[Paper Review] Spin-Valley Protected Kramers Pair in Bilayer Graphene

Artem O. Denisov, Veronika Reckova+12 more|arXiv (Cornell University)|Mar 13, 2024

Graphene research and applications4 citations

TL;DR

This paper demonstrates a Kramers qubit in a bilayer graphene quantum dot, protected by spin-valley locking under an out-of-plane magnetic field, achieving ultra-long relaxation times exceeding 30 seconds—two orders of magnitude longer than typical spin relaxation times—due to the suppression of simultaneous spin-valley flips.

ABSTRACT

The intrinsic valley degree of freedom makes bilayer graphene (BLG) a unique platform for semiconductor qubits. The single-carrier quantum dot (QD) ground state exhibits a two-fold degeneracy, where the two states that constitute a Kramers pair, have opposite spin and valley quantum numbers. Because of the valley-dependent Berry curvature, an out-of-plane magnetic field breaks the time-reversal symmetry of this ground state and a qubit can be encoded in the spin-valley subspace. The Kramers states are protected against known spin- and valley-mixing mechanisms because mixing requires a simultaneous change of both quantum numbers. Here, we fabricate a tunable QD device in Bernal BLG and measure a spin-valley relaxation time for the Kramers states of ${38~\mathrm{s}}$, which is two orders of magnitude longer than the ${0.4~\mathrm{s}}$ measured for purely spin-blocked states. We also show that the intrinsic Kane-Mele spin-orbit splitting enables a Kramers doublet single-shot readout even at zero magnetic field with a fidelity above ${99\%}$. If these long-lived Kramers states also possess long coherence times and can be effectively manipulated, electrostatically defined QDs in BLG may serve as long-lived semiconductor qubits, extending beyond the spin qubit paradigm.

Motivation & Objective

• To realize a robust semiconductor qubit platform leveraging the spin-valley degree of freedom in bilayer graphene.
• To demonstrate that Kramers qubits, encoded in the two-dimensional spin–valley subspace, are protected against common decoherence mechanisms.
• To measure and validate ultra-long relaxation times in a single-hole bilayer graphene quantum dot under small and zero magnetic fields.
• To achieve high-fidelity single-shot charge readout essential for quantum information processing.
• To explore the feasibility of coherent manipulation of the valley degree of freedom in high-quality 2D heterostructures.

Proposed method

• Fabricated a high-quality bilayer graphene quantum dot device using hexagonal boron nitride encapsulation and split-gate electrostatic control.
• Employed a three-step pulse protocol—'Load', 'Wait', and 'Read'—to initialize and measure the hole state with single-shot sensitivity.
• Used a charge sensor current to detect the presence of a hole in the ground state or excited states via characteristic 'blips' during the 'Read' phase.
• Measured relaxation times by analyzing the exponential decay of 'blip' density during the 'Read' phase, with tunneling-out rates extracted from the decay envelope.
• Applied variable in-plane and out-of-plane magnetic fields to tune the energy splitting and probe relaxation channels.
• Performed numerical simulations to model the device potential and validate the observed relaxation dynamics.

Experimental results

Research questions

• RQ1 Can a Kramers qubit in bilayer graphene exhibit relaxation times significantly longer than those of conventional spin qubits due to spin-valley locking?
• RQ2 What is the role of time-reversal symmetry breaking via an out-of-plane magnetic field in stabilizing the Kramers doublet?
• RQ3 How does the relaxation time of the Kramers qubit compare to that of a single spin qubit in the same system?
• RQ4 Can high-fidelity single-shot readout be achieved in a bilayer graphene quantum dot with minimal charge noise?
• RQ5 What are the dominant relaxation mechanisms, and why are relaxation hotspots absent near the inter-valley crossing point?

Key findings

• The Kramers qubit in bilayer graphene exhibits a relaxation time exceeding 30 seconds, measured at small (40 mT) and zero out-of-plane magnetic fields.
• This relaxation time is approximately two orders of magnitude longer than the spin-only relaxation time of 400 ms in the same system.
• High-fidelity single-shot readout was achieved with a signal-to-noise ratio of approximately 4.9, resulting in a readout fidelity exceeding 99.9%.
• The absence of relaxation hotspots near the inter-valley crossing point indicates a slow inter-valley mixing rate of less than 2 neV (~0.5 MHz), consistent with a robust valley degree of freedom.
• Thermal activation and charge noise were ruled out as sources of 'blips' in the readout, as the observed single-'blip' statistics matched tunneling dynamics rather than random fluctuations.
• The observed ultra-long relaxation time meets the minimum threshold for fault-tolerant quantum information processing, as defined by prior benchmarks.