Theoretical investigations of polarons in complex materials

A charge carrier moving through a solid interacts with all the solid’s elementary excitations, whether phonons, or magnons in magnetically ordered systems, or orbitons if there is orbital degeneracy in the ground-state, or particle-hole excitations including plasmons, excitons, etc., for finite charge carrier concentrations. This inevitably results in a dressed quasiparticle, called a polaron, dragging along a cloud of various such possible excitations that are continuously absorbed and re-emitted. The description of these dressed quasiparticles’ coherent and incoherent dynamics, and its influence on the physical properties of the host material, is one of the main challenges in the world of theoretical condensed matter physics.

Within the last few years, Prof. Berciu’s group at UBC has formulated a new, non-perturbative, so-called Momentum Average approximation (MA) for the Green’s function of single polarons [1]. MA is simple to implement in any dimension, becomes exact in certain asymptotic limits, can be systematically improved, and when checked against numerical data, it proves to be accurate over the entire range of couplings. For example, an impressive comparison of the ground-state energy and effective mass of a Holstein polaron vs. the effective electron-phonon coupling was presented for a 3D system in [1]. Various other analytical approximations, including self-consistent Born approximation (SCBA), were compared with these data and none of which captures the large-to-small polaron crossover.

Very recently, the MA was generalized to models with boson-modulated hopping. This is of interest when the bosons are phonons, to understand for example polaron properties of the Su-Schrieffer-Heeger Hamiltonian [2], or other types of bosons, such as magnons. The latter are relevant, for example, in cuprates at very low doping, where the motion of the doping hole disturbs the spin order [3]. The recent progress allows us to study this type of problems accurately, including the effects of closed loops such as the Trugman paths on equal footing with the effects of quantum fluctuations. It has been shown that the bare fermion has an infinite mass — the finite effective polaron mass is dynamically generated through boson emission and absorption [3].

We plan to extend earlier studies of quasiparticle behavior in cuprates to other models describing low dimensional systems, such as spin ladders in Cu2O5 planes [4], and to investigate recently found spin-polaron states with total spin S = 3/2 in CuO2 planes [5]. Having an opportunity of applying novel techniques developed in Berciu’s group we expect that these studies could provide unbiased information about the quasiparticle behavior in various situations. These studies are expected to provide valuable new information about the electronic structure of strongly correlated Cu-O systems and could be stimulating for future experimental studies of spectral properties of cuprate superconductors and related materials by the experimental groups within the MPG-UBC collaboration.

This project would also take such polaron studies to the next level, investigating cou pling to multiple types of bosons, e.g. the effect on the spectral weights of the interplay between coupling to both phonons and magnons, without the need for arbitrary approximations currently used, such as the non-crossing approximation for phonon and magnon lines. Such problems are relevant for understanding quasiparticles in manganites (here the motion of the doping charge also disturbs orbital order, besides coupling to phonons and magnons), or even more complex materials, such as certain vanadates and multiferroic oxides, where the charge carrier couples to both spin and orbital degrees of freedom [6]. The ability to extend the MA to these types of problems is an extremely exciting and promising perspective.


  • [1] M. Berciu, Phys. Rev. Lett. 97, 036402 (2006); G. L. Goodvin, M. Berciu, and G. A. Sawatzky, Phys. Rev. B 74, 245104 (2006); M. Berciu and G. L. Goodvin, Phys. Rev. B 76, 165109 (2007).
  • [2] D.Marchand, G. De Filippis, V. Cataudella, M. Berciu, N. Nagaosa, N. V. Prokof’ev, A. S. Mishchenko, and P. C. E. Stamp, Phys. Rev. Lett. 105, 266605 (2010).
  • [3] M. Berciu and H. Fehske, Phys. Rev. B 82, 085116 (2010).
  • [4] K. Wohlfeld, A. M. Oles, and G. A. Sawatzky, Phys. Rev. B 81, 214522 (2010).
  • [5] B. Lau, M. Berciu, and G. A. Sawatzky, Phys. Rev. Lett. 106, 036401 (2011); Phys. Rev. B 84, 165102 (2011).
  • [6] K. Wohlfeld, A. M. Oles, and P. Horsch, Phys. Rev. B 79, 224433 (2009); selected by the editors to the Viewpoint in Physics [7].
  • [7] M. Berciu, Physics 2, 55 (2009).

Principal investigators

Mona Berciu (UBC)

George A. Sawatzky (UBC)

Peter Horsch (MPI-FKF)

Andrzej M. Oles (MPI-FKF)

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