Portrait of Dr Jorge Quintanilla

Dr Jorge Quintanilla

Senior Lecturer in Condensed Matter Theory


Dr Jorge Quintanilla studied Physics at the University of Salamanca in his native Spain (Licenciado, 1992-1997) and at the University of Bristol (PhD, 1997-2001) where he completed a thesis on unconventional superconductors under the supervision of the late Balazs L. Gyorffy. He then moved to Brazil, where he held a postdoctoral position at the University of Sao Paulo at Sao Carlos (2002) and worked with Luiz Oliveira and Klaus Capelle on proximity effects in superconductors and with Vivaldo L. Campo on electronic statates in small-world networks.

Moving back to the UK to take up a research fellowship at the University of Birmingham (2003-2005), Jorge began new collaborations with his supervisor Andy Schofield, with Chris Hooley and, later, with Sam Carr. During this time his research interests broadened further to include quantum liquid crystal states and the Pomeranchuk instability and ultra-cold atoms. 

After Birmingham, Jorge took up the Atlas Research Fellowship in Condensed Matter Theory at the ISIS Facility in the STFC Rutherford-Appleton Laboratory, in Harwell, and at St Catherine's College, Oxford (2005-2010). At RAL, he developed a keen interest in extending, through his theoretical research, the capabilities of large-scale facilities employed in condensed matter research, including the muon and neutron instruments at the ISIS spallation neutron source.

During the course of his career Jorge has been an Individual Marie Curie Fellow; a Fellow of St Catherine’s College, Oxford; and an honorary research associate of the London Centre for Nanotechnology. He also chaired SEPnet's Atomic and Condensed Matter research theme (2010-2012) and is a founding member of the Hubbard Theory Consortium.

Research interests

Dr Jorge Quintanilla is a theorist working on quantum condensed matter and materials physics. His main interests are in the area of strongly correlated quantum matter and include unconventional superconductors, frustrated and quantum magnets, and other materials with strongly-correlated electrons. 

Jorge's current interests include broken time-reversal symmetry in centrosymmetric and non-centrosymmetric superconductors, topological defects and excitations in condensed matter and experimental signatures of quantum entanglement in magnetic materials. Past interests also include ultra-cold gases and complex networks. 


Jorge is involved in the teaching of superconductivity and magnetism, quantum mechanics and electricity and light. He is one of the lecturers in the biannual SEPnet GRADnet workshop on strong correlations. 


Jorge can offer PhD and MSc (R) projects in a number of areas, including unconventional superconductorsentanglement in quantum magnets and magnetic monopoles in spin ice. Every year he also offers one or more MPhys research projects. Visit his blog for more information on student research opportunities within his group.



  • Ghosh, S., Annett, J. and Quintanilla, J. (2018). Time-reversal symmetry breaking in superconductors through loop Josephson-current order. arXiv [Online]. Available at: https://arxiv.org/abs/1803.02618.
    We propose a superconducting instability where loop Josephson-currents form spontaneously
    within a unit cell at the critical temperature, T c . Such currents break time-reversal symmetry
    (TRS) without needing an unconventional pairing mechanism. Using Ginzburg-Landau theory we
    show how they emerge in a toy model and estimate the size of the resulting magnetization, which
    is consistent with recent muon-spin relaxation experiments. We discuss the crystal symmetry re-
    quirements and show that they are met by the Re 6 X (X=Zr, Hf, Ti) family of TRS-breaking, but
    otherwise seemingly conventional, superconductors.
  • Shang, T. et al. (2018). Time-reversal symmetry breaking in Re-based superconductors. Physical Review Letters [Online] 121. Available at: https://doi.org/10.1103/PhysRevLett.121.257002.
    To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed
    comparative muon-spin rotation/relaxation (µSR) studies of superconducting noncentrosymmetric
    Re0.82Nb0.18 (Tc = 8.8 K) and centrosymmetric Re (Tc = 2.7 K). In Re0.82Nb0.18, the low-temperature
    superfluid density and the electronic specific heat evidence a fully-gapped superconducting state, whose
    enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling.
    In both Re0.82Nb0.18 and pure Re, the spontaneous magnetic fields revealed by zero-field µSR below
    Tc indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant
    occurrence of TRSB in centrosymmetric Re and noncentrosymmetric ReT (T = transition metal), yet its
    preservation in the isostructural noncentrosymmetric superconductors Mg10Ir19B16 and Nb0.5Os0.5, strongly
    suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting
    state in Re and ReT. We discuss the superconducting order parameter symmetries that are compatible with
    the observations.
  • Whittlesea, P. et al. (2018). Can topological transitions be exploited to engineer intrinsically quench-resistant wires? IEEE Transactions on Applied Superconductivity [Online] 28:500305. Available at: https://doi.org/10.1109/TASC.2018.2791515.
    We investigate whether by synthesising superconductors that are tuned to a topological, node-reconstruction transition point we could create superconducting wires that are intrinsically resilient to quenches. Recent work shows that the exponent characterising the temperature dependence of the specific heat of a nodal superconductor is lowered over a region of the phase diagram near topological transitions where nodal lines form or reconnect. Our idea is that the resulting enhancement of the low-temperature specific heat could have potential application in the prevention of superconductor quenches. We perform numerical simulations of a simplified superconductor quench model. Results show that decreasing the specific heat exponent can prevent a quench from occurring and improve quench resilience, though in our simple model the effects are small. Further work will be necessary to establish the practical feasibility of this approach.
  • Irons, H. et al. (2017). Control of entanglement transitions in quantum spin clusters. Physical Review B: Condensed Matter and Materials Physics [Online] 96:224408-224408. Available at: http://dx.doi.org/10.1103/PhysRevB.96.224408.
    Quantum spin clusters provide a new platform for the experimental study of many-body entanglement. Here we address a simple model of a single-molecule nano-magnet featuring N interacting spins in a transverse field. The field can control an entanglement transition (ET). We calculate the magnetisation, low-energy gap and neutron-scattering cross-section and find that the ET has distinct signatures, detectable at temperatures as high as 5% of the interaction strength. The signatures are stronger for smaller clusters.
  • Weng, Z. et al. (2016). Two-gap superconductivity in LaNiGa2 with non-unitary triplet pairing and even parity gap symmetry. Physical Review Letters [Online] 117:27001. Available at: http://dx.doi.org/10.1103/PhysRevLett.117.027001.
    The nature of the pairing states of superconducting LaNiC2 and LaNiGa2 has to date remained a puzzling question. Broken time reversal symmetry has been observed in both compounds and a group theoretical analysis implies a non-unitary triplet pairing state. However all the allowed non-unitary triplet states have nodal gap functions but most thermodynamic and NMR measurements indicate fully gapped superconductivity in LaNiC2. Here we probe the gap symmetry of LaNiGa2 by measuring the London penetration depth, specific heat and upper critical field. These measurements demonstrate two-gap nodeless superconductivity in LaNiGa2, suggesting that this is a common feature of both compounds. These results allow us to propose a novel triplet superconducting state, where the pairing occurs between electrons of the same spin, but on different orbitals. In this case the superconducting wavefunction has a triplet spin component but isotropic even parity gap symmetry, yet the overall wavefunction remains antisymmetric under particle exchange. This model leads to a nodeless two-gap superconducting state which breaks time reversal symmetry, and therefore accounts well for the seemingly contradictory experimental results.
  • Tomasello, B. et al. (2015). Single-ion anisotropy and magnetic field response in the spin-ice materials Ho2Ti2O7 and Dy2Ti2O7. Physical Review B: Condensed Matter and Materials Physics [Online] 92:155120-1. Available at: http://dx.doi.org/10.1103/PhysRevB.92.155120.
    Motivated by its role as a central pillar of current theories of the dynamics of spin ice in and out of equilibrium, we study the single-ion dynamics of the magnetic rare-earth ions in their local environments, subject to the effective fields set up by the magnetic moments with which they interact. This effective field has a transverse component with respect to the local easy axis of the crystal electric field, which can induce quantum tunneling. We go beyond the projective spin-1/2 picture and use instead the full crystal-field Hamiltonian. We find that the Kramers versus non-Kramers nature, as well as the symmetries of the crystal-field Hamiltonian, result in different perturbative behavior at small fields (?1T), with transverse field effects being more pronounced in Ho2Ti2O7 than in Dy2Ti2O7. Remarkably, the energy splitting range we find is consistent with time scales extracted from experiments. We also present a study of the static magnetic response, which highlights the anisotropy of the system in the form of an off-diagonal g tensor, and we investigate the effects of thermal fluctuations in the temperature regime of relevance to experiments. We show that there is a narrow but accessible window of experimental parameters where the anisotropic response can be observed.
  • Slizovskiy, S. et al. (2014). Effect of paramagnetic fluctuations on a Fermi-surface topological transition in two dimensions. Physical Review B [Online] 90:165110. Available at: http://dx.doi.org/10.1103/PhysRevB.90.165110.
    We study the Fermi-surface topological transition of the pocket-opening type in a two-dimensional Fermi liquid. We find that the paramagnetic fluctuations in an interacting Fermi liquid typically drive the transition first order at zero temperature. We first gain insight from a calculation using second-order perturbation theory in the self-energy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. Experimental signatures are given in light of our results.
  • Singh, R. et al. (2014). Detection of Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor Re6Zr Using Muon-Spin Spectroscopy. Physical Review Letters: Moving Physics Forward [Online] 112. Available at: http://dx.doi.org/10.1103/PhysRevLett.112.107002.
    We have investigated the superconducting state of the non-centrosymmetric compound Re6Zr
    using magnetization, heat capacity, and muon-spin relaxation/rotation (?SR) measurements. Re6Zr
    has a superconducting transition temperature, Tc = 6.75±0.05 K. Transverse-field ?SR experiments,
    used to probe the superfluid density, suggest an s-wave character for the superconducting gap.
    However, zero and longitudinal-field ?SR data reveal the presence of spontaneous static magnetic
    fields below Tc indicating that time-reversal symmetry is broken in the superconducting state and
    an unconventional pairing mechanism. An analysis of the pairing symmetries identifies the ground
    states compatible with time-reversal symmetry breaking.
  • Bhattacharyya, A. et al. (2014). Broken time-reversal symmetry probed by muon spin relaxation in the caged type superconductor Lu5Rh6Sn18. Physical Review B: Condensed Matter and Materials Physics [Online] 91:060503-1-060503-5. Available at: http://link.aps.org/doi/10.1103/PhysRevB.91.060503.
    The superconducting state of the caged type compound Lu5Rh6Sn18 has been investigated by using magnetization, heat capacity, and muon spin relaxation or rotation (?SR) measurements, and the results interpreted on the basis of the group theoretical classifications of the possible pairing symmetries and a simple model of the resulting quasiparticle spectra. Our zero-field ?SR measurements clearly reveal the spontaneous appearance of an internal magnetic field below the transition temperature, which indicates that the superconducting state in this material is characterized by broken time-reversal symmetry. Further, the analysis of the temperature dependence of the magnetic penetration depth measured using the transverse-field ?SR measurements suggests an isotropic s?wave character for the superconducting gap. This is in agreement with the heat capacity behavior, and we show that it can be interpreted in terms of a nonunitary triplet state with point nodes and an open Fermi surface.
  • Mazidian, B. et al. (2013). Anomalous thermodynamic power laws near topological transitions in nodal superconductors. Physical Review B: Condensed Matter and Materials Physics [Online] 88:224504. Available at: http://dx.doi.org/10.1103/PhysRevB.88.224504.
    Unconventional superconductors are most frequently identified by the observation of power-law behavior on low-temperature thermodynamic or transport properties, such as specific heat. Here, we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. These new types of nodes typically occur when there are transitions between different types of gap node topology, for example, when point or line nodes first appear as a function of some physical parameter. We identify anomalous, noninteger thermodynamic power laws associated with these new nodal types, and give physical examples of superconductors in which they might be observed experimentally, including the noncentrosymmetric superconductor Li2Pd3?xPtxB.
  • Campo, V. et al. (2012). Thermal versus quantum fluctuations of optical-lattice fermions. Physical Review A: Atomic, Molecular and Optical Physics [Online] 85:33644. Available at: http://dx.doi.org/10.1103/PhysRevA.85.033644.
    We show that, for fermionic atoms in a one-dimensional optical lattice, the fraction of atoms in doubly occupied sites is a highly nonmonotonic function of temperature. We demonstrate that this property persists even in the presence of realistic harmonic confinement, and that it leads to a suppression of entropy at intermediate temperatures that offers a route to adiabatic cooling. Our interpretation of the suppression is that such intermediate temperatures are simultaneously too high for quantum coherence and too low for significant thermal excitation of double occupancy thus offering a clear indicator of the onset of quantum fluctuations.
  • Hillier, A. et al. (2012). Nonunitary Triplet Pairing in the Centrosymmetric Superconductor LaNiGa2. Physical Review Letters: Moving Physics Forward [Online] 109:0-0. Available at: http://link.aps.org/doi/10.1103/PhysRevLett.109.097001.
    Muon spin rotation and relaxation experiments on the centrosymmetric intermetallic superconductor LaNiGa2 are reported. The appearance of spontaneous magnetic fields coincides with the onset of superconductivity, implying that the superconducting state breaks time reversal symmetry, similarly to noncentrosymmetric LaNiC2. Only four triplet states are compatible with this observation, all of which are nonunitary triplets. This suggests that LaNiGa2 is the centrosymmetric analogue of LaNiC2. We argue that these materials are representatives of a new family of paramagnetic nonunitary superconductors.
  • Ciftja, O. and Quintanilla, J. (2010). Effective Interaction Potentials in the Uppermost Landau Level. Journal of Low Temperature Physics [Online] 159:189-192. Available at: http://dx.doi.org/10.1007/s10909-009-0123-5.
    We consider a quantum Hall system of electrons confined to the uppermost Landau level and assume that the lower Landau levels are full and inert causing no Landau level mixing. While it is known that the problem of electrons interacting with the Coulomb interaction in a higher Landau level is mathematically equivalent to the problem of electrons in the lowest Landau level interacting with an effective interaction, the way the effective interaction can be calculated is not unique. We focus on the details of two different calculations of such effective interaction potentials in the uppermost Landau level and discuss the influence of one or another form of the effective potential on the stability of various correlated electronic phases in the quantum Hall regime.
  • Carr, S., Quintanilla, J. and Betouras, J. (2010). Lifshitz transitions and crystallization of fully polarized dipolar fermions in an anisotropic two-dimensional lattice. Physical Review B: Condensed Matter and Materials Physics [Online] 82:045110 -1. Available at: http://dx.doi.org/10.1103/PhysRevB.82.045110.
    We consider a two-dimensional model of noninteracting chains of spinless fermions weakly coupled via a small interchain hopping and a repulsive interchain interaction. The phase diagram of this model has a surprising feature: an abrupt change in the Fermi surface as the interaction is increased. We study in detail this metanematic transition and show that the well-known 21/2-order Lifshitz transition is the critical end point of this first-order quantum phase transition. Furthermore, in the vicinity of the end point, the order parameter has a nonperturbative BCS-type form. We also study a competing crystallization transition in this model and derive the full phase diagram. This physics can be demonstrated experimentally in dipolar ultracold atomic or molecular gases. In the presence of a harmonic trap, it manifests itself as a sharp jump in the density profile.
  • Quintanilla, J. et al. (2010). Relativistic analysis of the pairing symmetry of the noncentrosymmetric superconductor LaNiC2. Physical Review B: Condensed Matter and Materials Physics [Online] 82:174511. Available at: http://dx.doi.org/10.1103/PhysRevB.82.174511.
    We present a relativistic symmetry analysis of the allowed pairing states in the noncentroymmetric superconductor LaNiC2. The case of zero spin-orbit coupling (SOC) is discussed first and then the evolution of the symmetry-allowed superconducting instabilities as SOC is adiabatically turned on is described. In addition to mixing singlet with triplet pairing, SOC splits some triplet pairing states with degenerate order-parameter spaces into nondegenerate pairing states with different critical temperatures. We address the breaking of time-reversal symmetry detected in recent muon spin-relaxation experiments and show that it is only compatible with such nonunitary triplet pairing states. In particular, an alternative scenario featuring conventional singlet pairing with a small admixture of triplet pairing is shown to be incompatible with the experimental data.
  • Quintanilla, J. and Hooley, C. (2009). The strong-correlations puzzle. Physics World 22:32-37.
    A solution to one of the most famous problems in theoretical physics, formulated almost 50 years ago, may at last be within reach. But as Jorge Quintanilla and Chris Hooley explain, it relies not on theory, but on experiments with ultracold atoms trapped by beams of light
  • Campo, V., Quintanilla, J. and Hooley, C. (2009). Possible critical behavior driven by the confining potential in optical lattices with ultra-cold fermions. Physica B: Condensed Matter [Online] 404:3328-3331. Available at: http://dx.doi.org/10.1016/j.physb.2009.07.089.
    A recent paper [V.L. Campo, et al., Phys. Rev. Lett. 99 (2007) 240403] has proposed a two-parameter scaling method to determine the phase diagram of the fermionic Hubbard model from optical lattice experiments. Motivated by this proposal, we investigate in more detail the behavior of the ground-state energy per site as a function of trap size (L) and confining potential (V(x) = t(x/L)(alpha)) in the one-dimensional case. Using the BALDA-DFT method, we find signatures of critical behavior as alpha ->infinity.
  • Hillier, A., Quintanilla, J. and Cywinski, R. (2009). Evidence for Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor LaNiC2. Physical Review Letters: Moving Physics Forward [Online] 102:117007 -1. Available at: http://dx.doi.org/10.1103/PhysRevLett.102.117007.
    Muon spin relaxation experiments on the noncentrosymmetric intermetallic superconductor LaNiC2 are reported. We find that the onset of superconductivity coincides with the appearance of spontaneous magnetic fields, implying that in the superconducting state time-reversal symmetry is broken. An analysis of the possible pairing symmetries suggests only four triplet states compatible with this observation, all of them nonunitary. They include the intriguing possibility of triplet pairing with the full point group symmetry of the crystal, which is possible only in a noncentrosymmetric superconductor.
  • Quintanilla, J., Carr, S. and Betouras, J. (2009). Metanematic, smectic, and crystalline phases of dipolar fermions in an optical lattice. Physical Review A: Atomic, Molecular and Optical Physics [Online] 79. Available at: http://dx.doi.org/10.1103/PhysRevA.79.031601.
    It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realization of this soft quantum matter physics in an ultracold gas. It uses optical lattices and dipolar interactions to realize a particularly simple model. Our analysis reveals a rich phase diagram featuring a metanematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes) and a crystalline "checkerboard" phase.
  • Carr, S., Quintanilla, J. and Betouras, J. (2009). Deconfinement and Quantum Liquid Crystalline States of Dipolar Fermions in Optical Lattices. International Journal of Modern Physics B [Online] 23:4074-4086. Available at: http://dx.doi.org/10.1142/S0217979209063262.
    We describe a simple model of fermions in quasi-one dimension that features interaction-induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice(1). The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on the basis of bosonization and detailed analysis of the RPA susceptibility.
  • Quintanilla, J., Capelle, K. and Oliveira, L. (2008). Density-functional description of superconducting and magnetic proximity effects across a tunneling barrier. Physical Review B: Condensed Matter and Materials Physics [Online] 78:1-10. Available at: http://dx.doi.org/10.1103/PhysRevB.78.205426.
    A density-functional formalism for superconductivity and magnetism is presented. The resulting relations unify previously derived Kohn-Sham equations for superconductors and for noncollinear magnetism. The formalism, which discriminates Cooper-pair singlets from triplets, is applied to two quantum liquids coupled by tunneling through a barrier. An exact expression is derived, relating the eigenstates and eigenvalues of the Kohn-Sham equations, unperturbed by tunneling, on one side of the barrier to the proximity-induced ordering potential on the other.
  • Quintanilla, J., Haque, M. and Schofield, A. (2008). Symmetry-breaking Fermi surface deformations from central interactions in two dimensions. Physical Review B: Condensed Matter and Materials Physics [Online] 78:35131. Available at: http://dx.doi.org/10.1103/PhysRevB.78.035131.
    We present a mean-field theory of the Pomeranchuk instability in two dimensions, starting from a generic central interaction potential described in terms of a few microscopic parameters. For a significant range of parameters, the instability is found to be pre-empted by a first-order quantum phase transition. We provide the ground-state phase diagram in terms of our generic parameters.
  • Quintanilla, J. et al. (2008). Pomeranchuk instability: Symmetry-breaking and experimental signatures. Physica B: Condensed Matter [Online] 403:1279-1281. Available at: http://dx.doi.org/10.1016/j.physb.2007.10.126.
    We discuss the emergence of symmetry-breaking via the Pomeranchuk instability from interactions that respect the underlying point-group symmetry. We use a variational mean-field theory to consider a 2D continuum and a square lattice. We describe two experimental signatures: a symmetry-breaking pattern of Friedel oscillations around an impurity; and a structural transition.
  • Campo, V. et al. (2007). Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling. Physical Review Letters: Moving Physics Forward [Online] 99. Available at: http://dx.doi.org/10.1103/PhysRevLett.99.240403.
    We propose an experiment to obtain the phase diagram of the fermionic Hubbard model, for any dimensionality, using cold atoms in optical lattices. It is based on measuring the total energy for a sequence of trap profiles. It combines finite-size scaling with an additional “finite-curvature scaling” necessary to reach the homogeneous limit. We illustrate its viability in the 1D case, simulating experimental data in the Bethe-ansatz local-density approximation. Including experimental errors, the filling corresponding to the Mott transition can be determined with better than 3% accuracy.
  • Quintanilla, J. and Campo, V. (2007). Electron in a tangled chain: Multifractality at the small-world critical point. Physical Review B: Condensed Matter and Materials Physics [Online] 75:1441204. Available at: http://dx.doi.org/10.1103/PhysRevB.75.144204.
    We study a simple model of conducting polymers in which a single electron propagates through a randomly tangled chain. The model has the geometry of a small-world network, with a small density p of crossings of the chain acting as shortcuts for the electron. We use numerical diagonalization and simple analytical arguments to discuss the density of states, inverse participation ratios, and wave functions. We suggest that there is a critical point at p=0 and demonstrate finite-size scaling of the energy and wave functions at the lower band edge. The wave functions are multifractal. The critical exponent of the correlation length is consistent with criticality due to the small-world effect, as distinct from the previously discussed, dimensionality-driven Anderson transition.
  • Quintanilla, J. and Schofield, A. (2006). Pomeranchuk and topological Fermi surface instabilities from central interactions. Physical Review B: Condensed Matter and Materials Physics 74.
    We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle
    interactions. We find that Pomeranchuk instabilities with all symmetries
    except l=1 can take place if the interaction is repulsive and has
    a finite range r(0) of the order of the interparticle distance. We
    demonstrate this by solving the mean field equations analytically
    for an explicit model interaction, as well as numerical results for
    more realistic potentials. We find in addition to the Pomeranchuk
    instability other, subtler phase transitions in which the Fermi surface
    changes topology without rotational symmetry breaking. We argue that
    such interaction-driven topological transitions may be as generic
    to such systems as the Pomeranchuk instability.
  • Hooley, C. and Quintanilla, J. (2006). Finite-curvature scaling in optical lattice systems. Physica B: Condensed Matter [Online] 378-80:1035-1036. Available at: http://dx.doi.org/10.1016/j.physb.2006.01.393.
    We address the problem posed by the inhomogeneous trapping fields when using ultracold fermions to simulate strongly correlated electrons.
    As a starting point, we calculate the density of states for a single
    atom. Using semiclassical arguments, we show that this can be made
    to evolve smoothly towards the desired limit by varying the curvature
    of the field profile. Implications for mutually interacting atoms
    in such potentials are briefly discussed. (c) 2006 Elsevier B.V.
    All rights reserved.
  • Hooley, C. and Quintanilla, J. (2004). Single-atom density of states of an optical lattice. Physical Review Letters: Moving Physics Forward [Online] 93:80404. Available at: http://dx.doi.org/10.1103/PhysRevLett.93.080404.
    We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation,
    with an extra parameter kappa denoting the strength of the harmonic
    trap. It is shown that the kappa-->0 limit of this problem is singular,
    in the sense that the density of states for a very shallow trap (kappa-->0)
    is qualitatively different from that of a translationally invariant
    lattice (kappa=0). The physics of this difference is discussed, and
    densities of states and wave functions are exhibited and explained.
  • Quintanilla, J. and Gyorffy, B. (2003). Cooper pairing with finite angular momentum: BCS versus Bose limits. Journal of Physics A: Mathematical and General 36:9379-9390.
    We revisit the old problem of exotic superconductivity as Cooper pairing with finite angular momentum emerging from a central potential.
    Based on some general considerations, we suggest that the phenomenon
    is associated with interactions that keep electrons at some particular,
    finite distance r(0), and occurs at a range of intermediate densities
    n similar to 1/r(0)(3). We discuss the ground state and the critical
    temperature in the framework of a standard functional-integral theory
    of the BCS to Bose crossover. We find that, due to the lower energy
    of two-body bound states with l = 0, the rotational symmetry of the
    ground state is always restored on approaching the Bose limit. Moreover
    in that limit the critical temperature is always higher for pairs
    with l = 0. The breaking of the rotational symmetry of the continuum
    by the superfluid state thus seems to be a property of weakly-attractive,
    non-monotonic interaction potentials, at intermediate densities.
  • Quintanilla, J., Capelle, K. and Oliveira, L. (2003). Comment on ``Anomalous proximity effect in underdoped YBa2Cu3O6+x Josephson junctions''. Physical Review Letters: Moving Physics Forward 90.
  • Quintanilla, J. and Gyorffy, B. (2002). On the nature of the superconducting gap in the cuprates. Journal of Physics: Condensed Matter 14:6591-6600.
    Recent experiments indicate that the excitation spectrum of the cuprates is characterized, in the superconducting state, by two energy scales:
    the coherence energy' Delta(c) and the `pseudogap' Delta(p) Here
    we consider a simple generalization of-the BCS model that yields
    exotic pairing and can describe, phenomenologically, the generic
    trends in the critical temperature T-c of cuprate superconductors.
    We use the model to predict the gap in the single-particle spectrum
    arising from the superconductivity and we find evidence that it corresponds
    to the lower of the two energy scales, Delta(c), seen in the experiments.
    This provides further support to the view that the origin of the
    pseudogap is not superconducting fluctuations.
  • Quintanilla, J. et al. (2002). Cooper pairing with finite angular momentum via a central attraction: From the BCS to the Bose limits. Physical Review B: Condensed Matter and Materials Physics [Online] 66:214526. Available at: http://dx.doi.org/10.1103/PhysRevB.66.214526.
    In the context of a simple model featuring an explicit, central interaction potential, and using a standard functional-integral technique, we
    study superconductivity with angular momentum quantum number l=2
    as an emergent property of the many-body system. Our interaction
    potential is attractive at a finite distance r(0), and the breaking
    of the rotational symmetry is the result of an interplay between
    r(0) and the interparticle distance r(s). This interplay is generic
    to interactions of this type and is responsible for the existence
    of d-wave pairing for a range of densities. However, we find that
    l=2 pairing takes place only in the BCS limit. In contrast, as the
    Bose-Einstein (BE) limit is approached the internal energy of the
    ``preformed pairs'' becomes the dominant contribution and there
    is a quantum phase transition in which the s-wave symmetry is restored.
    We also find that the limiting value of the critical temperature
    is k(B)T(c)-->3.315 h(2)/2m(*) [n/2(2l+1)](2/3), which coincides
    with the usual result only for l=0; for l>0, it differs in the degeneracy
    factor 1/(2l+1), which lowers T-c. Our results thus place constraints
    on exotic pairing in the BE limit, while at the same time indicating
    a particularly interesting route to pairing with l>0 in a BCS superconductor.
  • Quintanilla, J. and Gyorffy, B. (2000). Finite range model interaction potential for d-wave superconductors:T-c versus doping in the cuprates. Physica B: Condensed Matter 284:421-422.
    We study a simple, BCS like, model which describes unconventional superconductivity on the basis of an electron-electron attraction
    corresponding to the delta-shell potential: U(r(12)) = - g delta(r(12)
    - r(0)). It predicts a T-c versus doping behavior similar to that
    characteristic of the high T-c cuprates. (C) 2000 Elsevier Science
    B.V. All rights reserved.

Internet publication

  • Quintanilla, J. (2016). SPS Research into superconductivity highlighted in Physical Review Letters [Webpage]. Available at: https://www.kent.ac.uk/physical-sciences/news/front-page/new-form-superconductivity.html.
    Research conducted by Dr Jorge Quintanilla as part of an international collaboration has been chosen as an Editors' Suggestion on the Physical Review Letters website. The full article can be accessed here. Below is a summary from Dr Quintanilla about what the research was and how it is useful.
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