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arXiv:2104.02568 · Physical review. B./Physical review. B

Spin-orbit enabled quantum transport channels in a two-hole double quantum dot

Alex Bogan, Sergei Studenikin, Marek Korkusiński, Louis Gaudreau, Jason Phoenix, P. Zawadzki, Andy S. Sachrajda, Lisa Tracy, John L. Reno, Terry W. Hargett

Published Jun 14, 2021• 8 citations

Abstract

We analyze experimentally and theoretically the transport spectra of a gated lateral GaAs double quantum dot containing two holes. The strong spin-orbit interaction present in the hole subband lifts the Pauli spin blockade and allows to map out the complete spectra of the two-hole system. By performing measurements in both source-drain voltage directions, at different detunings and magnetic fields, we carry out quantitative fitting to a Hubbard two-site model accounting for the tunnel coupling to the leads and the spin-flip relaxation process. We extract the singlet-triplet gap and the magnetic field corresponding to the singlet-triplet transition in the double-hole ground state. Additionally, at the singlet-triplet transition we find a resonant enhancement (in the blockaded direction) and suppression of current (in the conduction direction). The current enhancement stems from the multiple resonance of two-hole levels, opening several conduction channels at once. The current suppression arises from the quantum interference of spin-conserving and spin-flipping tunneling processes.

DOI: 10.1103/physrevb.103.235310

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We analyze experimentally and theoretically the transport spectra of a gated lateral GaAs double quantum dot containing two holes. The strong spin-orbit interaction present in the hole subband lifts the Pauli spin blockade and allows to map out the complete spectra of the two-hole system. By performing measurements in both source-drain voltage directions, at different detunings and magnetic fields, we carry out quantitative fitting to a Hubbard two-site model accounting for the tunnel coupling to the leads and the spin-flip relaxation process. We extract the singlet-triplet gap and the magnetic field corresponding to the singlet-triplet transition in the double-hole ground state. Additionally, at the singlet-triplet transition we find a resonant enhancement (in the blockaded direction) and suppression of current (in the conduction direction). The current enhancement stems from the multiple resonance of two-hole levels, opening several conduction channels at once. The current suppression arises from the quantum interference of spin-conserving and spin-flipping tunneling processes.

We characterize numerically and analytically the signatures of the spin-orbit interaction in a two-electron GaAs double quantum dot in the presence of an external magnetic field. In particular, we obtain the return probability of the singlet state by simulating Landau-Zener voltage detuning sweeps which traverse the singlet-triplet ($S\ensuremath{-}{T}_{+}$) resonance. Our results indicate that non-spin-conserving interdot tunneling processes arising from the spin-orbit interaction have well defined signatures. These allow direct access to the spin-orbit interaction scales and are characterized by a frequency shift and Fourier amplitude modulation of the Rabi flopping dynamics of the singlet-triplet qubits $S\ensuremath{-}{T}_{0}$ and $S\ensuremath{-}{T}_{+}$. By applying the Bloch-Feshbach projection formalism, we demonstrate analytically that the aforementioned effects originate from the interplay between spin-orbit interaction and processes driven by the hyperfine interaction between the electron spins and those of the GaAs nuclei.

The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.

Abstract We investigate the effect of spin–orbit interaction on the intra- and interdot particle dynamics of a double quantum dot (QD) under ac electric fields. The former is modeled as an effective ac magnetic field that produces electric-dipole spin resonance transitions, while the latter is introduced via spin-flip tunneling amplitudes. We observe the appearance of non-trivial spin-polarized dark states (DSs), arising from an ac-induced interference between photo-assisted spin-conserving and spin-flip tunneling processes. These DSs can be employed to precisely measure the spin–orbit coupling in QD systems. Furthermore, we show that the interplay between photo-assisted transitions and spin-flip tunneling enables the system to operate as a highly tunable spin filter. Finally, we investigate the operation of the system as a resonant flopping-mode qubit for arbitrary ac voltage amplitudes, allowing for high tunability and enhanced qubit control possibilities.

Hole spin qubits in semiconductors are in the midst of revolutionizing solid-state quantum information processing, and different setups are being investigated to further improve their quality. In this work, the authors demonstrate that the interplay between the spin-orbit interaction and site-dependent

g

tensors of holes confined in a double quantum dot enables all-electrical orthogonal two-axis control of hole singlet-triplet qubits. Remarkably, leakage errors can be strongly suppressed at the same time by choosing an optimal direction of the external magnetic field.

We study theoretically the phonon-induced relaxation (

{T}_{1}

) and decoherence times (

{T}_{2}

) of singlet-triplet qubits in lateral GaAs double quantum dots (DQDs). When the DQD is biased, Pauli exclusion enables strong dephasing via two-phonon processes. This mechanism requires neither hyperfine nor spin-orbit interaction and yields ${T}_{2}\ensuremath{\ll}{T}_{1}$, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find ${T}_{2}\ensuremath{\simeq}2{T}_{1}$ and much longer lifetimes than in the biased DQD. For typical setups, the decoherence and relaxation rates due to one-phonon processes are proportional to the temperature

T

, whereas the rates due to two-phonon processes reveal a transition from

{T}^{2}

to higher powers as

T

is decreased. Remarkably, both

{T}_{1}

and

{T}_{2}

exhibit a maximum when the external magnetic field is applied along a certain axis within the plane of the two-dimensional electron gas. We compare our results with recent experiments and analyze the dependence of

{T}_{1}

and

{T}_{2}

on system properties such as the detuning, the spin-orbit parameters, the hyperfine coupling, and the orientation of the DQD and the applied magnetic field with respect to the main crystallographic axes.