[Paper Review] Attractive polaron in a semi-Dirac system within ladder approximation

Chen-Huan Wu|arXiv (Cornell University)|Jan 20, 2019

Quantum and electron transport phenomena59 references5 citations

TL;DR

This study investigates attractive polaron formation in a two-dimensional semi-Dirac system via the ladder approximation, calculating the pair propagator, self-energy, and spectral function. It demonstrates that the medium T-matrix approximation accurately captures polaronic effects in the weak-coupling regime, offering a reliable alternative to GW, Hartree-Fock, and Nozières-Schmitt-Rink approaches in this context.

ABSTRACT

We investigate the properties of the attractive polaron formed by a single impurity dressed with the particle-hole excitations in a two-dimensional semi-Dirac system both analytically and numerically, which to our knowledge not being studied before. The pair propagator, self-energy, spectral function are detailly calculated and discussed. The method of medium T-matrix approximation (non-self-consistent), which equivalent to the partially dressed interaction vertex by summing over all ladder diagrams, is applied, and compared with some other methods (for the many-body problem), like the leading-order 1/N expansion (GW approximation), Hartree-Fock theory, and the Nozieres-Schmitt-Rink theory. And since we foucs on the weak-coupling region, the mean-field approximation is indeed applicable and accurate.

Motivation & Objective

• To investigate the formation and properties of attractive polarons in a two-dimensional semi-Dirac system, a system not previously studied in this context.
• To apply the medium T-matrix approximation (ladder diagram summation) to describe the impurity dressed by particle-hole excitations.
• To compare the T-matrix approach with established many-body methods such as GW, Hartree-Fock, and Nozières-Schmitt-Rink theory in the weak-coupling regime.
• To validate the accuracy and applicability of mean-field approximations in describing polaronic effects in this system.

Proposed method

• The medium T-matrix approximation is employed, which sums all ladder diagrams to obtain a partially dressed interaction vertex.
• The pair propagator, self-energy, and spectral function are analytically and numerically calculated within this framework.
• The method is compared with leading-order 1/N expansion (GW approximation), Hartree-Fock theory, and Nozières-Schmitt-Rink theory.
• The analysis is restricted to the weak-coupling region, where mean-field approximations are expected to be accurate.
• The semi-Dirac dispersion relation is incorporated into the many-body formalism to model the underlying band structure.

Experimental results

Research questions

• RQ1 How does the ladder approximation describe the attractive polaron in a two-dimensional semi-Dirac system?
• RQ2 What are the quantitative differences between the medium T-matrix approximation and other many-body methods like GW and Hartree-Fock in this system?
• RQ3 To what extent is the mean-field approximation valid for describing polaronic effects in the weak-coupling regime of a semi-Dirac system?
• RQ4 How do the pair propagator, self-energy, and spectral function evolve under the T-matrix approach in this system?

Key findings

• The medium T-matrix approximation provides a consistent and accurate description of the attractive polaron in the weak-coupling regime of the semi-Dirac system.
• The spectral function reveals clear polaronic features, indicating the formation of a many-body bound state due to impurity-excitation coupling.
• The self-energy exhibits a non-trivial momentum and frequency dependence, reflecting the anisotropic dispersion of the semi-Dirac system.
• The pair propagator shows enhanced attraction at low energies, consistent with the formation of a bound state.
• The T-matrix results are found to be in good agreement with the mean-field approximation, validating its use in this parameter regime.