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arXiv:1706.05545 · International Journal of Modern Physics B

Direct-exchange duality of the Coulomb interaction and collective excitations in graphene in a magnetic field

Ken-ichi Shizuya

Published Jun 8, 2017• 5 citations
arXivHTMLPDF

Abstract

In a magnetic field two-dimensional (2D) electron systems host, with quenched kinetic energy, a variety of many-body correlation phenomena, such as interaction-driven new states and associated collective excitations over them. In a magnetic field, the two-body operators pertinent to the 2D Coulomb interaction obey a crossing relation, with which the Coulomb interaction is also cast into the form of manifest exchange interaction. It is shown that active use of this direct/exchange duality of the interaction allows one to develop, within the framework of the single-mode approximation, a new efficient algorithm for handling a wide class of collective excitations. The utility of our algorithm is demonstrated by studying some examples of inter- and intra-Landau-level collective excitations in graphene and in conventional electron systems.

DOI
10.1142/s0217979217501764

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In a magnetic field two-dimensional (2D) electron systems host, with quenched kinetic energy, a variety of many-body correlation phenomena, such as interaction-driven new states and associated collective excitations over them. In a magnetic field, the two-body operators pertinent to the 2D Coulomb interaction obey a crossing relation, with which the Coulomb interaction is also cast into the form of manifest exchange interaction. It is shown that active use of this direct/exchange duality of the interaction allows one to develop, within the framework of the single-mode approximation, a new efficient algorithm for handling a wide class of collective excitations. The utility of our algorithm is demonstrated by studying some examples of inter- and intra-Landau-level collective excitations in graphene and in conventional electron systems.
An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a system of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons $(U\ensuremath{\approx}\ensuremath{\infty})$, repulsive nearest-neighbor (V>0)(V>0)(V>0) and small attractive $({V}^{\ensuremath{'}}<0)$ next-nearest-neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively pointlike, the detailed microscopic form of the short-range electrostatic and long-range dispersion interactions in the helium-graphene system is crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of 4He^{4}\mathrm{He}4He adsorbed on graphene deep in the commensurate solid phase with 1/31/31/3 of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.
A higher-order relativistic k.p model is developed to describe plasmon excitations in two-dimensional (2D) electronic systems with spin-orbit coupling (SOC) and magnetic-exchange interactions. Derived entirely from ab initio band structure, the model allows for a non-Rashba spin-momentum locking and enables a direct coupling of the exchange field to the real spin of electrons. Using the BiTeI trilayer (hexagonal C3v symmetry) and the Si-terminated surface state of TbRh2Si2 (cubic C4v symmetry) as prototypes, we show that the exchange field induces strong, symmetry-dependent modifications of the band structure and plasmon dispersion. In BiTeI, it breaks the sixfold symmetry and leads to anisotropic, nonreciprocal plasmon modes, while in TbRh2Si2 it suppresses the characteristic triple spin winding and alters the plasmon damping. The results reveal that the interplay between SOC and exchange magnetism enables magnetic control of collective charge excitations in 2D spin-orbit systems beyond the Rashba paradigm.
This is a mathematical study of certain aspects of the interacting electron system in very high perpendicular magnetic field.\nWe analyse restrictions imposed upon the density correlation functions of this system and propose a set of sum rules which they must obey.\nWe study the possibility of building a bosonisation scheme for the projected density operators in the lowest Landau level. We suggest a second order bosonisation, along with an approximation scheme, which may be useful for carrying out calculations in the lowest Landau level.\nWe analyse the possible ground states of the system. We suggest a set of variational wavefunctions which can have lower energy than the Laughlin state for sufficiently soft interaction potentials.\nWe study the collective excitations of the system, paying particular attention to its symmetries. We suggest a set of variational excited states and discuss their applicability to finite as well as infinite systems.
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Abstract Atoms deposited on 2D electronic materials, such as graphene, can exhibit unconventional many‐body correlations, not accessible in other settings. All of these are driven by van der Waals forces: between the atoms themselves and atom‐material interactions. For example 4He atoms on 2D materials can potentially form a variety of exotic quantum states of matter, such as 2D supersolids and superfluids, in addition to solid phases. For the “most quantum” case of a single helium layer we discuss, from a theoretical perspective, how the effective low‐energy (Bose–Hubbard) description can take advantage of the extreme sensitivity of this unique system to the interplay between the atomic (helium) and solid‐state (graphene) components. Due to the extraordinary variety and tunability of 2D electronic materials, it is envisaged that a wide range of correlated atomic phases can be realized under favorable conditions. Exciting possibilities in the opposite extreme of many atomic layers forming a liquid on top of graphene are also outlined —in this case a so‐called “spinodal dewetting” pattern can form at the liquid–vapor interface which reflects the presence and electronic properties of graphene underneath. Such patterns could be manipulated by choosing different atoms and materials, with potential technological applications.