Measurements of the Fermi surface are a fundamental technique for determining the electrical and magnetic properties of solids. In two-dimensional (2D) systems, the area and diameter of the Fermi surface are typically measured using Shubnikov-de Haas oscillations and commensurability oscillations respectively. However, these techniques are unable to detect changes in the parity of the Fermi surface [i.e., when E(+k) not equal E(-k)]. Here, we show that transverse magnetic focusing can be used to detect such changes, because focusing only measures a well defined section of the Fermi surface and does not average over +k and -k. Furthermore, our results show that focusing is an order of magnitude more sensitive to changes in the Fermi surface than other 2D techniques. While we investigate a specific Fermi surface shift in this work, focusing could be used to investigate similar Fermi surface changes in other 2D systems.

Two-dimensional hole gases (2DHGs) have strong intrinsic spin-orbit coupling and could be used to build spin filters by utilizing transverse magnetic focusing (TMF). However, with an increase in the spin degree of freedom, holes demonstrate significantly different behavior to electrons in TMF experiments, making it difficult to interpret the results of these experiments. In this paper, we numerically model TMF in a 2DHG within a GaAs/AlxGa1-xAs heterostructure. Our band structure calculations show that the heavy ((Jz) = +/- 3/2) and light ((Jz) = +/- 1/2) hole states in the valence band mix at finite k, and the heavy-hole subbands which are spin-split due to the Rashba effect are not spin-polarized. This lack of spin polarization casts doubt on the viability of spin filtering using TMF in 2DHGs within conventional GaAs/AlxGa1-xAs heterostructures. We then calculate the transport properties of the 2DHG with spin projection and offer a different perspective on interpreting and designing TMF experiments in 2DHGs.

The study of phonon coupling in doped semiconductors via electrical transport measurements is challenging due to unwanted temperature-induced effects such as dopant ionization and parallel conduction. Here, we study phonon scattering in 2D electrons and holes in the 1.6-92.5 K range without the use of extrinsic doping, where both acoustic and longitudinal optic (LO) phonons come into effect. We use undoped GaAs/ AlxGa1-xAs heterostructures and examine the temperature dependence of the sample resistivity, extracting phonon coupling constants and the LO activation energy. Our results are consistent with results obtained through approaches other than transport measurements and highlight the benefit of this approach for studying electron-phonon and hole-phonon coupling.

Silicon hole quantum dots have been the subject of considerable attention thanks to their strong spin-orbit coupling enabling electrical control. The physics of silicon holes is qualitatively different from germanium holes and requires a separate theoretical description. In this work, we theoretically study the electrical control and coherence properties of silicon hole dots with different magnetic field orientations. We discuss possible experimental configurations to optimize the electric dipole spin resonance (EDSR) Rabi time, the phonon relaxation time, and the dephasing due to random telegraph noise. Our main findings are: (i) The in-plane $g$-factor is strongly influenced by the presence of the split-off band, as well as by any shear strain. The $g$-factor is a non-monotonic function of the top gate electric field, in agreement with recent experiments. This enables coherence sweet spots at specific values of the top gate field and specific magnetic field orientations. (ii) Even a small ellipticity (aspect ratios $\sim 1.2$) causes significant anisotropy in the in-plane $g$-factor, which can vary by $50\% - 100\%$ as the magnetic field is rotated in the plane. (iii) EDSR Rabi frequencies are comparable to Ge, and the ratio between the relaxation time and the EDSR Rabi time $\sim 10^5$. For an out-of-plane magnetic field the EDSR Rabi frequency is anisotropic with respect to the orientation of the driving electric field, varying by $\approx 20\%$ as the driving field is rotated in the plane. Our work aims to stimulate experiments by providing guidelines on optimizing configurations and geometries to achieve robust, fast and long-lived hole spin qubits in silicon.

The electronic properties of solids are determined by the crystal structure and interactions between electrons, giving rise to a variety of collective phenomena including superconductivity, strange metals and correlated insulators. The mechanisms underpinning many of these collective phenomena remain unknown, driving interest in creating artificial crystals which replicate the system of interest while allowing precise control of key parameters. Here we demonstrate the formation of highly tunable artificial crystals by superimposing a periodic electrostatic potential on the 2D electron gas in an ultra-shallow (25 nm deep) GaAs quantum well. The 100 nm period artificial crystal is identified by the formation of a new bandstructure, different from the original cubic crystal and specific to the artificial triangular lattice: transport measurements show the Hall coefficient changing sign as the chemical potential sweeps through the artificial bands. Uniquely, the artificial bandstructure can be continuously tuned to form linear graphene-like and flat kagome-like bands in a single device. A strong insulating state is observed at half filling of the kagome flat band, which is not expected in the absence of strong interactions. This state, unique to the kagome lattice, is consistent with a loop-current Wigner insulator, which arises from long-range Coulomb interaction and delocalised electrons between neighbouring empty sites. The ability to continuously tune the bandstructure and access flat bands through electrical gating within a single device opens a new route to studying collective quantum states.

Holes in silicon quantum dots are promising for spin qubit applications due to the strong intrinsic spin-orbit coupling. The spin-orbit coupling produces complex hole-spin dynamics, providing opportunities to further optimize spin qubits. Here, we demonstrate a singlet-triplet qubit using hole states in a planar metal-oxide-semiconductor double quantum dot. We observe rapid qubit control with singlet-triplet oscillations up to 400 MHz. The qubit exhibits promising coherence, with a maximum dephasing time of 600 ns, which is enhanced to 1.3 us using refocusing techniques. We investigate the magnetic field anisotropy of the eigenstates, and determine a magnetic field orientation to improve the qubit initialisation fidelity. These results present a step forward for spin qubit technology, by implementing a high quality singlet-triplet hole-spin qubit in planar architecture suitable for scaling up to 2D arrays of coupled qubits.

Quantum magnetic oscillations in crystals are typically understood in terms of Bohr-Sommerfeld quantisation, the frequency of oscillation is given by the area of a closed electron trajectory. However, since the 1970s, oscillations have been observed with frequencies that do not correspond to closed electron trajectories and this effect has remained not fully understood. Previous theory has focused on explaining the effect using various kinetic mechanisms, however, frequencies without a closed electron orbit have been observed in equilibrium and so a kinetic mechanism cannot be the entire story. In this work we develop a theory which explains these frequencies in equilibrium and can thus be used to understand measurements of both Shubnikov-de Haas and de Haas-van Alphen oscillations. We show, analytically, that these frequencies arise due to multi-electron correlations. We then extend our theory to explain a recent experiment on artificial crystals in GaAs two-dimensional electron gases, which revealed for the first time magnetic oscillations having frequencies that are half of those previously observed. We show that the half-frequencies arise in equilibrium from single-particle dynamics with account of impurities. Our analytic results are reinforced by exact numerics, which we also use clarify prior works on the kinetic regime.

We present a new double-layer design for 2D surface superlattice systems in GaAs-AlGaAs heterostructures. Unlike previous studies, our device (1) uses an in-situ gate, which allows very short period superlattice in high mobility, shallow heterostructures; (2) enables independent control of the carrier density and the superlattice modulation potential amplitude over a wide range. We characterise this device design using low-temperature magneto-transport measurements and show that the fabrication process caused minimal damage to the system. We demonstrate the tuning of potential modulation from weak (much smaller than Fermi energy) to strong (larger than the Fermi energy) regimes.

In this work, we probe the sensitivity of hole-spin properties to hole occupation number in a planar silicon double-quantum dot device fabricated on a 300 mm integrated platform. Using DC transport measurements, we investigate the g-tensor and spin-relaxation induced leakage current within the Pauli spin-blockade regime as a function of magnetic-field orientation at three different hole occupation numbers. We find the g-tensor and spin-leakage current to be highly anisotropic due to light-hole/heavy-hole mixing and spin-orbit mixing, but discover the anisotropies to be relatively insensitive to the dot hole number. Furthermore, we extract the dominant inter-dot spin-orbit coupling mechanism as surface Dresselhaus, with an in-plane orientation parallel to transport and magnitude t_SO ≈ 300 neV. Finally, we observe a strong correlation between the g-factor difference (δg) between each dot and the spin-leakage current anisotropy, as a result of δg providing an additional spin-relaxation pathway, and should be considered. ]Our findings indicate that hole-spin devices are not as sensitive to precise operating conditions as anticipated. This has important implications optimizing spin control and readout based on magnetic-field direction, together with tuning large arrays of QDs as spin-qubits.

A supersolid, a counterintuitive quantum state in which a rigid lattice of particles flows without resistance, has to date not been unambiguously realized. Here we reveal a supersolid ground state of excitons in a double-layer semiconductor heterostructure over a wide range of layer separations outside the focus of recent experiments. This supersolid conforms to the original Chester supersolid with one exciton per supersolid site, as distinct from the alternative version reported in cold-atom systems of a periodic density modulation or clustering of the superfluid. We provide the phase diagram augmented by the supersolid. This new phase appears at layer separations much smaller than the predicted exciton normal solid, and it persists up to a solid-solid transition where the quantum phase coherence collapses. The ranges of layer separations and exciton densities in our phase diagram are well within reach of the current experimental capabilities.

The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.

In two-dimensional systems with a spin-orbit interaction, magnetic focusing can be used to create a spatial separation of particles with different spin. Here we measure hole magnetic focusing for two different magnitudes of the Rashba spin-orbit interaction. We find that when the Rashba spin-orbit magnitude is large there is significant attenuation of one of the focusing peaks, which is conventionally associated with a change in the spin polarization. We instead show that in hole systems with a k3 spin-orbit interaction, this peak suppression is due to a change in the scattering of one spin state, not a change in spin polarization. We also show that the change in scattering length extracted from magnetic focusing is consistent with results obtained from measurements of Shubnikov-de Haas oscillations. This result suggests that scattering must be considered when relating focusing peak amplitude to spin polarization in hole systems.

Holes in silicon quantum dots are receiving attention due to their potential as fast, tunable, and scalable qubits in semiconductor quantum circuits. Despite this, challenges remain in this material system including difficulties using charge sensing to determine the number of holes in a quantum dot, and in controlling the coupling between adjacent quantum dots. We address these problems by fabricating an ambipolar complementary metal-oxide-semiconductor (CMOS) device using multilayer palladium gates. The device consists of an electron charge sensor adjacent to a hole double quantum dot. We demonstrate control of the spin state via electric dipole spin resonance. We achieve smooth control of the interdot coupling rate over 1 order of magnitude and use the charge sensor to perform spin-to-charge conversion to measure the hole singlet-triplet relaxation time of 11 μs for a known hole occupation. These results provide a path toward improving the quality and controllability of hole spin-qubits.

The surface area of Bi2Te3 thin films was increased by introducing nanoscale porosity. Temperature dependent resistivity and magnetotransport measurements were conducted both on as-grown and porous samples (23 and 70 nm). The longitudinal resistivity of the porous samples became more metallic, indicating the increased surface area resulted in transport that was more surface-like. Weak antilocalization (WAL) was present in all samples, and remarkably the phase coherence length doubled in the porous samples. This increase is likely due to the large Fermi velocity of the Dirac surface states. Our results show that the introduction of nanoporosity does not destroy the topological surface states but rather enhances them, making these nanostructured materials promising for low energy electronics, spintronics and thermoelectrics.

Imposing an external periodic electrostatic potential to the electrons confined in a quantum well makes it possible to engineer synthetic two-dimensional band structures, with electronic properties different from those in the host semiconductor. Here we report the fabrication and study of a tunable triangular artificial lattice on a GaAs/AlGaAs heterostructure where it is possible to transform from the original GaAs band structure and a circular Fermi surface to a new band structure with multiple artificial Fermi surfaces simply by altering a gate bias. For weak electrostatic modulation magnetotransport measurements reveal multiple quantum oscillations and commensurability oscillations due to the electron scattering from the artificial lattice. Increasing the strength of the modulation reveals new commensurability oscillations of the electrons from the artificial Fermi surface scattering from the triangular artificial lattice. These results show that low disorder gate-tunable lateral superlattices can be used to form artificial two-dimensional crystals with designer electronic properties.

Thermoelectric (TE) materials and devices are crucial for renewable thermal-to-electrical energy conversion applications. The optimization of TE performance can be achieved by manipulating four fundamental degrees of freedom: charge, lattice, spin and orbital. Historically, most strategies to improve TE performance focus on phonon and electron charge transport properties. However, in the past 15 years, the field of spin caloritronics, which explores the interplay among heat, charge and spin, has emerged. The inclusion of spins has introduced conceptually innovative mechanisms and versatile functionalities for solid-state thermal-to-electrical energy conversion. Here, we review the recent theoretical and experimental progress in the field of spin caloritronics. We discuss the strategic role of spin-related mechanisms in improving charge-based TE performance and the recent developments in the novel magneto-TE and thermospin effects as well as their potential applications. This Review offers a perspective for understanding the role of spin in TE, designing new high-efficiency TE materials and developing new TE technology beyond the conventional framework. Spin caloritronics explores the interplay among spin, heat and charges in condensed matter towards new thermoelectric functionalities and applications. This Review provides an analysis of the role of spin in enhancing charge-based thermoelectricity, magneto-thermoelectricity and thermospin effects.

A bstract A search for the exclusive decays of the Higgs and Z bosons to a ϕ or ρ meson and a photon is performed with a pp collision data sample corresponding to an integrated luminosity of up to 35 . 6 fb −1 collected at $$ \sqrt{s}=13 $$ s = 13 TeV with the ATLAS detector at the CERN Large Hadron Collider. These decays have been suggested as a probe of the Higgs boson couplings to light quarks. No significant excess of events is observed above the background, as expected from the Standard Model. Upper limits at 95% confidence level were obtained on the branching fractions of the Higgs boson decays to ϕ γ and ρ γ of 4 . 8 × 10 −4 and 8 . 8 × 10 −4 , respectively. The corresponding 95% confidence level upper limits for the Z boson decays are 0 . 9 × 10 −6 and 25 × 10 −6 for ϕ γ and ρ γ, respectively.

Hole spin qubits in group-IV semiconductors, especially Ge and Si, are actively investigated as platforms for ultrafast electrical spin manipulation thanks to their strong spin-orbit coupling. Nevertheless, the theoretical understanding of spin dynamics in these systems is in the early stages of development, particularly for in-plane magnetic fields as used in the vast majority of experiments. In this work, we present a comprehensive theory of spin physics in planar Ge hole quantum dots in an in-plane magnetic field, where the orbital terms play a dominant role in qubit physics, and provide a brief comparison with experimental measurements of the angular dependence of electrically driven spin resonance. We focus the theoretical analysis on electrical spin operation, phonon-induced relaxation, and the existence of coherence sweet spots. We find that the choice of magnetic field orientation makes a substantial difference for the properties of hole spin qubits. Specifically, we find that (i) EDSR for in-plane magnetic fields varies nonlinearly with the field strength and weaker than for perpendicular magnetic fields. (ii) The EDSR Rabi frequency is maximized when the a.c. electric field is aligned parallel to the magnetic field, and vanishes when the two are perpendicular. (iii) The orbital magnetic field terms make the in-plane g-factor strongly anisotropic in a squeezed dot, in excellent agreement with experimental measurements. (iv) Focusing on random telegraph noise, we show that the effect of noise in an in-plane magnetic field cannot be fully mitigated, as the orbital magnetic field terms expose the qubit to all components of the defect electric field. These findings will provide a guideline for experiments to design ultrafast, highly coherent hole spin qubits in Ge.

We demonstrate that a lightly strained germanium channel ([Formula: see text]) in an undoped Ge/Si0.1Ge0.9 heterostructure field effect transistor supports a two-dimensional (2D) hole gas with mobility in excess of [Formula: see text] cm2/Vs and percolation density less than [Formula: see text] cm−2. This low disorder 2D hole system shows tunable fractional quantum Hall effects at low densities and low magnetic fields. The low-disorder and small effective mass ([Formula: see text]) defines lightly strained germanium as a basis to tune the strength of the spin–orbit coupling for fast and coherent quantum hardware.

In a blueprint for topological electronics, edge state transport in a topological insulator material can be controlled by employing a gate-induced topological quantum phase transition. Here, by studying the width dependence of electronic properties, it is inferred that zigzag-Xene nanoribbons are promising materials for topological electronics with a display of unique physical characteristics associated with the intrinsic band topology and the finite-size effects on gate-induced topological switching. First, due to intertwining with intrinsic band topology-driven energy-zero modes in the pristine case, spin-filtered chiral edge states in zigzag-Xene nanoribbons remain gapless and protected against backward scattering even with finite inter-edge overlapping in ultra-narrow ribbons, i.e., a 2D quantum spin Hall material turns into a 1D topological metal. Second, mainly due to width- and momentum-dependent tunability of the gate-induced inter-edge coupling, the threshold-voltage required for switching between gapless and gapped edge states reduces as the width decreases, without any fundamental lower bound. Third, when the width of zigzag-Xene nanoribbons is smaller than a critical limit, topological switching between edge states can be attained without bulk bandgap closing and reopening. This is primarily due to the quantum confinement effect on the bulk band spectrum which increases the nontrivial bulk bandgap with decrease in width. The existence of such protected gapless edge states and reduction in threshold-voltage accompanied by enhancement in the bulk bandgap overturns the general wisdom of utilizing narrow-gap and wide channel materials for reducing the threshold-voltage in a standard field effect transistor analysis and paves the way toward low-voltage topological devices.