arXiv subjects
Publications and source records attributed to Mona Berciu.
In arXiv:1108.5413v1, Lee and Lee use several comparisons to argue that the physics of the three-band model found (Phys. Rev. Lett. 106 036401 (2011)) can be explained in the one-band model's framework (Phys. Rev. Lett. 91 057001 (2003)). While superficial similarities exist between the two sets of results, for reasons discussed in this reply, we disagree that they describe the same physics.
We show that a proper consideration of the contribution of Trugman loops leads to a fairly low effective mass for a hole moving in a square lattice Ising antiferromagnet, if the bare hopping and the exchange energy scales are comparable. This contradicts the general view that because of the absence of spin fluctuations, this effective mass must be extremely large. Moreover, in the presence of a transverse magnetic field, we show that the effective hopping integrals acquire an unusual dependence on the magnetic field, through Aharonov-Bohm interference, in addition to significant retardation effects. The effect of the Aharonov-Bohm interference on the cyclotron frequency (for small magnetic fields) and the Hofstadter butterfly (for large magnetic fields) is analyzed.
We device and investigate numerically a minimal yet detailed spin polaron model that describes lightly doped CuO$_2$ layers. The low-energy physics of a hole is studied by total-spin-resolved exact diagonalization on clusters of up to 32 CuO$_2$ unit cells, revealing features missed by previous studies. In particular, spin-polaron states with total spin 3/2 are the lowest eigenstates in several regions of the Brillouin zone. In these regions, and also at other points the quasiparticle weight is identically zero, indicating orthogonal states to those represented in the one electron Green's function. This highlights the importance of proper treatment of spin fluctuations in the many-body background.
We study the Holstein polaron in transverse magnetic field using non-perturbational methods. At strong fields and large coupling, we show that the polaron has a Hofstadter spectrum, however very distorted and of lower symmetry than that of a (heavier) bare particle. For weak magnetic fields, we identify non-perturbational behaviour of the Landau levels not previously known.
We generalize the momentum average approximation to study the properties of single polarons in models with boson affected hopping, where the fermion-boson scattering depends explicitly on both the fermion's and the boson's momentum. As a specific example, we investigate the Edwards fermion-boson model in both one and two dimensions. In one dimension, this allows us to compare our results with exact diagonalization results, to validate the accuracy of our approximation. The generalization to two-dimensional lattices allows us to calculate the polaron's quasiparticle weight and dispersion throughout the Brillouin zone and to demonstrate the importance of Trugman loops in generating a finite effective mass even when the free fermion has an infinite mass.
We investigate the existence of end points in the dispersion of Holstein polarons in various dimensions, using the Momentum Average approximation which has proved to be very accurate for this model. An end point separates momenta for which the lowest-energy state is a discrete level, i.e., an infinitely-lived polaron, from those where the lowest-energy feature is a continuum in which the "polaron'" is signalled by a resonance with a finite lifetime. While such end points are known to not appear in 1D, we show here that they are generic in 3D if the particle-boson coupling is not too strong. The 2D case is "critical": a pure 2D Holstein model has no end points, like the 1D case. However, any amount of interlayer hopping leads to 3D-like behavior. As a result, such end points are expected to appear in the spectra of layered, quasi-2D systems described by Holstein models. Generalizations to other models are also briefly discussed.
We introduce a novel parametrization scheme for the Hilbert space of a spin-1/2 Heisenberg antiferromagnet (AFM) based on an octapartite description of the square lattice. Our formulation provides an efficient yet systematic way to model the singlet ground-state wave function within a truncated basis. We demonstrate its effectiveness by using exact diagonalization to study systems with up to 64 spins. At significantly reduced computational cost, we obtain ground-state energies within less than 1% of the lowest values published. The non-iterative nature of this formulation and the fact that spatial symmetries remain unexploited lead to opportunities for extensions such as the incorporation into established iterative methods and the application to interacting models, for example in the study of the propagation of charged fermions in a 2D antiferromagnet.
We demonstrate that the proper calculation of the linear response for finite-size systems can only be performed if the coupling to the leads/baths is explicitly taken into consideration. We exemplify this by obtaining a Kubo-type formula for heat transport in a finite-size system coupled to two thermal baths, kept at different temperatures. We show that the proper calculation results in a well-behaved response, without the singular contributions from degenerate states encountered when Kubo formulae for infinite-size systems are inappropriately used for finite-size systems.
We investigate heat transport in various quantum spin chains, using the projector operator technique. We find that anomalous heat transport is linked not to the integrability of the Hamiltonian, but to whether it can be mapped to a model of non-interacting fermions. Our results also suggest how seemingly anomalous transport may occur at low temperatures in a much wider class of models.
Non-local, inhomogeneous and retarded response observed in experiments is reproduced by introducing the Inhomogeneous Momentum Average (IMA) method to study single polaron problems with disorder in the on-site potential and/or spatial variations of the electron-phonon couplings and/or phonon frequencies. We show that the electron-phonon coupling gives rise to an additional inhomogeneous, strongly retarded potential, which makes instant approximations questionable. The accuracy of IMA is demonstrated by comparison with results from the approximation free Diagrammatic Monte Carlo (DMC) method. Its simplicity allows for easy study of many problems that were previously unaccessible. As an example, we show how inhomogeneities in the electron-phonon coupling lead to nonlocal, retarded response in scanning tunneling microscopy (STM) images.
We investigate the effect of single and multiple impurities on the Zeeman-localized, spin polarized bound states in dilute magnetic semiconductor hybrid system. Such bound states appear whenever a dilute magnetic semiconductor showing giant Zeeman effect is exposed to an external magnetic field showing nanoscale inhomogeneity. We consider the specific example of a superconductor-dilute magnetic semiconductor hybrid, calculate the energy spectrum and the wave functions of the bound states in the presence of a single impurity, and monitor the evolution of the bound state as a function of the impurity strength and impurity location with respect to the center of the Zeeman trapping potential. Our results have important experimental implications as they predict robust spin textures even for than than ideal samples. We find that for all realistic impurity strengths the Zeeman bound state survives the presence of the impurity. We also investigate the effect of a large number of impurities and perform ensemble averages with respect to the impurity locations. We find that the spin polarized Zeeman bound states are very robust, and they remain bound to the external field inhomogeneity throughout the experimentally relevant region of impurity concentration and scattering strength.
We present a simpler derivation of the exact solution of a spin-polaron in a ferromagnet and generalize it to complex lattices and/or longer range exchange interactions. As a specific example, we analyze a two-dimensional MnO$_2$-like lattice (as in the ferromagnetic layers in LaMnO$_3$) and discuss the properties of the resulting spin-polaron in various regimes. At strong couplings the solution is reminiscent of the Zhang-Rice singlet, however the electronic wavefunction involved in the singlet is dependent on the momentum of the singlet, and multiple bands may appear.
We study the effects of the Rashba spin-orbit coupling on the polaron formation, using a suitable generalization of the Momentum Average approximation. Contrary to previous investigations of this problem, we find that the spin-orbit interaction decreases the effective electron-phonon coupling. It is thus possible to lower the effective mass of the polaron by increasing the spin-orbit coupling. We also show that when the spin-orbit coupling is large as compared to the phonon energy, the polaron retains only one of the spin polarized bands in its coherent spectrum. This has major implications for the propagation of spin-polarized currents in such materials, and thus for spintronic applications.
Superconductivity is a fascinating example of how "more is different". It is due to electrons binding into bosonic Cooper pairs, which exhibit coherent behavior across a macroscopic sample. Finding the mechanism responsible for this binding is one of the more difficult tasks of condensed matter physics. For conventional superconductors the solution was given by the BCS theory as being due to exchange of phonons. For the cuprate high-Tc superconductors a widely-accepted explanation is still missing despite intense effort. The recently discovered Fe-based high-Tc superconductors pose now a new challenge. We present here a quantum mechanical theory for pnictides describing the influence of the large electronic polarizability of the heavy anions. We demonstrate that its inclusion results in electronic polarons as the low-energy quasi-particles and also unveils a pairing mechanism for these electronic polarons.
We generalize the momentum average (MA) approximation to study the properties of models with momentum-dependent electron-phonon coupling. As in the case of the application of the original MA to the Holstein model, the results are analytical, numerically trivial to evaluate, exact for both zero bandwidth and for zero electron-phonon coupling, and are accurate everywhere in parameter space. Comparison with available numerical data confirms this accuracy. We then show that further improvements can be obtained based on variational considerations, using the one-dimensional breathing-mode Hamiltonian as a specific example. For example, by using this variational MA, we obtain ground state energies within at most 0.3% error of the numerical data.
We study the effects of the rippling of the graphene sheet on the quasiparticle dispersion. This is achieved using a generalization to the honeycomb lattice of the Momentum Average approximation, which is accurate for all coupling strengths and at all energies. We show that even though the position of the Dirac points may move and the Fermi speed can be renormalized significantly, quasiparticles with very long lifetimes survive near the Dirac points even for very strong couplings.
In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/ϕ_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $ϕ_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the top and bottom of the broadened LL, while states in the center of the LL (the critical region) remain delocalized. This well-known phenomenology is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE) [1]. One unnoticed issue is where the new states appear as the magnetic field is increased. Here we demonstrate that they appear predominantly inside the critical region. This leads to a certain ``spectral ordering'' of the localized states that explains the stripes observed in measurements of the local inverse compressibility [2-3], of two-terminal conductance [4], and of Hall and longitudinal resistances [5] without invoking interactions as done in previous work [6-8].
We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave-functions of the two lowest-energy eigenstates for any momentum, as well as a scheme to compute directly the polaron Greens function. We contrast these results with results for the 1D Holstein polaron. In particular, we find that the crossover from a large to a small polaron is significantly sharper. Unlike for the Holstein model, at moderate and large couplings the breathing-mode polaron dispersion has non-monotonic dependence on the polaron momentum k. Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation.