arXiv subjects
Publications and source records attributed to Allan H. MacDonald.
We show that quasi-one-dimensional (1D) quantum wires can be written onto the surface of magnetic topological insulator (MTI) thin films by gate arrays. When the MTI is in a quantum anomalous Hall (QAH) state, MTI$/$superconductor quantum wires have especially broad stability regions for both topological and non-topological states, facilitating creation and manipulation of Majorana particles on the MTI surface.
Antiferromagnetic insulators (AFMI) are robust against stray fields, and their intrinsic dynamics could enable ultrafast magneto-optics and ultrascaled magnetic information processing. Low dissipation, long distance spin transport and electrical manipulation of antiferromagnetic order are much sought-after goals of spintronics research. Here, we report the first experimental evidence of robust long-distance spin transport through an AFMI, in our case the gate-controlled, canted antiferromagnetic (CAF) state that appears at the charge neutrality point of graphene in the presence of an external magnetic field. Utilizing gate-controlled quantum Hall (QH) edge states as spin-dependent injectors and detectors, we observe large, non-local electrical signals across a 5 micron-long, insulating channel only when it is biased into the nu=0 CAF state. Among possible transport mechanisms, spin superfluidity in an antiferromagnetic state gives the most consistent interpretation of the non-local signal's dependence on magnetic field, temperature and filling factors. This work also demonstrates that graphene in the QH regime is a powerful model system for fundamental studies of antiferromagnetic, and in the case of a large in-plane field, ferromagnetic spintronics.
We present a combined experimental and theoretical study of valley populations in the valence bands of trilayer WSe$_2$. Shubnikov$-$de Haas oscillations show that trilayer holes populate two distinct subbands associated with the $K$ and $Γ$ valleys, with effective masses 0.5$m_e$ and $1.2m_e$, respectively; $m_e$ is the bare electron mass. At a fixed total hole density, an applied transverse electric field transfers holes from $Γ$ orbitals to $K$ orbitals. We are able to explain this behavior in terms of the larger layer polarizability of the $K$ orbital subband.
We present a general quantum kinetic theory of low-field magnetotransport in weakly disordered crystals that accounts fully for the interplay between electric-field induced interband coherence, Bloch-state scattering, and an external magnetic field. The quantum kinetic equation we derive for the Bloch-state density matrix naturally incorporates the momentum-space Berry phase effects whose influence on Bloch-state wavepacket dynamics is normally incorporated into transport theory in an ad hoc manner. The Berry phase correction to the momentum-space density of states in the presence of an external magnetic field implied by semiclassical wavepacket dynamics is captured by our theory as an intrinsic density-matrix response to a magnetic field. We propose a simple and general procedure for expanding the linear response of the Bloch-state density matrix to an electric field in powers of magnetic field. As an illustration, we apply our theory to magnetotransport in Weyl semimetals. We show that the chiral anomaly (positive magnetoconductivity quadratic in magnetic field) that appears when separate Fermi surface pockets surround distinct Weyl points survives only when intervalley scattering is very weak compared to intravalley scattering.
The discovery of intriguing properties related to the Dirac states in graphene has spurred huge interest in exploring its two-dimensional group-IV counterparts, such as silicene, germanene, and stanene. However, these materials have to be obtained via synthesizing on substrates with strong interfacial interactions, which usually destroy their intrinsic $π$($p_z$)-orbital Dirac states. Here we report a theoretical study on the existence of Dirac states arising from the $p_{x,y}$ orbitals instead of $p_z$ orbitals in silicene on 4H-SiC(0001), which survive in spite of the strong interfacial interactions. We also show that the exchange field together with the spin-orbital coupling give rise to a detectable band gap of 1.3 meV. Berry curvature calculations demonstrate the nontrivial topological nature of such Dirac states with a Chern number $C = 2$, presenting the potential of realizing quantum anomalous Hall effect for silicene on SiC(0001). Finally, we construct a minimal effective model to capture the low-energy physics of this system. This finding is expected to be also applicable to germanene and stanene, and imply great application potentials in nanoelectronics.
We systematically investigate the electronic structure and magnetic properties of two dimensional (2D) MPX$_3$ (M= V, Cr, Mn, Fe, Co, Ni, Cu, Zn, and X = S, Se, Te) transition metal chacogenophosphates to examine their potential role as single-layer van der Waals materials that exhibit magnetic order. Our {\em ab initio} calculations predict that most of these single-layer materials are antiferromagnetic semiconductors. The band gaps of the antiferromagnetic states decrease as the atomic number of the chalcogen atom increases (from S to Se, Te), leading in some cases to half-metallic ferromagnetic states or to non-magnetic metallic states. We find that the phase transition from antiferromagnetic semiconductor to ferromagnetic half-metal can be controlled by gating or by strain engineering. The sensitive interdependence we find between magnetic, structural, and electronic properties establishes the potential of this 2D materials class for applications in spintronics.
We present a density functional theory study of the carrier-density and strain dependence of magnetic order in two-dimensional (2D) MAX$_3$ (M= V, Cr, Mn, Fe, Co, Ni; A= Si, Ge, Sn, and X= S, Se, Te) transition metal trichalcogenides. Our {\em ab initio} calculations show that this class of compounds includes wide and narrow gap semiconductors and metals and half-metals, and that most of these compounds are magnetic. Although antiferromagnetic order is most common, ferromagnetism is predicted in MSiSe$_3$ for M= Mn, Ni, in MSiTe$_3$ for M= V, Ni, in MnGeSe$_3$, in MGeTe$_3$ for M=Cr, Mn, Ni, in FeSnS$_3$, and in MSnTe$_3$ for M= V, Mn, Fe. Among these compounds CrGeTe$_3$ and VSnTe$_3$ are ferromagnetic semiconductors. Our calculations suggest that the competition between antiferromagnetic and ferromagnetic order can be substantially altered by strain engineering, and in the semiconductor case also by gating. The associated critical temperatures can be substantially enhanced by means of carrier doping and strains.
In solid state conductors, linear response to a steady electric field is normally dominated by Bloch state occupation number changes that are correlated with group velocity and lead to a steady state current. However, for a number of important physical observables, the most important response even in conductors can be electric-field induced coherence between Bloch states in different bands, such as that responsible for screening in dielectrics. Examples include the anomalous and spin-Hall effects, spin torques, minimum conductivities and the chiral anomaly. In this paper we present a general quantum kinetic theory of linear response to an electric field which can be applied to solids with arbitrarily complicated band structures and includes the inter-band coherence response and the Bloch-state repopulation responses on an equal footing. We aim to enable extensive transport theory applications using computational packages based on maximally localized Wannier functions. The formalism is based on density-matrix equations of motion, on a Born approximation treatment of disorder, and on an expansion in scattering rate to leading non-trivial order. The quasiparticle bands are treated in a completely general manner that allows for arbitrary forms of the spin-orbit interaction and for the broken time reversal symmetry of magnetic conductors. We demonstrate that the inter-band response in conductors consists primarily of two terms: an intrinsic contribution due to the entire Fermi sea that captures the Berry curvature contribution to wave-packet dynamics, and an anomalous contribution caused by scattering that is sensitive to the presence of the Fermi surface. We solve for some electric-field response properties of simple model systems that are known to be dominated by interband coherence contributions and discuss an extensive list of complicated problems that cannot be solved analytically.
Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moiré pattern pseudospin fields. Here, we present the moiré-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab-initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moiré patterns, leading to primary Dirac point gaps when the moiré strains give rise to a finite average mass, and to secondary gaps when the moiré pseudospin components are mixed appropriately. The pseudomagnetic strain fields which can reach values of up to $\sim$40 Tesla near symmetry points in the moiré cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moiré strains.
The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a chapter in the spintronics story. In this article, we review the emerging research field that is exploring synergies between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in an antiferromagnetic topological superconductors, to control topological protection of Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of zero net moment antiferromagnets. We explain the basic physics concepts behind these proposals, and discuss potential applications of topological antiferromagnetic spintronics.
The spin-Seebeck effect refers to voltage signals induced in metals by thermally driven spin currents in adjacent magnetic systems. We present a theory of the spin-Seebeck signal in the case where the conductor that supports the voltage signal is the topologically protected two-dimensional surface-state system at the interface between a ferromagnetic insulator (FI) and a topological insulator (TI). Our theory uses a Dirac model for the TI surface-states and assumes Heisenberg exchange coupling between the TI quasiparticles and the FI magnetization. The spin-Seebeck voltage is induced by the TI surface states scattering off the nonequilibrium magnon population at the surface of the semi-infinite thermally driven FI. Our theory is readily generalized to spin-Seebeck voltages in any two-dimensional conductor that is exchange-coupled to the surface of a FI. Surface-state carrier-density-dependent signal strengths calculated using Bi$_2$Te$_3$ and yttrium iron garnet material parameters are consistent with recent experiments.
According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moiré patterns produced by small misalignments between its individual layer honeycomb lattices. We have realized bilayer graphene moiré crystals with accurately controlled twist angles smaller than 1 degree and studied their properties using scanning probe microscopy and electron transport. We observe conductivity minima at charge neutrality, satellite gaps that appear at anomalous carrier densities for twist angles smaller than 1 degree, and tunneling densities-of-states that are strongly dependent on carrier density. These features are robust up to large transverse electric fields. In perpendicular magnetic fields, we observe the emergence of a Hofstadter butterfly in the energy spectrum, with four-fold degenerate Landau levels, and broken symmetry quantum Hall states at filling factors 1, 2, 3. These observations demonstrate that at small twist angles, the electronic properties of bilayer graphene moiré crystals are strongly altered by electron-electron interactions.
Recent optical studies of monolayer transition metal dechalcogenides have demonstrated that their excitonic absorption feature splits into two widely separated peaks at finite carrier densities. The additional peak is usually attributed to the presence of trions, bound states of two electrons and a hole or an electron and two holes. Here we argue that in the density range over which the trion peak is well resolved, it cannot be interpreted in terms of weakly coupled three-body systems, and that the appropriate picture is instead one in which excitons are dressed by interactions with a Fermi sea of excess carriers. This coupling splits the exciton spectrum into a lower energy attractive exciton-polaron branch, normally identified as a trion branch, and a higher energy repulsive exciton-polaron branch, normally identified as an exciton branch. We have calculated the frequency and doping dependence of the optical conductivity and found that: (i) the splitting varies linearly with the Fermi energy of the excess quasiparticles; (ii) the trion peak is dominant at high carrier densities; (iii) and the trion peak width is considerably smaller than that of the excitonic peak. Our results are in good agreement with recent experiments.
The classical picture of the force on a capacitor assumes a large density of electronic states, such that the electrochemical potential of charges added to the capacitor is given by the external electrostatic potential and the capacitance is determined purely by geometry. Here we consider capacitively driven motion of a nano-mechanical resonator with a low density of states, in which these assumptions can break down. We find three leading-order corrections to the classical picture: the first of is a modulation in the static force due to variation in the internal chemical potential, the second and third are change in static force and dynamic spring constant due to the rate of change of chemical potential, expressed as the quantum (density of states) capacitance. As a demonstration, we study a capacitively driven graphene mechanical resonators, where the chemical potential is modulated independently of the gate voltage using an applied magnetic field to manipulate the energy of electrons residing in discrete Landau levels. In these devices, we observe large periodic frequency shifts consistent with the three corrections to the classical picture. In devices with extremely low strain and disorder, the first correction term dominates and the resonant frequency closely follows the chemical potential. The theoretical model fits the data with only one adjustable parameter representing disorder-broadening of the Landau levels. The underlying electromechanical coupling mechanism is not limited the particular choice of material, geometry, or mechanism for variation in chemical potential, and can thus be extended to other low-dimensional systems.
We present a theory of spatially indirect exciton condensate states in systems composed of a pair of electrically isolated Bernal graphene bilayers. The ground state phase diagram in a two-dimensional displacement-field/inter-bilayer-bias space includes layer-polarized semiconductors, spin-density-wave states, exciton condensates, and states with mixed excitonic and spin order. We find that two different condensate states, distinguished by a chirality index, are stable under different electrical control conditions.
There is growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime in which electron-electron interactions are expected to play a pivotal role. Focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron-electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which soften at a characteristic wave vector of the order of the inverse magnetic length.
The emerging field of valleytronics aims to exploit the valley pseudospin of electrons residing near Bloch band extrema as an information carrier. Recent experiments demonstrating optical generation and manipulation of exciton valley coherence (the superposition of electron-hole pairs at opposite valleys) in monolayer transition metal dichalcogenides (TMDs) provide a critical step towards control of this quantum degree of freedom. The charged exciton (trion) in TMDs is an intriguing alternative to the neutral exciton for control of valley pseudospin because of its long spontaneous recombination lifetime, its robust valley polarization, and its coupling to residual electronic spin. Trion valley coherence has however been unexplored due to experimental challenges in accessing it spectroscopically. In this work, we employ ultrafast two-dimensional coherent spectroscopy to resonantly generate and detect trion valley coherence in monolayer MoSe$_2$ demonstrating that it persists for a few-hundred femtoseconds. We conclude that the underlying mechanisms limiting trion valley coherence are fundamentally different from those applicable to exciton valley coherence. Based on these observations, we suggest possible strategies for extending valley coherence times in two-dimensional materials.
Nematic quantum fluids with wavefunctions that break the underlying crystalline symmetry can form in interacting electronic systems. We examine the quantum Hall states that arise in high magnetic fields from anisotropic hole pockets on the Bi(111) surface. Spectroscopy performed with a scanning tunneling microscope shows that a combination of local strain and many-body Coulomb interactions lift the six-fold Landau level (LL) degeneracy to form three valley-polarized quantum Hall states. We image the resulting anisotropic LL wavefunctions and show that they have a different orientation for each broken-symmetry state. The wavefunctions correspond precisely to those expected from pairs of hole valleys and provide a direct spatial signature of a nematic electronic phase.