Current Research

The Campbell Group is part of the Condensed Matter Theory section at the Physics Department of Boston University.  We currently conduct research in three areas: ultracold atomic gases, graphene devices and the functional renormalization group.  Our broader interests include chaos, nonlinear phenomena, exotic ground states, strongly correlated electronic systems, and low-dimensional materials.

Ultracold atomic gases

A cartoon of the BEC dimer.  Bosons can hop between two modes; within the same mode, every pair of bosons interacts repulsively.

Cartoon of the BEC dimer. Bosons hop between two modes; within the same mode, every pair of bosons interacts repulsively.

My long-term interest in “intrinsic localized modes” (ILMs) (also known as “discrete breathers”) [1,2] has recently led to a study of their role in “avalanches” of Bose-Einstein Condensates (BEC) in (tilted) optical lattices in the semi-classical limit [3]. This, in turn, led to a further study of quantum effects beyond the semi-classical limit, using a global phase space (GPS) approach [4]. Currently, we are extending this GPS approach to the case where dissipation is present, with the surprising result that dissipation can actually enhance coherence and entanglement, effectively through the creation of stable ILMs in individual wells of the optical lattice [5].

The energy contours and sample trajectory of a trimer.

The energy contours and sample trajectory of a BEC trimer.

Relevant papers:

  1. David K. Campbell, Sergej Flach, and Yuri S. Kivshar (2004), Localizing Energy Through Nonlinearity and Discreteness Click here for a pdf version of the article
  2. J. Dorignac, J. Zhou, and D. K. Campbell (2008), Discrete breathers in nonlinear Schrödinger hypercubic lattices with arbitrary power nonlinearity Click here for a pdf version of the article
  3. H. Hennig, J. Dorignac and D. K. Campbell (2010), Transfer of Bose-Einstein condensates through discrete breathers in an optical lattice Click here for a pdf version of the article
  4. H. Hennig, D. Witthaut and D. K. Campbell (2012), Global phase space of coherence and entanglement in a double-well Bose-Einstein condensate Click here for a pdf version of the article
  5. T. Pudlik, H. Hennig, D. Witthaut and D. K. Campbell (2013),  Dynamics of entanglement in a dissipative Bose–Hubbard dimer Click here for a pdf version of the article

Graphene and other 2D electronic materials

Bandstructure of a graphene nanoribbon (zigzag).

Bandstructure of graphene nanoribbon (zigzag).

The isolation and characterization of graphene as an atomically thin monolayer of pure carbon by Novoselov, Geim, and their collaborators in 2004 produced an avalanche of interest across the condensed matter physics community, from theorists to experimentalists to applied materials scientists and device builders. Working with a number of collaborators, we have studied several different aspects of this exceptional material. For monolayer graphene, we developed a simple model for the phonon spectrum [1] and studied how the monolayer adhered to a patterned substrate [2]. For bilayer graphene, we explored the electronic compressibility [3] and the effects of electron-electron interactions [4]. Very recent studies include modeling the effects on electronic transport of the pseudomagnetic fields produced by non-uniform strain in graphene [5] and exploring a novel non-equilibrium steady state mechanism for inducing an effective gap in graphene [6]. We are currently extending our transport calculations to graphene “bubbles” of arbitrary shape, generated, for example, by applying gas pressure to graphene stretched over a nanocavity.

Graphene, while of enormous recent theoretical and experimental interest, is limited in its application in electronics by its gaplessness. Hence we are extending our research to other two-dimensional materials, and in particular to the semiconducting transition metal dichalcogenides (TMDCs), many of which have direct bandgaps on the order of 1-2 eV in monolayer form. We plan to apply the same approaches to these materials as used in our studies of graphene [5].

Relevant papers:

  1. S. Viola-Kusminsky, D. K. Campbell, and A. H. Castro Neto (2009), Lenosky’s energy and the phonon dispersion of graphene Click here for a pdf version of the article
  2. S. Viola Kusminsky, D. K. Campbell, A. H. Castro Neto, F. Guinea (2011), 2D Membrane on top of a patterned substrate: the case of graphene Click here for a pdf version of the article
  3. S. Viola-Kusminsky, Johan Nilsson, D. K. Campbell, and A. H. Castro Neto (2007), Electronic Compressibility of a graphene bilayer Click here for a pdf version of the article
  4. S. Viola-Kusminsky, D. K. Campbell, and A. H. Castro Neto (2009), Electron-electron interactions in graphene bilayers Click here for a pdf version of the article
  5. Z. Qi, D. A. Bahamon, V. M. Pereira, H. S. Park, D. K. Campbell and A. H. Castro Neto (2013), Resonant tunneling in graphene pseudomagnetic quantum dots Click here for a pdf version of the article
  6. Thomas Iadecola. David Campbell, Claudio Chamon, Chang-Yu Hou, Roman Jackiw, So-Young Pi, and Silvia Viola Kusminskiy (2013), Materials Design from Nonequilibrium Steady States: Driven Graphene as a Tunable Semiconductor with Topological Properties Click here for a pdf version of the article

Functional Renormalization Group

For nearly a decade, working with several different collaborators, we have applied variants of the functional renormalization group (FRG) to a wide range of models for novel, strongly correlated electronic systems. Examples have included superconductors in the strong coupling limit [1, 2, 3], the half-filled 1D extended Hubbard model [4], the two-leg Holstein-Hubbard ladder [5], the effects of dynamical phonons (retardation) on the half-filled 1D Holstein-Hubbard model [6], the validity of the Tomonga-Luttinger liquid relations for the 1D Holstein model [7], and the existence of dominant superconducting fluctuations in the 1D extended Hubbard-extended Holstein model [8]. Our most recent work in this area extends the FRG approach to the case of a mixture of two ultracold Fermionic atoms in a two-dimensional square optical lattice and predicts the existence of a novel dxy number density wave state for certain ranges of the parameters in the theory [9].

Relevant papers:

  1. S. W. Tsai, A.H.C. Neto, R. Shankar, and D. K. Campbell (2005), Renormalization-group approach to strong-coupled superconductors Click here for a pdf version of the article
  2. S. W. Tsai, A.H.C. Neto, R. Shankar, and D. K. Campbell (2006), Strong coupling superconductivity via an asymptotically exact renormalization-group framework Click here for a pdf version of the article
  3. S. W. Tsai, A.H.C. Neto, R. Shankar, and D. K. Campbell (2006), Renormalization-group approach to superconductivity: from weak to strong electron-phonon coupling Click here for a pdf version of the article
  4. K. M. Tam, S. W. Tsai, and D. K. Campbell (2006), Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model Click here for a pdf version of the article
  5. Ka-Ming Tam, S.-W. Tsai, D. K. Campbell, and A.H. Castro Neto (2007), Phase Diagram of the Holstein-Hubbard Two-Leg Ladder Click here for a pdf version of the article
  6. Ka-Ming Tam, S.-W. Tsai, D. K. Campbell, and A. H. Castro Neto (2007), Retardation effects in the Holstein-Hubbard chain at half-filling Click here for a pdf version of the article
  7. Ka-Ming Tam, S.-W. Tsai, and D. K. Campbell (2011), Validity of the Tomonaga-Luttinger Liquid relations for the one-dimensional Holstein model Click here for a pdf version of the article
  8. Ka-Ming Tam, Shan-Wen Tsai, and David K. Campbell (2013) Dominant superconducting fluctuations in the 1D extended Holstein-extended Hubbard model
  9. Chen-Yen Lai, Wen-Min Huang, David K. Campbell, and Shan-Wen Tsai, dxy-density wave in fermion-fermion cold atom mixtures