arXiv subjects

Daniel E. Sheehy

Publications and source records attributed to Daniel E. Sheehy.

At least 19 recordsLinked to original sources

arXiv2026

Pairing near the boundary of a box-shaped trap in the BEC-BCS crossover

We study pairing of attractively interacting fermions confined to a box-shaped trap. In contrast to the infinite translationally-invariant case, where the local pairing order is spatially uniform and undergoes the Bose-Einstein Condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover as interactions are varied, in this case the local pairing is expected to vary rapidly near the edge of the box. We address this problem in the limit of a semi-infinite superfluid, finding that the nature of the edge pairing depends sensitively on the coupling. The local pairing exhibits Friedel-like oscillations in the weak coupling BCS regime that are suppressed with increasing coupling strength towards the BEC regime.

cond-mat.quant-gas↗

arXiv2025

Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems

We study two-dimensional massless Dirac fermions at neutrality, coupled to bosonic modes through a Yukawa interaction. We then examine the intriguing possibility that such a system, devoid of carriers at zero temperature, might nevertheless exhibit superconductivity. Remarkably, we find that superconductivity emerges in the vicinity of Gross-Neveu quantum criticality, provided the fermions cease to behave as well-defined quasiparticles, that is, once their anomalous dimension in the normal state becomes sufficiently large. In other words, well-defined fermions do not superconduct, whereas ill-defined ones do. We analyze four symmetry-distinct bosonic modes, each capable of driving normal-state criticality and, in three of the four cases, giving rise to a distinct superconducting phase. While phase fluctuations are strong in this regime, we argue that they do not destroy the superconducting state. We further characterize the resulting pairing states for a concrete Dirac model of spin-orbit coupled systems with orbitals of different parity. Our results are obtained using the SYK-inspired framework for Dirac systems introduced by Kim et al.[1], which provides a controlled approach to the strongly coupled regime of Dirac fluids near Gross-Neveu criticality.

cond-mat.str-el↗

arXiv2025

Superconductivity of Incoherent Electrons near the Relativistic Mott Transition in Twisted Dirac Materials

We demonstrate that superconductivity driven by strong quantum-critical fluctuations can emerge near relativistic Mott transitions in twisted two-dimensional materials, taking on a remarkably rich character. In twisted double-bilayer WSe$_2$, all time-reversal-even, gap-opening collective modes promote pairing, whereas time-reversal-odd modes do not. In a Dirac model of twisted bilayer graphene, the Gross-Neveu transition into inter-valley-coherent insulators gives rise to a spectrum of degenerate and nearly degenerate superconducting states. More generally, we show that the richer the Dirac structure, the more readily pairs can form. A crucial ingredient of the theory is that critical fluctuations render the electronic states strongly incoherent, allowing attractive pairing channels to overcome the bare Dirac semi-metal behavior. Finally, we demonstrate a direct relation between boson-mediated pairing and the formation of charge-carrying skyrmionic excitations in the proximate insulating state.

cond-mat.str-el↗

arXiv2025

Phonon Dynamics in Spherically-Curved Analog-Gravity Bose-Einstein Condensates

We study the low energy phonon dynamics of a Bose-Einstein condensate (BEC) with a density profile that is equivalent, via a coordinate transformation, to phonons traveling in a \lq\lq spherical\rq\rq\ curved spacetime that realizes the Friedman-Lemaître-Robertson-Walker (FLRW) metric. The metric of this BEC is characterized by its curvature $κ$ and a time-depdendent scale factor $a(t)$, with an increase in the latter corresponding to an expansion of the analog FLRW universe. We study the propagation of classical phonons in such BECs, finding that a sudden change in the scale factor induces ripples in the wave motion. In addition, we study quantum phonon creation (or vacuum amplification) due to the scale-factor modification and quantify their entanglement.

cond-mat.quant-gas↗

arXiv2024

Analog Unruh effect of inhomogeneous one-dimensional Dirac fermions

We study one-dimensional Dirac fermions in the presence of a spatially-varying Dirac velocity $v(x)$, that can form an approximate lab-based Rindler Hamiltonian describing an observer accelerating in Minkowski spacetime. A sudden switch from a spatially homogeneous velocity ($v(x)$ constant) to a spatially-verying velocity ($v(x)$ inhomogeneous) leads to the phenomenon of particle creation, i.e., an analog Unruh effect. We study the dependence of the analog Unruh effect on the precise form of the velocity profile, finding that while the ideal Unruh effect occurs for $v(x) \propto |x|$, a modified Unruh effect still occurs for more realistic velocity profiles that are linear for $|x|$ smaller than a length scale $λ$ and constant for $|x|\gg λ$ (such as $v(x)\propto \tanh \big(|x|/λ\big)$). We show that the associated particle creation is localized to $|x|\ll λ$.

cond-mat.mes-hall↗

arXiv2024

Inflationary Dynamics and Particle Production in a Toroidal Bose-Einstein Condensate

We present a theoretical study of the dynamics of a Bose-Einstein condensate (BEC) trapped inside an expanding toroid that can realize an analogue inflationary universe. As the system expands, we find that phonons in the BEC undergo redshift and damping due to quantum pressure effects, owing to the thinness of the ring. We predict that rapidly expanding toroidal BEC's can exhibit spontaneous particle creation, and study this phenomenon in the context of an initial coherent state wavefunction. We show how particle creation would be revealed in the atom density and density correlations, and discuss connections to the cosmological theory of inflation.

cond-mat.quant-gas↗

arXiv2023

Entanglement in an expanding toroidal Bose-Einstein condensate

Recent experiments have employed rapidly expanding toroidal Bose-Einstein condensates (BECs) to mimic the inflationary expansion in the early universe. One expected signature of the expansion in such experiments is spontaneous particle creation (of phonons) which is observable in density-density correlations. We study entanglement of these particles, which are known to result in a two-mode squeezed state. Using techniques for Gaussian states of continuous variable systems, we quantify the entanglement generated in this system, including effects such as decoherence and the use of an initially squeezed state, which can suppress and enhance entanglement, respectively. We also describe a protocol to experimentally measure the correlations entering the covariance matrix, allowing an experimental quantification of the entanglement properties of the inflationary BEC.

cond-mat.quant-gas↗

arXiv2023

Unruh Effect and Takagi's Statistics Inversion in Strained Graphene

We present a theoretical study of how a spatially-varying quasiparticle velocity in honeycomb lattices, achievable using strained graphene or in engineered cold-atom optical lattices that have a spatial dependence to the local tunneling amplitude, can yield the Rindler Hamiltonian embodying an observer accelerating in Minkowski spacetime. Within this setup, a sudden switch-on of the spatially-varying tunneling (or strain) yields a spontaneous production of electron-hole pairs, an analogue version of the Unruh effect characterized by the Unruh temperature. We discuss how this thermal behavior, along with Takagi's statistics inversion, can manifest themselves in photo-emission and scanning tunneling microscopy experiments. We also calculate the average electronic conductivity and find that it grows linearly with frequency $ω$. Finally, we find that the total system energy at zero environment temperature looks like Planck's blackbody result for photons due to the aforementioned statistics inversion, whereas for an initial thermally excited state of fermions, the total internal energy undergoes stimulated particle reduction.

cond-mat.mes-hall↗

arXiv2021

Andreev spectroscopy of nonhelical spin textures in topological insulators

We study how nonhelical spin textures affect the proximity-induced superconductivity of topological insulator (TI)-superconductor (SC) interface states. In particular we calculate the conductance of lateral heterojunctions which comprise a TI surface that is only partially covered by a superconducting material. Interface potentials at the TI-SC interface may lead to a Fermi velocity and spin texture mismatch between the two regions of the lateral heterojunction. By enforcing the hermiticity of the total Hamiltonian, we derive the boundary conditions and calculate the conductance of the structure in both the normal and superconducting state. The total Andreev conductance is calculated for both $s$-wave and spin-triplet parent SCs, and for several examples of nonhelical spin textures which lead to different Fermi surface mismatches between the two planar regions of the heterojunction. We find that for spin-triplet SCs, nonzero conductance signatures only appear for certain combinations of nonhelical spin textures and parent superconducting material.

cond-mat.supr-con↗

arXiv2020

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Ground state Hartree-Fock-Bogoliubov (HFB) theory is applied to imbalanced spin-1/2 one-dimensional Fermi systems that are spatially confined by either a harmonic or a hard-wall trapping potential. It has been hoped that such systems, which can be realized using ultracold atomic gases, would exhibit the long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. The HFB formalism generalizes the standard Bogoliubov quasi-particle transformation, by allowing for Cooper pairing to exist between all possible single-particle states, and accounts for the effects of the inhomogeneous trapping potential as well as the mean-field Hartree potential. This provides an unbiased framework to describe inhomgenous densities and pairing correlations in the FFLO state of a confined 1D gas. In a harmonic trap, numerical minimization of the HFB ground state energy yields a spatially oscillating order parameter reminiscent of the FFLO state. However, we find that this state has almost no imprint in the local fermion densities (consistent with experiments that found no evidence of the FFLO phase). In contrast, for a hard-wall geometry, we find a strong signature of the spatial oscillations of the FFLO pairing amplitude reflected in the local in situ densities. In the hard wall case, the excess spins are strongly localized near regions where there is a node in the pairing amplitude, creating an unmistakeable crystalline modulation of the density.

cond-mat.quant-gas↗

arXiv2020

Volkov-Pankratov states in topological superconductors

We study the in-gap states that appear at the boundaries of both 1D and 2D topological superconductors. While the massless Majorana quasiparticles are guaranteed to arise by the bulk-edge correspondence, we find that they could be accompanied by massive Volkov-Pankratov (VP) states which are present only when the interface is sufficiently smooth. These predictions can be tested in an s-wave superconductor with Rashba spin-orbit coupling placed on top of a magnetic domain wall. We calculate the spin-resolved local density of states of the VP states about the band inversion generated by a magnetic domain wall and find that they are oppositely spin-polarized on either side of the topological phase boundary. We also demonstrate that the spatial position, energy-level spacing, and spin polarization of the VP states can be modified by the introduction of in-plane electric fields.

cond-mat.supr-con↗

arXiv2019

Renormalization group approach to the normal phase of 2D Fermi gases

We present results on the effect of short-range, attractive interactions on the properties of balanced 2D Fermi gases in the non-superfluid (normal) phase. Our approach combines the renormalization group (RG) with perturbation theory, yielding observables such as the equation of state and compressibility. We find good agreement with recent experiments that measured the equation of state in trapped gases in the balanced regime, showing that these results are consistent with logarithmic corrections in the equation of state.

cond-mat.quant-gas↗

arXiv2018

Elastic response of the electron fluid in intrinsic graphene: The collisionless regime

The elastic response of an electron fluid at finite frequencies is defined by the electron viscosity $η(ω)$. We determine $η(ω)$ for graphene at the charge neutrality point in the collisionless regime, including the leading corrections due to the electron-electron Coulomb interaction. We find interaction corrections to $η(ω)$ that are significantly larger if compared to the corresponding corrections to the optical conductivity. In addition, we find comparable contributions to the dynamic momentum flux due to single-particle and many-particle effects. We also demonstrate that $η(ω)$ is directly related to the nonlocal energy-flow response of graphene at the Dirac point. The viscosity in the collisionless regime is determined with the help of the strain generators in the Kubo formalism. Here, the pseudo-spin of graphene describing its two sublattices plays an important role in obtaining a viscosity tensor that fulfills the symmetry properties of a rotationally symmetric system.

cond-mat.str-el↗

arXiv2018

Proximity-Induced Superconductivity at Non-Helical Topological Insulator Interfaces

We study how non-helical spin textures at the boundary between a topological insulator (TI) and a superconductor (SC) affect the proximity-induced superconductivity of the TI interface state. We consider TIs coupled to both spin-singlet and spin-triplet SCs, and show that for the spin-triplet parent SCs the resulting order parameter induced onto the interface state sensitively depends on the symmetries which are broken at the TI-SC boundary. For chiral spin-triplet parent SCs, we find that nodal proximity-induced superconductivity emerges when there is broken twofold rotational symmetry which forces the spins of the non-helical topological states to tilt away from the interface plane. We furthermore show that the Andreev conductance of lateral heterostructures joining TI-vacuum and TI-SC interfaces yields experimental signatures of the reduced symmetries of the interface states.

cond-mat.supr-con↗

arXiv2018

Topological phases of topological insulator thin films

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi$_2$Se$_3$ and Bi$_2$Te$_3$. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi$_2$Se$_3$, making Bi$_{2}$Te$_{3}$, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators.

cond-mat.mes-hall↗

arXiv2017

Microcanonical analysis of Boltzmann and Gibbs Entropies in trapped cold atomic gases

We analyze a gas of noninteracting fermions confined to a one-dimensional harmonic oscillator potential, with the aim of distinguishing between two proposed definitions of the thermodynamic entropy in the microcanonical ensemble, namely the standard Boltzmann entropy and the Gibbs (or volume) entropy. The distinction between these two definitions is crucial for systems with an upper bound on allowed energy levels, where the Boltzmann definition can lead to the notion of negative absolute temperature. Although negative temperatures do not exist for the system of fermions studied here, we still find a significant difference between the Boltzmann and Gibbs entropies, and between the corresponding temperatures with the Gibbs temperature being closer (for small particle number) to the temperature based on a grand canonical picture.

cond-mat.stat-mech↗

arXiv2017

Trapped imbalanced fermionic superfluids in one dimension: A variational approach

We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Although we find no signature of the FFLO state in the densities of the two fermion species, we show that the oscillations of the order parameter appear in density-density correlations, both in-situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.

cond-mat.quant-gas↗

arXiv2016

Interface symmetry and spin control in topological insulator-semiconductor heterostructures

Heterostructures combining topological and non-topological materials constitute the next frontier in the effort to incorporate topological insulators (TIs) into functional electronic devices. We show that the properties of the interface states appearing at the planar boundary between a topologically-trivial semiconductor (SE) and a TI are controlled by the symmetry of the interface. In contrast to the well-studied helical Dirac surface states, SE-TI interface states exhibit elliptical contours of constant energy and complex spin textures with broken helicity. We derive a general effective Hamiltonian for SE-TI junctions, and propose experimental signatures such as an out of plane spin accumulation under a transport current and the opening of a spectral gap that depends on the direction of an applied in-plane magnetic field.

cond-mat.mes-hall↗