
Csire, G., Annett, J., Quintanilla, J. and Újfalussy, B. (2020). Firstprinciples based theory of spinorbit coupling induced triplet pairing: Application to the superconducting ground state of rhenium. arXiv.org [Online]. Available at: https://arxiv.org/abs/2005.05702.
Recent μSR measurements revealed that spontaneous magnetism exists in the superconducting state of rhenium and it also appears in other rhenium based materials like Re6Zr, Re6Hf, Re6Ti. The superconducting state of these materials show swavelike properties and the pairing mechanism is most likely driven by electronphonon coupling. In this paper we take elemental rhenium as a testbed and investigate its ground state. By developing an LCAO formalism for the solution of the spingeneralized Bogoliubovde Gennes equation we use every details of the firstprinciples bandstructure together with spinorbit coupling. In this paper we provide a possible explanation of the spontaneous timereverseal symmetry breaking in the superconducting ground state of rhenium by arguing that taking into account the orbital degrees of freedom, spinorbit coupling is inducing evenparity oddorbital spin triplet Cooper pairs, and Cooper pairs' migration between the equalspin triplet states may lower the total energy. We show how magnetism emerges and the structure of the gap changes as a function of the triplet component of the interaction strength.

Santos, D., Faust, J. and Quintanilla, J. (2020). Feedback: A brief history of kite physics. Physics World [Online] 33:2021. Available at: http://dx.doi.org/10.1088/20587058/33/2/28.
In reply to Margaret Harris's feature on the challenges and opportunities for airborne wind energy ("Harnessing the wind" December 2019, pp26–30).

Tomasello, B., Castelnovo, C., Moessner, R. and Quintanilla, J. (2019). Correlated Quantum Tunneling of Monopoles in Spin Ice. Physical Review Letters [Online] 123. Available at: https://dx.doi.org/10.1103/PhysRevLett.123.067204.
The spin ice materials Ho\(_2\)Ti\(_2\)O\(_7\) and Dy\(_2\)Ti\(_2\)O\(_7\) are by now perhaps the beststudied classical frustrated magnets. A crucial step towards the understanding of their low temperature behaviour  both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution  is a quantitative understanding of the spinflip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a singleion subject to the crystal, exchange and dipolar fields from neighbouring ions. By studying the fundamental quantum mechanical mechanisms, we discover a bimodal distribution of hopping rates which depends on the local spin configuration, in broad agreement with rates extracted from experiment. Applying the same analysis to Pr\(_2\)Sn\(_2\)O\(_7\) and Pr\(_2\)Zr\(_2\)O\(_7\), we find an even more pronounced separation of timescales signalling the likelihood of coherent manybody dynamics.

Shang, T., Smidman, M., Ghosh, S., Baines, C., Chang, L., Gawryluk, D., Barker, J., Singh, R., Paul, D., Balakrishnan, G., Pomjakushina, E., Shi, M., Medarde, M., Hillier, A., Yuan, H., Quintanilla, J., Mesot, J. and Shiroka, T. (2018). Timereversal symmetry breaking in Rebased superconductors. Physical Review Letters [Online] 121. Available at: https://dx.doi.org/10.1103/PhysRevLett.121.257002.
To trace the origin of timereversal symmetry breaking (TRSB) in Rebased superconductors, we performed comparative muonspin rotation/relaxation (µSR) studies of superconducting noncentrosymmetric Re\(_{0.82}\)Nb\(_{0.18}\) (\(T\)\(_c\) = 8.8 K) and centrosymmetric Re (\(T\)\(_c\) = 2.7 K). In Re\(_{0.82}\)Nb\(_{0.18}\), the lowtemperature superfluid density and the electronic specific heat evidence a fullygapped superconducting state, whose enhanced gap magnitude and specificheat discontinuity suggest a moderately strong electronphonon coupling. In both Re\(_{0.82}\)Nb\(_{0.18}\) and pure Re, the spontaneous magnetic fields revealed by zerofield µSR below \(T\)\(_c\) indicate timereversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric Re\(T\) (\(T\) = transition metal), yet its preservation in the isostructural noncentrosymmetric superconductors Mg\(_{10}\)Ir\(_{19}\)B\(_{16}\) and Nb\(_{0.5}\)Os\(_{0.5}\), strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and Re\(T\). We discuss the superconducting order parameter symmetries that are compatible with the observations.

Ghosh, S., Annett, J. and Quintanilla, J. (2018). Timereversal symmetry breaking in superconductors through loop Josephsoncurrent order. arXiv [Online]. Available at: https://arxiv.org/abs/1803.02618.
We propose a superconducting instability where loop Josephsoncurrents form spontaneously
within a unit cell at the critical temperature, T c . Such currents break timereversal symmetry
(TRS) without needing an unconventional pairing mechanism. Using GinzburgLandau theory we
show how they emerge in a toy model and estimate the size of the resulting magnetization, which
is consistent with recent muonspin 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 TRSbreaking, but
otherwise seemingly conventional, superconductors.

Whittlesea, P., Quintanilla, J., Annett, J., Hillier, A. and Hooley, C. (2018). Can topological transitions be exploited to engineer intrinsically quenchresistant wires?. IEEE Transactions on Applied Superconductivity [Online] 28. Available at: https://doi.org/10.1109/TASC.2018.2791515.
We investigate whether by synthesising superconductors that are tuned to a topological, nodereconstruction 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 lowtemperature 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., Quintanilla, J., Perring, T., Amico, L. and Aeppli, G. (2017). Control of entanglement transitions in quantum spin clusters. Physical Review B: Condensed Matter and Materials Physics [Online] 96:224408224408. Available at: http://dx.doi.org/10.1103/PhysRevB.96.224408.
Quantum spin clusters provide a new platform for the experimental study of manybody entanglement. Here we address a simple model of a singlemolecule nanomagnet featuring N interacting spins in a transverse field. The field can control an entanglement transition (ET). We calculate the magnetisation, lowenergy gap and neutronscattering crosssection 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., Zhang, J., Smidman, M., Shang, T., Quintanilla, J., Annett, J., Nicklas, M., Pang, G., Jiao, L., Jiang, W., Chen, Y., Stelgich, F. and Yuan, H. (2016). Twogap superconductivity in LaNiGa\(_2\) with nonunitary triplet pairing and even parity gap symmetry. Physical Review Letters [Online] 117. Available at: http://dx.doi.org/10.1103/PhysRevLett.117.027001.
The nature of the pairing states of superconducting LaNiC\(_2\) and LaNiGa\(_2\) has to date remained a puzzling question. Broken time reversal symmetry has been observed in both compounds and a group theoretical analysis implies a nonunitary triplet pairing state. However all the allowed nonunitary triplet states have nodal gap functions but most thermodynamic and NMR measurements indicate fully gapped superconductivity in LaNiC\(_2\). Here we probe the gap symmetry of LaNiGa\(_2\) by measuring the London penetration depth, specific heat and upper critical field. These measurements demonstrate twogap nodeless superconductivity in LaNiGa\(_2\), 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 twogap superconducting state which breaks time reversal symmetry, and therefore accounts well for the seemingly contradictory experimental results.

Tomasello, B., Castelnovo, C., Moessner, R. and Quintanilla, J. (2015). Singleion anisotropy and magnetic field response in the spinice materials Ho2Ti2O7 and Dy2Ti2O7. Physical Review B: Condensed Matter and Materials Physics [Online] 92:1551201. 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 singleion dynamics of the magnetic rareearth 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 spin1/2 picture and use instead the full crystalfield Hamiltonian. We find that the Kramers versus nonKramers nature, as well as the symmetries of the crystalfield 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 offdiagonal 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., Betouras, J., Carr, S. and Quintanilla, J. (2014). Effect of paramagnetic fluctuations on a Fermisurface 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 Fermisurface topological transition of the pocketopening type in a twodimensional 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 secondorder perturbation theory in the selfenergy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the selfconsistent fluctuation approximation. Experimental signatures are given in light of our results.

Singh, R., Hillier, A., Mazidian, B., Quintanilla, J., Annett, J., Paul, D., Balakrishnan, G. and Lees, M. (2014). Detection of TimeReversal Symmetry Breaking in the Noncentrosymmetric Superconductor Re\(_6\)Zr Using MuonSpin Spectroscopy. Physical Review Letters [Online] 112. Available at: http://dx.doi.org/10.1103/PhysRevLett.112.107002.
We have investigated the superconducting state of the noncentrosymmetric compound Re\(_6\)Zr using magnetization, heat capacity, and muonspin relaxation/rotation (\(\mu\)SR) measurements. Re\(_6\)Zr has a superconducting transition temperature, T\(_c\) = 6.75±0.05 K. Transversefield \(\mu\)SR experiments, used to probe the superfluid density, suggest an \(s\)wave character for the superconducting gap. However, zero and longitudinalfield \(\mu\)SR data reveal the presence of spontaneous static magnetic fields below \(T\)\(_c\) indicating that timereversal symmetry is broken in the superconducting state and an unconventional pairing mechanism. An analysis of the pairing symmetries identifies the ground states compatible with timereversal symmetry breaking.

Bhattacharyya, A., Adroja, D., Quintanilla, J., Hillier, A., Kase, N., Strydom, A. and Akimitsu, J. (2014). Broken timereversal symmetry probed by muon spin relaxation in the caged type superconductor Lu5Rh6Sn18. Physical Review B: Condensed Matter and Materials Physics [Online] 91:0605031. 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 zerofield ?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 timereversal symmetry. Further, the analysis of the temperature dependence of the magnetic penetration depth measured using the transversefield ?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., Quintanilla, J., Hillier, A. and Annett, J. (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 powerlaw behavior on lowtemperature 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., Capelle, K., Hooley, C., Quintanilla, J. and Scarola, V. (2012). Thermal versus quantum fluctuations of opticallattice 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 onedimensional 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., Quintanilla, J., Mazidian, B., Annett, J. and Cywinski, R. (2012). Nonunitary Triplet Pairing in the Centrosymmetric Superconductor LaNiGa2. Physical Review Letters: Moving Physics Forward [Online] 109:00. 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.

Quintanilla, J., Hillier, A., Annett, J. and Cywinski, R. (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 spinorbit coupling (SOC) is discussed first and then the evolution of the symmetryallowed 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 orderparameter spaces into nondegenerate pairing states with different critical temperatures. We address the breaking of timereversal symmetry detected in recent muon spinrelaxation 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.

Carr, S., Quintanilla, J. and Betouras, J. (2010). Lifshitz transitions and crystallization of fully polarized dipolar fermions in an anisotropic twodimensional 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 twodimensional 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 wellknown 21/2order Lifshitz transition is the critical end point of this firstorder quantum phase transition. Furthermore, in the vicinity of the end point, the order parameter has a nonperturbative BCStype 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.

Ciftja, O. and Quintanilla, J. (2010). Effective Interaction Potentials in the Uppermost Landau Level. Journal of Low Temperature Physics [Online] 159:189192. Available at: http://dx.doi.org/10.1007/s1090900901235.
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.

Campo, V., Quintanilla, J. and Hooley, C. (2009). Possible critical behavior driven by the confining potential in optical lattices with ultracold fermions. Physica B: Condensed Matter [Online] 404:33283331. 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 twoparameter 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 groundstate energy per site as a function of trap size (L) and confining potential (V(x) = t(x/L)(alpha)) in the onedimensional case. Using the BALDADFT method, we find signatures of critical behavior as alpha >infinity.

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] 23:40744086. Available at: http://dx.doi.org/10.1142/S0217979209063262.
We describe a simple model of fermions in quasione dimension that features interactioninduced 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 stronglycorrelated fermions, featuring metanematic, 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. and Hooley, C. (2009). The strongcorrelations puzzle. Physics World 22:3237.
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

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.

Hillier, A., Quintanilla, J. and Cywinski, R. (2009). Evidence for TimeReversal 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 timereversal 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., Capelle, K. and Oliveira, L. (2008). Densityfunctional description of superconducting and magnetic proximity effects across a tunneling barrier. Physical Review B: Condensed Matter and Materials Physics [Online] 78:110. Available at: http://dx.doi.org/10.1103/PhysRevB.78.205426.
A densityfunctional formalism for superconductivity and magnetism is presented. The resulting relations unify previously derived KohnSham equations for superconductors and for noncollinear magnetism. The formalism, which discriminates Cooperpair 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 KohnSham equations, unperturbed by tunneling, on one side of the barrier to the proximityinduced ordering potential on the other.

Quintanilla, J., Haque, M. and Schofield, A. (2008). Symmetrybreaking 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 meanfield 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 preempted by a firstorder quantum phase transition. We provide the groundstate phase diagram in terms of our generic parameters.

Quintanilla, J., Hooley, C., Powell, B., Schofield, A. and Haque, M. (2008). Pomeranchuk instability: Symmetrybreaking and experimental signatures. Physica B: Condensed Matter [Online] 403:12791281. Available at: http://dx.doi.org/10.1016/j.physb.2007.10.126.
We discuss the emergence of symmetrybreaking via the Pomeranchuk instability from interactions that respect the underlying pointgroup symmetry. We use a variational meanfield theory to consider a 2D continuum and a square lattice. We describe two experimental signatures: a symmetrybreaking pattern of Friedel oscillations around an impurity; and a structural transition.

Campo, V., Capelle, K., Quintanilla, J. and Hooley, C. (2007). Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by twoparameter 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 finitesize scaling with an additional “finitecurvature scaling” necessary to reach the homogeneous limit. We illustrate its viability in the 1D case, simulating experimental data in the Betheansatz localdensity 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 smallworld 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 smallworld 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 finitesize 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 smallworld effect, as distinct from the previously discussed, dimensionalitydriven 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 particleparticle
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 interactiondriven topological transitions may be as generic
to such systems as the Pomeranchuk instability.

Hooley, C. and Quintanilla, J. (2006). Finitecurvature scaling in optical lattice systems. Physica B: Condensed Matter [Online] 37880:10351036. 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). Singleatom 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 tightbinding 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 36:93799390.
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 functionalintegral theory
of the BCS to Bose crossover. We find that, due to the lower energy
of twobody 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 weaklyattractive,
nonmonotonic 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., Gyorffy, B., Annett, J. and Wallington, J. (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 functionalintegral technique, we
study superconductivity with angular momentum quantum number l=2
as an emergent property of the manybody 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 dwave pairing for a range of densities. However, we find that
l=2 pairing takes place only in the BCS limit. In contrast, as the
BoseEinstein (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 swave 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 Tc. 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. (2002). On the nature of the superconducting gap in the cuprates. Journal of Physics: Condensed Matter [Online] 14:65916600. Available at: http://dx.doi.org/10.1088/09538984/14/25/325.
Recent experiments indicate that the excitation spectrum of the cuprates is characterized, in the superconducting state, by two energy scales: the 'coherence energy' Δc and the 'pseudogap' Δp. 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 singleparticle spectrum arising from the superconductivity and we find evidence that it corresponds to the lower of the two energy scales, Δc, seen in the experiments. This provides further support to the view that the origin of the pseudogap is not superconducting fluctuations.

Quintanilla, J. and Gyorffy, B. (2000). Finite range model interaction potential for dwave superconductors:Tc versus doping in the cuprates. Physica B: Condensed Matter 284:421422.
We study a simple, BCS like, model which describes unconventional superconductivity on the basis of an electronelectron attraction
corresponding to the deltashell potential: U(r(12)) =  g delta(r(12)
 r(0)). It predicts a Tc versus doping behavior similar to that
characteristic of the high Tc cuprates. (C) 2000 Elsevier Science
B.V. All rights reserved.