The Holstein Hamiltonian describes fermions hopping on a lattice and interacting locally with dispersionless phonon degrees of freedom. In the low-density limit, dressed quasiparticles, polarons and bipolarons, propagate with an effective mass. At higher densities, pairs can condense into a low-temperature superconducting phase and, at or near commensurate filling on a bipartite lattice, to charge density wave (CDW) order. CDW formation breaks a discrete symmetry and hence occurs via a second-order (Ising) transition and therefore at a finite ${T}_{\mathrm{cdw}}$ in two dimensions. Quantum Monte Carlo calculations have determined ${T}_{\mathrm{cdw}}$ for a variety of geometries, including square, honeycomb, and Lieb lattices. The superconducting transition, on the other hand, in $d=2$ is in the Kosterlitz-Thouless universality class and is much less well characterized. In this paper we determine ${T}_{\mathrm{sc}}$ for the square lattice for several values of the density $\ensuremath{\rho}$ and phonon frequency ${\ensuremath{\omega}}_{0}$. We find that quasilong-range order sets in at ${T}_{\mathrm{sc}}\ensuremath{\lesssim}t/20$, where $t$ is the near-neighbor hopping amplitude, consistent with previous rough estimates from simulations which extrapolated to only the temperatures we reach from considerably higher $T$. We also show evidence of a discontinuous evolution of the density as the CDW transition is approached at half filling.

Superconductivity and charge density wave order in the two-dimensional Holstein model

We present an experimental study of the infrared conductivity, transmission, and reflection of a gated bilayer graphene and their theoretical analysis within the Slonczewski-Weiss-McClure (SWMc) model. The infrared response is shown to be governed by the interplay of the interband and the intraband transitions among the four bands of the bilayer. The position of the main conductivity peak at the charge-neutrality point is determined by the interlayer tunneling frequency. The shift of this peak as a function of the gate voltage gives information about less known parameters of the SWMc model such as those responsible for the electron-hole and sublattice asymmetries. These parameter values are shown to be consistent with recent electronic structure calculations for the bilayer graphene and the SWMc parameters commonly used for the bulk graphite.

Determination of the electronic structure of bilayer graphene from infrared spectroscopy results

Band gap variation in bi, tri and few-layered 2D graphene/hBN heterostructures

Using the momentum average approximation we study the importance of adding higher-than-linear terms in the electron-phonon coupling on the properties of single polarons described by a generalized Holstein model. For medium and strong linear coupling, even small quadratic electron-phonon coupling terms are found to lead to very significant quantitative changes in the properties of the polaron, which cannot be captured by a linear Holstein Hamiltonian with renormalized parameters. We argue that the bi-polaron phase diagram is equally sensitive to addition of quadratic coupling terms if the linear coupling is large. These results suggest that the linear approximation is likely to be inappropriate to model systems with strong electron-phonon coupling, at least for low carrier concentrations.

https://www.phas.ubc.ca/%7Eberciu/PAPERS/paper71.pdf

Going beyond the linear approximation in describing electron-phonon coupling: Relevance for the Holstein model

Going beyond the linear approximation in describing electron- phonon coupling: relevance for the Holstein model

We use numerically exact quantum Monte Carlo (QMC) to compute the properties of three-dimensional bipolarons for interaction strengths where perturbation theory fails. For intermediate electron-phonon coupling and Hubbard $U$, we find that bipolarons can be both small and light, a prerequisite for bipolaron superconductivity. We use the QMC results to make estimates of transition temperatures, which peak at between 90--120 K and are demonstrated to be insensitive to Coulomb repulsion and impurities.

Mobile small bipolarons on a three-dimensional cubic lattice

For graphene to be utilized in the digital electronics industry the challenge is to create bandgaps of order 1 eV as simply as possible. The most successful methods for the creation of gaps in graphene are (a) confining the electrons in nanoribbons, which is technically difficult or (b) placing a potential difference across bilayer graphene, which is limited to gaps of around 300 meV for reasonably sized electric fields. Here we propose that electronic band gaps can be created without applying an external electric field, by using the electron–phonon interaction formed when bilayer graphene is sandwiched between highly polarisable ionic materials. We derive and solve self-consistent equations, finding that a large gap can be formed for intermediate electron–phonon coupling. The gap originates from the amplification of an intrinsic Coulomb interaction due to the proximity of carbon atoms in neighbouring planes.

https://iopscience.iop.org/article/10.1088/0953-8984/26/22/225601/pdf

Bias free gap creation in bilayer graphene.

For graphene to be utilized in the digital electronics industry the challenge is to create bandgaps of order 1eV as simply as possible. The most successful methods for the creation of gaps in graphene are (a) confining the electrons in nanoribbons, which is technically difficult or (b) placing a potential difference across bilayer graphene, which is limited to gaps of around 300meV for reasonably sized electric fields. Here we propose that electronic band gaps can be created without applying an external electric field, by using the electron-phonon interaction formed when bilayer graphene is sandwiched between highly polarisable ionic materials. We derive and solve self-consistent equations, finding that a large gap can be formed for intermediate electron-phonon coupling. The gap originates from the amplification of an intrinsic Coulomb interaction due to the proximity of carbon atoms in neighbouring planes.

Bias Free Gap Creation in Bilayer Graphene

Bilayers of graphitic materials have potential applications in field effect transistors (FETs). A potential difference applied between certain ionic bilayers made from insulating graphitic materials such as BN, ZnO and AlN could reduce gap sizes, turning them into useful semiconductors. On the other hand, opening of a small semiconducting gap occurs in graphene bilayers under applied field. The aim here is to investigate to what extent substrate induced electron–phonon interactions (EPIs) modify this gap change. We examine EPIs in several lattice configurations of graphitic bilayers, using a perturbative approach. The typical effect of EPIs on the ionic bilayers is an undesirable gap widening. The size of this gap change varies considerably with lattice structure and the magnitude of the bias. When bias is larger than the non-interacting gap size, EPIs have the smallest effect on the bandgap, especially in configurations with $A{{A}^{\prime}}$ and $AB$ structures. Thus careful selection of substrate, lattice configuration and bias strength to minimise the effects of EPIs could be important for optimising the properties of electronic devices. We use parameters related to BN in this article. In practice, the results presented here are broadly applicable to other graphitic bilayers, and are likely to be qualitatively similar in metal dichalcogenide bilayers such as MoS2, which are already of high interest for their use in FETs.

/pdf/role-of-substrate-induced-electron-phonon-interactions-in-5m4euaaqf4.pdf

Role of substrate induced electron-phonon interactions in biased graphitic bilayers.

Bilayers of graphitic materials have potential applications in field effect transistors (FETs). A potential difference applied between certain ionic bilayers made from insulating graphitic materials such as BN, ZnO and AlN could reduce gap sizes, turning them into useful semiconductors. On the other hand, opening of a small semiconducting gap occurs in graphene bilayers under applied field. The aim here is to investigate to what extent substrate induced electron-phonon interactions (EPIs) modify this gap change. We examine EPIs in several lattice configurations, using a perturbative approach. The typical effect of EPIs on the ionic bilayers is an undesirable gap widening. The size of this gap change varies considerably with lattice structure and the magnitude of the bias. When bias is larger than the non-interacting gap size, EPIs have the smallest effect on the bandgap, especially in configurations with $AA^{\prime}$ and $AB$ structures. Thus careful selection of substrate, lattice configuration and bias strength to minimise the effects of EPIs could be important for optimising the properties of electronic devices. We use parameters related to BN in this article. In practice, the results presented here are broadly applicable to other graphitic bilayers, and are likely to be qualitatively similar in metal dichalcogenide bilayers such as MoS$_2$, which are already of high interest for their use in FETs.

/pdf/role-of-substrate-induced-electron-phonon-interactions-in-5em5q41hl2.pdf

A. R. Davenport

Papers

Mobile small bipolarons on a three-dimensional cubic lattice

Bias free gap creation in bilayer graphene.

Bias Free Gap Creation in Bilayer Graphene

Role of substrate induced electron-phonon interactions in biased graphitic bilayers.

Role of substrate induced electron-phonon interactions in biased graphitic bilayers