arXiv subjects

James H. Cullen

Publications and source records attributed to James H. Cullen.

13 recordsLinked to original sources

arXiv2026

Inter-band coherence effects in disordered crystals: beyond the non-crossing approximation

We develop a quantum kinetic theory for Bloch electrons driven by a uniform dc electric field, extending the nonequilibrium density-matrix formalism beyond the non-crossing approximation. This extension is required to capture steady-state terms that are nominally zeroth order in disorder strength and compete with intrinsic band-geometric responses, as in anomalous Hall and related spin, orbital, and valley transport. Working in the length gauge with Gaussian white-noise disorder, we include impurity scattering to fourth order in the disorder potential. An iterative solution for the impurity-induced density-matrix fluctuations yields a connected $V^4$ collision integral after subtracting disconnected impurity pairings, thereby avoiding double counting. The resulting terms separate into self-energy corrections, ladder-type vertex renormalization, and crossed quantum-interference contributions. We clarify the correspondence between this density-matrix kinetic equation and the Keldysh formalism, and decompose the response into Fermi-surface and Fermi-sea components. As an application, we study the two-dimensional massive Dirac fermion model. We obtain analytical expressions for the single-particle lifetime, transport relaxation time, and longitudinal conductivity at the Born level, and then evaluate the anomalous Hall conductivity including crossed impurity processes. These processes generate an extrinsic contribution of order $τ^0$ that coexists with the intrinsic Berry-curvature term; for Gaussian white-noise disorder in this model, the $Ψ$-type contribution cancels while the $X$-type term remains finite. The formalism provides a consistent route for incorporating band geometry and crossed-disorder corrections into multiband transport, with applications to spin, pseudospin, orbital, and valley phenomena.

cond-mat.mes-hall↗

arXiv2026

Orbital Hall effect in spin-3/2 hole-doped semiconductors and its implications for orbitronics

State-of-the-art magnetic devices rely on faster, more efficient memory elements. A major recent advance is the discovery of orbital torques, which use the orbital angular momentum of Bloch electrons to switch the magnetisation of an adjacent ferromagnet, motivating the search for orbitronic materials with strong orbital responses, exemplified by the orbital Hall effect (OHE). Here we propose $p$-type semiconductors, with a focus on Ge, as orbitronic platforms. We demonstrate that bulk holes in five common semiconductors exhibit a large orbital Hall conductivity of order $10^3 (\hbar/e)Ω^{-1}$cm$^{-1}$, exceeding the spin-Hall effect by 2-3 orders of magnitude. The calculation is performed within the framework of the modern theory of orbital magnetisation, while incorporating recently-discovered quantum corrections to the OHE. Moreover, we argue that bulk $p$-type Ge and Si serve as ideal testbeds for the orbital torque resulting from a charge current, since the spin- and orbital-Edelstein effects are forbidden by symmetry. Our results provide a blueprint for producing strong orbital torques in magnetic devices with $p$-type semiconductors, guiding experimental work in this direction.

cond-mat.mes-hall↗

arXiv2026

Ge as an orbitronic platform: giant in-plane orbital magneto-electric effect in a 2-dimensional hole gas

Increasing demand for computational power has initiated the hunt for energy efficient and stable memory devices. This is the overarching motivation behind the recent rise of \textit{orbitronics}, which looks to harness the orbital angular momentum of charge carriers in computing devices. Orbitronic devices require materials with efficient generation of orbital angular momentum (OAM). In 2D materials, OAM can be electrically generated via the orbital magneto-electric effect (OME). In this paper we report the calculation of the OME in 2 dimensional hole gases (2DHGs). We show that the OME in Ge holes is very large, for an applied electric field of the order $10^4$ V$/$m the OAM density is of the order $10^{12}$ $\hbar/$cm$^{2}$. Furthermore, we find the OME to be an order of magnitude larger than the Rashba-Edelstein effect in 2DHGs. The OME we calculated in 2DHGs generates OAM aligned in the plane and arises due to transitions between heavy and light hole states, which is unique to this system. Our results put Ge, as well as other p-type semiconductors, forward as strong candidates for building future orbitronic devices.

cond-mat.mes-hall↗

arXiv2025

Giant orbital Hall effect due to the bulk states of 3D topological insulators

The highly efficient torques generated by 3D topological insulators make them a favourable platform for faster and more efficient magnetic memory devices. Recently, research into harnessing orbital angular momentum in orbital torques has received significant attention. Here we study the orbital Hall effect in topological insulators. We find that the bulk states give rise to a sizeable orbital Hall effect that is up to 3 orders of magnitude larger than the spin Hall effect in topological insulators. This is partially because the orbital angular momentum that each conduction electron carries is up to an order of magnitude larger than the $\hbar/2$ carried by its spin. Our results imply that the large torques measured in topological insulator/ferromagnet devices can be further enhanced through careful engineering of the heterostructure to optimise orbital-to-spin conversion.

cond-mat.mes-hall↗

arXiv2025

Quantum geometry and dipolar dynamics in the orbital magneto-electric effect

We show that the orbital magneto-electric effect (OME) -- the generation of a steady-state orbital angular momentum density -- is partly the result of a nonequilibrium dipole moment generated via Zitterbewegung and proportional to the quantum metric. For tilted massive Dirac fermions this dipole gives the only contribution to the OME in the insulating case, while the intrinsic and extrinsic OMEs occur for different electric field orientations, yielding an experimental detection method. Our results suggest quantum metric engineering as a route towards maximizing orbital torques.

cond-mat.mes-hall↗

arXiv2025

Quantum correction to the orbital Hall effect

Evaluations of the orbital Hall effect (OHE) have only retained inter-band matrix elements of the position operator. Here we evaluate the OHE including all matrix elements of the position operator, including the technically challenging intra-band elements. We recover previous results and find quantum corrections due to the non-commutativity of the position and velocity operators and inter-band matrix elements of the orbital angular momentum. The quantum corrections dominate the OHE responses of the topological antiferromagnet CuMnAs and of massive Dirac fermions.

cond-mat.mes-hall↗

arXiv2024

Spin-orbit torques due to topological insulator surface states: an in-plane magnetization as a probe of extrinsic spin-orbit scattering

Topological insulator (TI) surface states exert strong spin-orbit torques. When the magnetization is in the plane its interaction with the TI conduction electrons is non-trivial, and is influenced by extrinsic spin-orbit scattering. This is expected to be strong in TIs but is difficult to calculate and to measure unambiguously. Here we show that extrinsic spin-orbit scattering sizably renormalizes the surface state spin-orbit torque resulting in a strong density dependence. The magnitude of the renormalization of the spin torque and the effect of spin-orbit scattering on the relative sizes of the in-plane and out-of-plane field-like torques have strong implications for experiment: We propose two separate experimental signatures for the measurement of its presence.

cond-mat.mes-hall↗

arXiv2024

Spin-Hall effect in topological materials: Evaluating the proper spin current in systems with arbitrary degeneracies

The spin-Hall effect underpins some of the most active topics in modern physics, including spin torques and the inverse spin-Hall effect, yet it lacks a proper theoretical description. This makes it difficult to differentiate the SHE from other mechanisms, as well as differentiate band structure and disorder contributions. Here, by exploiting recent analytical breakthroughs in the understanding of the intrinsic spin-Hall effect, we devise a density functional theory method for evaluating the conserved (proper) spin current in a generic system. Spin non-conservation makes the conventional spin current physically meaningless, while the conserved spin current has been challenging to evaluate since it involves the position operator between Bloch bands. The novel method we introduce here can handle band structures with arbitrary degeneracies and incorporates all matrix elements of the position operator, including the notoriously challenging diagonal elements, which are associated with Fermi surface, group velocity, and dipolar effects but often diverge if not treated correctly. We apply this method to the most important classes of spin-Hall materials: topological insulators, 2D quantum spin-Hall insulators, non-collinear antiferromagnets, and strongly spin-orbit coupled metals. We demonstrate that the torque dipole systematically suppresses contributions to the conventional spin current such that, the proper spin current is generally smaller in magnitude and often has a different sign. Remarkably, its energy-dependence is relatively flat and featureless, and its magnitude is comparable in all classes of materials studied. These findings will guide the experiment in characterizing charge-to-spin interconversion in spintronic and orbitronic devices. We also discuss briefly a potential generalisation of the method to calculate extrinsic spin currents generated by disorder scattering.

cond-mat.mes-hall↗

arXiv2023

Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current

The substantial amount of recent research into spin torques has been accompanied by a revival of interest in the spin-Hall effect. This effect contributes to the spin torque in many materials, including topological insulator/ferromagnet devices, Weyl semimetals, and van der Waals heterostructures. In general the relative sizes of competing spin torque mechanisms remain poorly understood. Whereas a consensus is beginning to emerge on the evaluation of a conserved spin current, the role of extrinsic disorder mechanisms in the spin-Hall effect has not been clarified. In this work we present a comprehensive calculation of the extrinsic spin Hall effect while focussing on the bulk states of topological insulators as a prototype system and employing a fully quantum mechanical formalism to calculate the proper spin current. Our calculation of the proper spin current employs a 4x4 k.p Hamiltonian describing the bulk states of topological insulators. At the same time, we provide a qualitative explanation of the proper spin currents calculated based on an effective $2\times2$ Hamiltonian obtained via a Schrieffer-Wolf transformation. We find that the extrinsic contribution to the proper spin current, driven by side jump, skew scattering and related mechanisms, is of a comparable magnitude to the intrinsic contribution, making it vital to take such disorder effects into account when seeking to understand experiments. Among the scattering effects considered, side jump scattering is the primary contributor to the extrinsic spin Hall effect. The total spin susceptibility calculated here is too small to explain experimentally measured spin torques, hence we expect the spin Hall effect to make a negligible contribution to the spin torque in topological insulator structures.

cond-mat.mes-hall↗

arXiv2023

Topological nature of the proper spin current and the spin-Hall torque

Spin currents are key to spin torque devices, but determining the proper spin current is non-trivial. Here we derive a general quantum-mechanical formula for the intrinsic proper spin current showing that it is topological and can be finite in the gap. For topological insulators with an out of plane magnetization and the chemical potential in the surface state gap, the net spin torque is determined by the competition between the topological spin-Hall torque due to the bulk and the topological Edelstein effect due to the surface states. We also discuss spin-3/2 hole quantum wells.

cond-mat.mes-hall↗

arXiv2023

Spin transfer torques due to the bulk states of topological insulators

Spin torques at topological insulator (TI)/ferromagnet interfaces have received considerable attention in recent years with a view towards achieving full electrical manipulation of magnetic degrees of freedom. The most important question in this field concerns the relative contributions of bulk and surface states to the spin torque, a matter that remains incompletely understood. Whereas the surface state contribution has been extensively studied, the contribution due to the bulk states has received comparatively little attention. Here we study spin torques due to TI bulk states and show that: (i) There is no spin-orbit torque due to the bulk states on a homogeneous magnetisation, in contrast to the surface states, which give rise to a spin-orbit torque via the well-known Edelstein effect. (ii) The bulk states give rise to a spin transfer torque (STT) due to the inhomogeneity of the magnetisation in the vicinity of the interface. This spin transfer torque, which has not been considered in TIs in the past, is somewhat unconventional since it arises from the interplay of the bulk TI spin-orbit coupling and the gradient of the monotonically decaying magnetisation inside the TI. Whereas we consider an idealised model in which the magnetisation gradient is small and the spin transfer torque is correspondingly small, we argue that in real samples the spin transfer torque should be sizable and may provide the dominant contribution due to the bulk states. We show that an experimental smoking gun for identifying the bulk states is the fact that the field-like component of the spin transfer torque generates a spin density with the same size but opposite sign for in-plane and out-of-plane magnetisations. This distinguishes them from the surface states, which are expected to give a spin density of a similar size and the same sign for both an in-plane and out-of-plane magnetisations.

cond-mat.mes-hall↗

arXiv2021

Optimal operation points for ultrafast, highly coherent Ge hole spin-orbit qubits

Strong spin-orbit interactions make hole quantum dots central to the quest for electrical spin qubit manipulation enabling fast, low-power, scalable quantum computation. Yet it is important to establish to what extent spin-orbit coupling exposes qubits to electrical noise, facilitating decoherence. Here, taking Ge as an example, we show that group IV gate-defined hole spin qubits generically exhibit optimal operation points, defined by the top gate electric field, at which they are both fast and long-lived: the dephasing rate vanishes to first order in electric field noise along all directions in space, the electron dipole spin resonance strength is maximised, while relaxation is drastically reduced at small magnetic fields. The existence of optimal operation points is traced to group IV crystal symmetry and properties of the Rashba spin-orbit interaction unique to spin-3/2 systems. Our results overturn the conventional wisdom that fast operation implies reduced lifetimes, and suggest group IV hole spin qubits as ideal platforms for ultra-fast, highly coherent scalable quantum computing.

cond-mat.mes-hall↗

arXiv2020

Generating a topological anomalous Hall effect in a non-magnetic conductor

The ordinary Hall effect is driven by the Lorentz force, while its anomalous counterpart occurs in ferromagnets. Here we show that the Berry curvature monopole of non-magnetic 2D spin-3/2 holes leads to a novel Hall effect linear in an applied in-plane magnetic field B_x. There is no Lorentz force hence no ordinary Hall effect, while all disorder contributions vanish to leading order in B_x. This intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a non-quantized footprint of topological transport directly accessible in p-type semiconductors.

cond-mat.mes-hall↗