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Papers by Romilly Hills

Research paper thumbnail of Current-Voltage Characteristics of Weyl Semimetal Semiconducting Devices, Veselago Lenses and Hyperbolic Dirac Phase

The current-voltage characteristics of a new range of devices built around Weyl semimetals has be... more The current-voltage characteristics of a new range of devices built around Weyl semimetals has been predicted using the Landauer formalism. The potential step and barrier have been reconsidered for a three-dimensional Weyl semimetals, with analogies to the two-dimensional material graphene and to optics. With the use of our results we also show how a Veselago lens can be made from Weyl semimetals, e.g. from NbAs and NbP. Such a lens may have many practical applications and can be used as a probing tip in a scanning tunneling microscope (STM). The ballistic character of Weyl fermion transport inside the semimetal tip, combined with the ideal focusing of the Weyl fermions (by Veselago lens) on the surface of the tip may create a very narrow electron beam from the tip to the surface of the studied material. With a Weyl semimetal probing tip the resolution of the present STMs can be improved significantly, and one may image not only individual atoms but also individual electron orbitals or chemical bonding and therewith to resolve the long-term issue of chemical and hydrogen bond formation. We show that applying a pressure to the Weyl semimental, having no centre of spacial inversion one may model matter at extreme conditions such as those arising in the vicinity of a black hole. As the materials Cd3As2 and Na3Bi show an asymmetry in their Dirac cones, a scaling factor was used to model this asymmetry. The scaling factor created additional regions of no propagation and condensed the appearance of resonances. We argue that under an external pressure there may arise a topological phase transition in Weyl semimetals, where the electron transport changes character and becomes anisotropic. There a hyperbolic Dirac phases occurs where there is a strong light absorption and photo-current generation.

Research paper thumbnail of Physical Properties of Zener Tunnelling Nano-devices in Graphene

By considering the direction of charge carriers and the conservation of probablity current the tr... more By considering the direction of charge carriers and the conservation of probablity current the transmission properties of graphene Zener tunnelling nano-devices were obtained. The scattering properties were then used with an adaptation of the Landauer formalism to calculate an analytical expression for current and conductance. The numerical results of the IV characteristics were then briefly discussed for the graphene step and Zener barrier. A comparison between the theoretical model and experimental results shows the similarities of graphene nanoribbons and infinite sheet graphene.

Books by Romilly Hills

Research paper thumbnail of From graphene and topological insulators to Weyl semimetals

Symmetry, Spin Dynamics and the Properties of Nanostructures, Dec 2015

Here we present a short introduction into physics of Dirac materials. In particular we review mai... more Here we present a short introduction into physics of Dirac materials. In particular we review main physical properties of various two-dimensional crystals such as graphene, sil-icene, germanene and others. We comment on the origin of their buckled two-dimensional shape, and address the issues created by Mermin-Wagner theorem prohibiting the existence of strictly two-dimensional, flat crystals. Then we describe main ideas which were leading to the discovery of two and three-dimensional topological insulators and Weyl fermions. We describe some of their outstanding electronic properties which have been originating due to the existence of the Dirac gapless spectrum. We also compare simplest devices made of Dirac materials. Analogies and differences between Dirac materials and optics are also discussed.

Thesis Chapters by Romilly Hills

Research paper thumbnail of Physical properties of graphene nano-devices

In this doctoral thesis the two dimensional material graphene has been studied in depth with part... more In this doctoral thesis the two dimensional material graphene has been studied in depth with particular respect to Zener tunnelling devices. From the hexagonal structure the Hamiltonian at a Dirac point was derived with the option of including an energy gap.
This Hamiltonian was then used to obtain the tunnelling properties of various graphene nano-devices; the devices studied include Zener tunnelling potential barriers such as single and double graphene potential steps. A form of the Landauer formalism was obtained for graphene devices. Combined with the scattering properties of potential barriers the current and conductance was found for a wide range of graphene nano-devices. These results were then compared to recently obtained experimental results for graphene nanoribbons, showing many similarities between nanoribbons and infinite sheet graphene. The methods studied were then applied to materials which have been shown to possess three dimensional Dirac cones known as topological insulators. In the case of Cd3As2 the Dirac cone is asymmetrical with respect to the z direction, the effect of this asymmetry has been discussed with comparison to the symmetrical case.

Research paper thumbnail of Current-Voltage Characteristics of Weyl Semimetal Semiconducting Devices, Veselago Lenses and Hyperbolic Dirac Phase

The current-voltage characteristics of a new range of devices built around Weyl semimetals has be... more The current-voltage characteristics of a new range of devices built around Weyl semimetals has been predicted using the Landauer formalism. The potential step and barrier have been reconsidered for a three-dimensional Weyl semimetals, with analogies to the two-dimensional material graphene and to optics. With the use of our results we also show how a Veselago lens can be made from Weyl semimetals, e.g. from NbAs and NbP. Such a lens may have many practical applications and can be used as a probing tip in a scanning tunneling microscope (STM). The ballistic character of Weyl fermion transport inside the semimetal tip, combined with the ideal focusing of the Weyl fermions (by Veselago lens) on the surface of the tip may create a very narrow electron beam from the tip to the surface of the studied material. With a Weyl semimetal probing tip the resolution of the present STMs can be improved significantly, and one may image not only individual atoms but also individual electron orbitals or chemical bonding and therewith to resolve the long-term issue of chemical and hydrogen bond formation. We show that applying a pressure to the Weyl semimental, having no centre of spacial inversion one may model matter at extreme conditions such as those arising in the vicinity of a black hole. As the materials Cd3As2 and Na3Bi show an asymmetry in their Dirac cones, a scaling factor was used to model this asymmetry. The scaling factor created additional regions of no propagation and condensed the appearance of resonances. We argue that under an external pressure there may arise a topological phase transition in Weyl semimetals, where the electron transport changes character and becomes anisotropic. There a hyperbolic Dirac phases occurs where there is a strong light absorption and photo-current generation.

Research paper thumbnail of Physical Properties of Zener Tunnelling Nano-devices in Graphene

By considering the direction of charge carriers and the conservation of probablity current the tr... more By considering the direction of charge carriers and the conservation of probablity current the transmission properties of graphene Zener tunnelling nano-devices were obtained. The scattering properties were then used with an adaptation of the Landauer formalism to calculate an analytical expression for current and conductance. The numerical results of the IV characteristics were then briefly discussed for the graphene step and Zener barrier. A comparison between the theoretical model and experimental results shows the similarities of graphene nanoribbons and infinite sheet graphene.

Research paper thumbnail of From graphene and topological insulators to Weyl semimetals

Symmetry, Spin Dynamics and the Properties of Nanostructures, Dec 2015

Here we present a short introduction into physics of Dirac materials. In particular we review mai... more Here we present a short introduction into physics of Dirac materials. In particular we review main physical properties of various two-dimensional crystals such as graphene, sil-icene, germanene and others. We comment on the origin of their buckled two-dimensional shape, and address the issues created by Mermin-Wagner theorem prohibiting the existence of strictly two-dimensional, flat crystals. Then we describe main ideas which were leading to the discovery of two and three-dimensional topological insulators and Weyl fermions. We describe some of their outstanding electronic properties which have been originating due to the existence of the Dirac gapless spectrum. We also compare simplest devices made of Dirac materials. Analogies and differences between Dirac materials and optics are also discussed.

Research paper thumbnail of Physical properties of graphene nano-devices

In this doctoral thesis the two dimensional material graphene has been studied in depth with part... more In this doctoral thesis the two dimensional material graphene has been studied in depth with particular respect to Zener tunnelling devices. From the hexagonal structure the Hamiltonian at a Dirac point was derived with the option of including an energy gap.
This Hamiltonian was then used to obtain the tunnelling properties of various graphene nano-devices; the devices studied include Zener tunnelling potential barriers such as single and double graphene potential steps. A form of the Landauer formalism was obtained for graphene devices. Combined with the scattering properties of potential barriers the current and conductance was found for a wide range of graphene nano-devices. These results were then compared to recently obtained experimental results for graphene nanoribbons, showing many similarities between nanoribbons and infinite sheet graphene. The methods studied were then applied to materials which have been shown to possess three dimensional Dirac cones known as topological insulators. In the case of Cd3As2 the Dirac cone is asymmetrical with respect to the z direction, the effect of this asymmetry has been discussed with comparison to the symmetrical case.