the layers of the material.
• The Observation: As they slowly turned up the voltage, they watched the electrons flow through their narrow channel. They saw the "traffic" split into four distinct lanes.

4. The Big Discovery: Electricity is Stronger than Magnets

Here is the most exciting part. The researchers compared two ways to split the electron lanes:

1. Using a Giant Magnet: They applied a massive magnetic field (9 Tesla, which is incredibly strong, like a hospital MRI machine). This split the electron paths by about 2 units of energy.
2. Using a Tiny Electric Knob: They applied a very small change in voltage (just a tiny twist of the knob). This split the electron paths by about 7 units of energy.

The Analogy: Imagine trying to push a heavy door open.

• Using the magnet is like trying to push the door with a small child's hand. It moves a little bit.
• Using the electric voltage is like using a hydraulic press. With a tiny bit of pressure, the door flies open much wider.

The paper shows that using electricity to control these spins is more than three times more powerful than using a giant magnet.

5. Why the "Thin" Device Worked Best

The team tested two devices: one with 14 layers of material and one with only 5 layers.

• The 14-layer device: It was like a thick, muddy road. The electric signal got lost in the middle layers, and the results were a bit messy and confusing.
• The 5-layer device: This was like a thin, clear glass pane. The electric signal went straight through, and the "traffic splitting" was perfectly clear and easy to read. This proved that the effect comes from the interaction between the layers and the electric field.

6. The Conclusion

The scientists successfully demonstrated that they can take electrons, force them into a narrow channel, and use a simple electric voltage to sort them by their spin and valley. They proved that this electric method is a much more efficient and powerful way to manipulate these tiny particles than using heavy magnets.

In short: They found a way to use a tiny electric switch to do the job of a giant magnet, sorting electrons with high precision. This is a major step toward building future computers that are faster and use much less battery power.

Technical Summary

Technical Summary: Non-magnetic spin splitting driven by spin-valley-layer coupling in multilayer WSe₂

Problem Statement
Transition metal dichalcogenides (TMDCs) offer a platform for spin-valley physics, where spin and valley degrees of freedom are intrinsically coupled. While monolayer TMDCs exhibit spin-valley locking at the K and K' valleys, multilayer systems introduce an additional layer degree of freedom through spin-valley-layer (SVL) coupling. Previous studies have demonstrated gate-voltage-induced Zeeman-type spin splitting in multilayer TMDCs, yet a definitive demonstration of electrically induced, non-magnetic spin splitting with systematic control via SVL coupling remains elusive. Furthermore, distinguishing this effect from magnetic-field-induced valley-Zeeman splitting and understanding the role of layer thickness and electrostatic screening in confined geometries are critical challenges for developing low-power spintronic devices.

Methodology
The authors employed quantum-point-contact (QPC) spectroscopy to investigate n-type multilayer WSe₂ devices. Two distinct devices were fabricated with different layer counts: Device #1 (14 layers) and Device #2 (5 layers). The devices featured a global Si back-gate, a hexagonal boron nitride (h-BN) dielectric, and split-gate electrodes defining a QPC channel with an effective width of approximately 5–6 nm. Indium (In) contacts were used for source and drain electrodes to ensure efficient carrier injection.

Transport measurements were conducted at cryogenic temperatures (down to 3–4 K) using differential conductance ($dG/dV$) spectroscopy. The researchers systematically varied the back-gate voltage ($V_{BG}$) to tune the out-of-plane displacement field ($D$) and the split-gate voltage ($V_{QPC}$) to define the 1D confinement. Additionally, magnetic field ($B$) dependent measurements were performed up to 9 T to compare electric-field-induced effects with magnetic-field-induced Zeeman splitting. The study utilized finite-bias transconductance maps to extract subband energy scales ($\Delta_n$) and analyzed temperature-dependent conductance to characterize transport regimes (quasi-ballistic vs. ballistic) and phase coherence.

Key Contributions and Results

1. Observation of Four Distinct Spin-Resolved Subbands:
   In the thinner Device #2 ($N_L=5$), the researchers observed four distinct conductance quantization steps corresponding to subband energy scales $\Delta_{1/2}$, $\Delta_1$, $\Delta_{3/2}$, and $\Delta_2$. These steps were identified as spin-resolved subbands arising from the Q and Q' valleys. The energy scales were extracted from diamond-shaped features in transconductance maps ($dG/dV_{QPC}$ vs. $V_{SD}$).

2. Systematic Control via Displacement Field:
   By tuning the back-gate voltage, the authors demonstrated that the displacement field ($D$) systematically modulates these four energy scales. Specifically, as $D$ increased (by increasing $V_{BG}$), the energy scales $\Delta_1$ and $\Delta_2$ increased, while $\Delta_{1/2}$ and $\Delta_{3/2}$ decreased. This contrasting behavior provided direct spectroscopic evidence of SVL coupling, where the electric field induces opposite energy shifts in the Q and Q' valleys localized in adjacent layers.

3. Dominance of Electric-Field-Induced Splitting:
   The study quantified the magnitude of the splitting. A change in displacement field of $\sim 0.08$ V/nm induced a spin splitting of $\sim 7$ meV. In contrast, a magnetic field of 9 T yielded a valley-Zeeman splitting of only $\sim 2$ meV. This demonstrates that electric-field-induced SVL coupling is a significantly more powerful mechanism for manipulating spin states than conventional magnetic fields in this system.

4. Role of Layer Thickness and Screening:
   A comparison between Device #1 (14 layers) and Device #2 (5 layers) revealed the critical impact of electrostatic screening. In the thicker Device #1, the electric field was screened by the upper layers, leading to complex interlayer scattering and inconsistent scaling of energy scales between different measurement axes. In the thinner Device #2, the electric field effectively penetrated the channel, minimizing bulk-like interference and allowing for the clear observation of the idealized SVL coupling mechanism.

5. Transport Regime Characterization:
   The devices operated in a phase-coherent quasi-ballistic regime. While the effective channel length was comparable to or shorter than the mean free path, low-temperature measurements revealed peak-dip conductance fluctuations due to quantum resonant backscattering. The effective channel width ($W_{eff} \approx 5.6$ nm) was comparable to half the Fermi wavelength, enabling the isolation of fundamental 1D subbands.

6. Suppression of Valley Zeeman Effect:
   Analysis of the Landé g-factor under magnetic fields suggested a significant reduction in the valley g-factor ($g_v$) compared to bulk values. The authors attribute this to the quenching of the orbital magnetic moment due to strong lateral confinement within the QPC, which restricts the spatial extent of the electronic wave packet necessary to sustain valley-dependent circulating currents.

Significance
The paper claims to provide unambiguous evidence of electric-field-induced spin splitting in multilayer WSe₂ driven by SVL coupling. By utilizing QPC spectroscopy, the authors successfully isolated and controlled spin-resolved density of states without the need for external magnetic fields. The results highlight that gate-voltage control can achieve spin splitting magnitudes far exceeding those possible with high magnetic fields (9 T). This work establishes a robust platform for engineering spin-valley degrees of freedom through purely electrical means, representing a significant step toward the realization of practical, low-power spintronic and quantum information technologies based on TMDC heterostructures. The study also clarifies the importance of device thickness and electrostatic screening in observing these quantum phenomena, offering design guidelines for future experiments.