T. M. Fromhold

Resonant tunnelling and negative differential conductance in graphene transistors.

The chemical stability of graphene and other free-standing two-dimensional crystals means that they can be stacked in different combinations to produce a new class of functional materials, designed for specific device applications. Here we report resonant tunnelling of Dirac fermions through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. The resonance occurs when the electronic spectra of the two electrodes are aligned. The resulting negative differential conductance in the device characteristics persists up to room temperature and is gate voltage-tuneable due to graphene’s unique Dirac-like spectrum. Although conventional resonant tunnelling devices comprising a quantum well sandwiched between two tunnel barriers are tens of nanometres thick, the tunnelling carriers in our devices cross only a few atomic layers, offering the prospect of ultra-fast transit times. This feature, combined with the multi-valued form of the device characteristics, has potential for applications in high-frequency and logic devices.

Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures

Recent developments in the technology of van der Waals heterostructures made from two-dimensional atomic crystals have already led to the observation of new physical phenomena, such as the metal-insulator transition and Coulomb drag, and to the realization of functional devices, such as tunnel diodes, tunnel transistors and photovoltaic sensors. An unprecedented degree of control of the electronic properties is available not only by means of the selection of materials in the stack, but also through the additional fine-tuning achievable by adjusting the built-in strain and relative orientation of the component layers. Here we demonstrate how careful alignment of the crystallographic orientation of two graphene electrodes separated by a layer of hexagonal boron nitride in a transistor device can achieve resonant tunnelling with conservation of electron energy, momentum and, potentially, chirality. We show how the resonance peak and negative differential conductance in the device characteristics induce a tunable radiofrequency oscillatory current that has potential for future high-frequency technology.

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices.

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov–Arnold–Moser (KAM) theorem—a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, ‘non-KAM’ chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

Controlling and enhancing terahertz collective electron dynamics in superlattices by chaos-assisted miniband transport

We show that a tilted magnetic field transforms the structure and THz dynamics of charge domains in a biased semiconductor superlattice. At critical field values, strong coupling between the Bloch and cyclotron motion of a miniband electron triggers chaotic delocalization of the electron orbits, causing strong resonant enhancement of their drift velocity. This dramatically affects the collective electron behavior by inducing multiple propagating charge domains and GHz-THz current oscillations with frequencies ten times higher than with no tilted field.

Effect of temperature on resonant electron transport through stochastic conduction channels in superlattices

We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room temperature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localized to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric-field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between the thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency.

Graphene-hexagonal boron nitride resonant tunneling diodes as high-frequency oscillators

We assess the potential of two-terminal graphene-hexagonal boron nitride-graphene resonant tunneling diodes as high-frequency oscillators, using self-consistent quantum transport and electrostatic simulations to determine the time-dependent response of the diodes in a resonant circuit. We quantify how the frequency and power of the current oscillations depend on the diode and circuit parameters including the doping of the graphene electrodes, device geometry, alignment of the graphene lattices, and the circuit impedances. Our results indicate that current oscillations with frequencies of up to several hundred GHz should be achievable.

Tailoring the electronic properties of GaAs/AlAs superlattices by InAs layer insertions

We investigate the electrical and optical properties of GaAs/AlAs superlattices (SLs) in which a thin (⩽1.2 monolayers) InAs layer is inserted in the central plane of each GaAs quantum well. The InAs layer modifies the structure of the SL unit cell and provides an additional design parameter for tailoring the energy of the lowest miniband and the size of the minigap. We exploit this effect to enhance electron injection from a doped contact layer into the first miniband and to inhibit interminiband coupling.

Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field

We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics.

Resonant tunnelling between the chiral Landau states of twisted graphene lattices

A class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer. An exemplar of such a structure is a transistor device in which relativistic Dirac fermions can resonantly tunnel through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. An applied magnetic field quantizes graphene’s gapless conduction and valence band states into discrete Landau levels, allowing us to resolve individual inter-Landau-level transitions and thereby demonstrate that the energy, momentum and chiral properties of the electrons are conserved in the tunnelling process. We also demonstrate that the change in the semiclassical cyclotron trajectories, following an inter-layer tunnelling event, is analogous to the case of intra-layer Klein tunnelling. For small twist angles, electrons can resonantly tunnel between graphene layers in a van der Waals heterostructure. It is now shown that the tunnelling not only preserves energy and momentum, but also the chirality of electronic states.

Controlling high-frequency collective electron dynamics via single-particle complexity

We demonstrate, through experiment and theory, enhanced high-frequency current oscillations due to magnetically-induced conduction resonances in superlattices. Strong increase in the ac power originates from complex single-electron dynamics, characterized by abrupt resonant transitions between unbound and localized trajectories, which trigger and shape propagating charge domains. Our data demonstrate that external fields can tune the collective behavior of quantum particles by imprinting configurable patterns in the single-particle classical phase space.