We show that the topological Majorana modes in nanowires much longer than the superconducting coherence length are adiabatically connected with discrete zero-energy states generically occurring in short nanowires. We demonstrate that these zero-energy crossings can be tuned by an external magnetic field and are protected by the particle-hole symmetry. We study the evolution of the low-energy spectrum and the splitting oscillations as a function of magnetic field, wire length, and chemical potential, manifestly establishing that the low-energy physics of short wires is related to that occurring in long wires. This physics, which represents a hallmark of spinless p-wave superconductivity, can be observed in tunneling conductance measurements.
We study the behavior of Cooper pair amplitudes that emerge when a two-dimensional superconductor is coupled to two parallel nanowires, focusing on the conditions for realizing odd-frequency pair amplitudes in the absence of spin-orbit coupling or magnetism. In general, any finite tunneling between the superconductor and the two nanowires induces odd-frequency spin-singlet pair amplitudes in the substrate as well as a substantial odd-frequency interwire pairing, both of which vanish locally. Interestingly, in the regime of strong superconductor-nanowire tunneling, we find that the presence of …
Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhom…
We consider a system of two one-dimensional nanowires coupled via an $s$-wave superconducting strip, a geometry that is capable of supporting Kramers pairs of Majorana fermions. By performing an exact analytical diagonalization of a tunneling Hamiltonian describing the proximity effect (via a Bogoliubov transformation), we show that the excitation gap of the system varies periodically on the scale of the Fermi wavelength in the limit where the interwire separation is shorter than the superconducting coherence length. Comparing with the excitation gaps in similar geometries containing only dire…
We have investigated the proximity effect in superconductor/ferromagnet junctions in a systematic manner to discuss the relationship between the zero-energy peak (ZEP) of the local density of states (LDOS) and spin-triplet odd-frequency pairing. By exactly solving the nonlinear Usadel equations, we have found that the ZEP is realized in a wide range of geometrical and material parameters in the case of the noncollinear magnetization. This strongly suggests the robustness of the ZEP induced by spin-triplet odd-frequency pairing in such systems. We also found that the crossover from singlet pair…
We theoretically investigate the transport properties of a quasi one dimensional ferromagnet-superconductor junction where the superconductor consists of mixed singlet and triplet pairings. We show that the relative orientation of the stoner field ($\bf{\tilde{h}}$) in the ferromagnetic lead and the $\bf{d}$ vector of the superconductor acts like a on-off switch for the zero bias conductance of the device. In the regime, where triplet pairing amplitude dominates over the singlet counterpart (topological phase), a pair of Majorana zero modes appear at each end of the superconducting part of the…
In this Letter, we first formulate an effective theory, which generally captures long-range proximity effects of a surface system weakly coupled to an s-wave superconductor. The long-range proximity effects include both the emergent long-range pairing and hopping interactions in the surface system. We then model the Rashba spin-orbit-coupled nanowire in proximity with an s-wave superconductor by taking into account the emergent nonlocal effects in the weak-coupling limit. In this limit the induced superconducting pair potential is found much smaller than that of the host superconductor, which …
It is difficult to unambiguously confirm the existence of Majorana zero modes (MZMs) due to the absence of smoking-gun signatures in charge transport measurements. Recent studies suggest that the spin degree of freedom of MZMs may provide an alternative detection method. We study the spin properties of the superconducting state in Majorana nanowires and the associated unconventional Josephson effect with realistic experimental parameters taken from [Zhang {\it et al.}, Nature 556, 74 (2018)]. For a superconducting thin film with in-plane polarized spin-triplet pairing, an out-of-plane electric…
Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip processes replacing the tunneling of Cooper pairs. When the quantum phase-slip amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can…
The novel idea that spin-orbit coupling (SOC) and $s$-wave pairing can lead to induced $p$-wave pairing at strong magnetic limit has stimulated widespread interests in the whole community for the searching of Majorana Fermions (MFs), a self-hermitian particle, in semiconductor-superconductor hybrid structures. However, this system has several inherent limitations that prohibit the realization and identification of MFs with the major advances of semiconductor nanotechnology. We show that these limitations can be resolved by replacing the $s$-wave superconductor with type-II Fulde-Ferrell (FF) s…
We discuss pairing signatures in mesoscopic nanowires with variable attractive pairing interaction. Depending on wire length, density, and interaction strength, these systems realize a simultaneous bulk-to-mesoscopic and BCS-BEC crossover, which we describe in terms of the parity parameter that quantifies the odd-even energy difference and generalizes the bulk Cooper pair binding energy to mesoscopic systems. We show that the parity parameter can be extracted from recent measurements of conductance oscillations in SrTiO$_3$ nanowires by G. Cheng et al. [Nature 521, 196 (2015)], where it marks …
Odd-frequency superconductivity, originally proposed by Berezinskii in 1974, is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. The pair potential is an odd function of frequency, leading to a vanishing static superconducting order parameter and exotic types of pairing seemingly inconsistent with Fermi statistics. Motivated by recent experimental progress in the realization of Majorana zero modes in semiconducting nanowires, we show that odd-frequency superconductivity generically appears in a spin-polarized nanowire coupled to Majorana zero…
We study the change in condensation energy from a single pair of fermionic atoms to a large number of pairs interacting via the reduced BCS potential. We find that the energy-saving due to correlations decreases when the pair number increases because the number of empty states available for pairing gets smaller ("moth-eaten effect"). However, this decrease dominates the 3D kinetic energy increase of the same amount of noninteracting atoms only when the pair number is a sizeable fraction of the number of states available for pairing. As a result, in BEC-BCS crossover of 3D systems, the condensa…
Among the different platforms to engineer Majorana fermions in one-dimensional topological superconductors, topological insulator nanowires remain a promising option. Threading an odd number of flux quanta through these wires induces an odd number of surface channels, which can then be gapped with proximity induced pairing. Because of the flux and depending on energetics, the phase of this surface pairing may or may not wind around the wire in the form of a vortex. Here we show that for wires with discrete rotational symmetry, this vortex is necessary to produce a fully gapped topological supe…
Strong evidence for pairing and superfluidity has recently been found in atomic Fermi gases at the BCS-BEC crossover both in collective modes and RF excitation energies. It is argued that the scale for the effective pairing gaps measured in RF experiments is set by the lowest quasiparticle in-gap excitation energies. These are calculated at the BCS-BEC crossover from semiclassical solutions to the Bogoliubov-deGennes equations. The strong damping of the radial breathing mode observed in the BCS limit occur when the lowest quasiparticle excitation energies coincide with the radial frequency, wh…
We show that in two-band $s$-wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband $s$-wave interactions, in sharp contrast to single-band $s$-wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: (I) BCS pairing in both b…
We study a double-nanowire setup proximity coupled to an $s$-wave superconductor and search for the bulk signatures of the topological phase transition that can be observed experimentally, for example, with an STM tip. Three bulk quantities, namely, the charge, the spin polarization, and the pairing amplitude of intrawire superconductivity are studied in this work. The spin polarization and the pairing amplitude flip sign as the system undergoes a phase transition from the trivial to the topological phase. In order to identify promising ways to observe bulk signatures of the phase transition i…
We report the fabrication of strongly coupled nanohybrid superconducting junctions using PbS semiconductor nanowires and Pb0.5In0.5 superconducting electrodes. The maximum supercurrent in the junction reaches up to ~15 μA at 0.3 K, which is the highest value ever observed in semiconductor-nanowire-based superconducting junctions. The observation of microwave-induced constant voltage steps confirms the existence of genuine Josephson coupling through the nanowire. Monotonic suppression of the critical current under an external magnetic field is also in good agreement with the narrow junction mod…
Recent experiments in semiconductor nanowires with a spin-orbit coupling and proximity-induced superconductivity exhibit signatures of Majorana bound states predicted to exist in the topological phase. In this work we predict that these nanowire systems exhibit unconventional magnetoelectric effects showing a sharp crossover behavior at the topological phase transition. We find that magnetic fields with a component parallel to the spin-orbit field can give rise to currents in equilibrium. Surprisingly, also fields perpendicular to the spin-orbit field may induce currents and can be employed in…
We study superfluid properties of fermions on a 2D lattice using a finite-range pairing interaction derivable from an extended Hubbard model. We obtain signatures of unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^*$), in the BCS-BEC crossover region. The fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k/u_k$, and the Fourier transform of $v_k^2$ are among the properties that are strikingly different for d- and $s^*$ symmetries in the crossover region. Fermionic atoms in 2D optical lattices may provide a way to observe these s…
We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by JILA group [J. T. Stewart {\it et al}., Nature \textbf{454}, 744 (2008)]. This quantity gives us very useful information about single-particle properties in the BCS-BEC crossover. In this letter, including pairing fluctuations within a $T$-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential is an important key to understand the observed spectrum. In the crossover region, whi…
The exact numerical diagonalization and thermodynamics in an ensemble of small Hubbard clusters in the ground state and finite temperatures reveal intriguing insights into the nascent charge and spin pairings, Bose condensation and ferromagnetism in nanoclusters. The phase diagram off half filling strongly suggests the existence of subsequent transitions from electron pairing into unsaturated and saturated ferromagnetic Mott-Hubbard like insulators, driven by electron repulsion. Rigorous criteria for the existence of quantum critical points in the ground state and corresponding crossovers at f…
We measure quantum and thermal phase-slip rates using the standard deviation of the switching current in superconducting nanowires at high bias current. Our rigorous quantitative analysis provides firm evidence for the presence of quantum phase slips (QPS) in homogeneous nanowires. We observe that as temperature is lowered, thermal fluctuations freeze at a characteristic crossover temperature Tq, below which the dispersion of the switching current saturates to a constant value, indicating the presence of QPS. The scaling of the crossover temperature Tq with the critical temperature Tc is linea…
A one-dimensional spin-orbit coupled nanowire with proximity-induced pairing from a nearby s-wave superconductor may be in a topological nontrivial state, in which it has a zero energy Majorana bound state at each end. We find that the topological trivial phase may have fermionic end states with an exponentially small energy, if the confinement potential at the wire's ends is smooth. The possible existence of such near-zero energy levels implies that the mere observation of a zero-bias peak in the tunneling conductance is not an exclusive signature of a topological superconducting phase even i…
We investigate the superconductivity in the $t-J-U$ model within a slave-spin formalism. We show that the BCS mean-field theory implemented with the slave spin formalism naturally predicts two distinct gaps which are the pairing gap of the spinons $Δ_f$ and the Cooper pairing gap of the electrons $Δ_{SC} = ZΔ_f$, where $Z$ is the quasiparticle weight. Furthermore, we find that the nature of the superconducting state depends crucially on the interaction providing the pairing mechanism. For spin interactions, the bandwidth of the spinon hopping term is renormalized by $Z$ but the its pairing ter…
We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^*$), in the BCS-BEC crossover region. We find that the fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k/u_k$, and the Fourier transform of $v_k^2$ are strikingly different for $d$- and $s^*$ symmetries in the crossover region. The chemical potential and the gaps functions for both pairing symmetries show several interesting features as a function of interaction. Fermion…
By adopting a $T$-matrix based method within $G_0G$ approximation for the pair susceptibility, we studied the effects of pairing fluctuation on the BCS-BEC crossover in symmetric nuclear matter. The pairing fluctuation induces a pseudogap in the excitation spectrum of nucleon in both superfluid and normal phases. The critical temperature of superfluid transition was calculated. It differs from the BCS result remarkably when density is low. We also computed the specific heat which shows a nearly ideal BEC type temperature dependence at low density but a BCS type behavior at high density. This q…
We have demonstrated that it is possible to access a crossover scenario starting with a weak coupling (BCS) d-wave superconductor to a strongly coupled Bose-Einstein condensate (BEC) phase as the exchange interaction is tuned in a two dimensional system described by a t-J-U model via numerically solving the Bogoliubov-de Gennes (BdG) equations. While in the extreme dilute limit, the electronic pairing phenomena is independent of the Coulomb repulsion, U, the superconductivity depends on U, and so does the crossover. Further, the effect of variation in the carrier density on the BCS-BEC crossov…
At a superconductor (S)-normal metal (N) junction pairing correlations can "leak-out" into the N region. This proximity effect [1, 2] modifies the system transport properties and can lead to supercurrent flow in SNS junctions [3]. Recent experimental works showed the potential of semiconductor nanowires (NWs) as building blocks for nanometre-scale devices [4-7], also in combination with superconducting elements [8-12]. Here, we demonstrate an InAs NW Josephson transistor where supercurrent is controlled by hot-quasiparticle injection from normal-metal electrodes. Operational principle is based…
We determine the optimal conditions to achieve topological superconducting phases having spin-singlet pairing for a planar nanowire with finite lateral width in the presence of an in-plane external magnetic field. We employ a microscopic description that is based on a three-band electronic model including both the atomic spin-orbit coupling and the inversion asymmetric potential at the interface between oxide band-gap insulators. We consider amplitudes of the pairing gap, spin-orbit interactions and electronic parameters that are directly applicable to nanowires of LaAlO$_3$-SrTiO$_3$. The lat…
We study the subgap Yu-Shiba-Rusinov (YSR) states in the Richardson's model of a superconductor with a magnetic impurity for different electron pairing strengths from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime to the strong-coupling Bose-Einstein-condensate (BEC) regime. We observe that the effect of the increasing pairing strength on the YSR excitation spectrum as a function of hybridisation strength and impurity on-site potential is only quantitative and, in fact, rather weak when the results are appropriately rescaled. We furthermore show that the problem is analytically solva…
Odd-frequency superconductivity is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. Majorana zero modes exhibit pure odd-frequency superconducting correlations due to their specific properties. Thus, by tunnel-coupling an array of Majorana zero modes to a spin-polarized wire, it is in principle possible to engineer a bulk one-dimensional odd-frequency spinless $s$-wave superconductor. We here point out that each tunnel coupling element, being dependent on a large number of material-specific parameters, is generically complex with sample varia…
We build a holographic model for the pairing fluctuation pseudogap phase in fermionic high temperature superconductivity/superfluidity based on the BCS-BEC crossover scenario. The pseudogap originates from incoherent Cooper pairing and has been observed in recent cold atom experiments. The strength of Cooper pairing and hence the BCS-BEC crossover is controlled by an effective 4-Fermi interaction and we argue that the double-trace deformation for charged scalar operator is a close analog in large N field theories. We employ the double-trace deformed Abelian Higgs model of holographic supercond…
We have fabricated disordered superconducting nanowires of molybdenium silicide. A molybdenium nanowire is first deposited on top of silicon, and the alloy is formed by rapid thermal annealing. The method allows tuning of the crystal growth to optimise, e.g., the resistivity of the alloy for potential applications in quantum phase slip devices and superconducting nanowire single-photon detectors. The wires have effective diameters from 42 to 79 nm, enabling the observation of crossover from conventional superconductivity to regimes affected by thermal and quantum fluctuations. In the smallest …
We study the superfluid critical temperature in a two-band attractive Fermi system with strong pairing fluctuations associated with both interband and intraband couplings. We focus specifically on a configuration where the intraband coupling is varied from weak to strong in a shallow band coupled to a weakly-interacting deeper band. The whole crossover from the Bardeen-Cooper-Schrieffer (BCS) condensation of largely overlapping Cooper pairs to the Bose-Einstein condensation (BEC) of tightly bound molecules is covered by our analysis, which is based on the extension of the Nozières-Schmitt-Rink…
We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen--Cooper--Schrieffer--Bose--Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic $T$ matrix approach, we~report how thermodynamic quantities such as the critical temperature, chemical potential, {and~momentum distributions} undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan's contact to a two band system and report the two contac…
The orbital effect on the Fulde-Ferrell (FF) phase is investigated in superconducting core/shell nanowires subjected to the axial magnetic field. The confinement in the radial direction results in the quantization of the electron motion with energies determined by the radial $j$ and orbital $m$ quantum numbers. In the external magnetic field the twofold degeneracy with respect to the orbital magnetic quantum number $m$ is lifted which leads to the Fermi wave vector mismatch between the paired electrons $(k, j,m,\uparrow) \leftrightarrow (-k, j,-m,\downarrow)$. This mismatch is transfered to th…
The theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in the BCS (weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc…
We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described b…
We study the key features of the Josephson transport through a curved semiconducting nanowire. Based on numerical simulations and analytical estimates within the framework of the Bogoliubov-de Gennes equations we find the ground-state phase difference $φ_0$ between the superconducting leads tuned by the spin splitting field $h$ driving the system from the topologically trivial to the nontrivial superconducting state. The phase $φ_0$ vanishes for rather small $h$, grows in a certain field range around the topological transition, and then saturates at large $h$ in the Kitaev regime. Both the sub…
We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $χ_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $χ_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing f…
We investigate effects of ordinary nonmagnetic disorder in the bulk of a superconductor on magnetic adatom-induced Shiba states and on the proximity-induced superconductivity in a nanowire that is tunnel coupled to the bulk superconductor. Within the formalism of self-consistent Born approximation, we show that, contrary to widespread belief, the proximity-induced topological superconductivity can be adversely affected by the bulk superconducting disorder even in the absence of any disorder in the nanowire (or the superconductor-nanowire interface) when the proximity tunnel coupling is strong.…
We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a …
BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory
Charles University（查理大学）；São Paulo State University (UNESP)（圣保罗州立大学）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）
For superconducting nanowire with the pairing of extended s-type symmetry, Rashba spin-orbit interaction in a magnetic field, the influence of strong intersite charge correlations on single-particle Majorana excitations is analyzed. This problem is investigated on the basis of the density matrix renormalization group numerical method. It is shown that with an increase in the repulsion intensity of electrons located at the neighboring sites, two subbands emerge in the lower Hubbard band of the open system. Based on calculations of the Majorana polarization and degeneracy of the entanglement spe…
High temperature superconductivity is a property of doped antiferromagnetic insulators. The electronic structure is inhomogeneous on short length and time scales, and, as the temperature decreases, it evolves via two crossovers, before long range superconducting order is achieved. Except for overdoped materials, pairing and phase coherence occur at different temperatures, and phase fluctuations determine both T$_c$ and the temperature dependence of the superfluid density for a wide range of doping. A mechanism for obtaining a high pairing scale in a short coherence length material with a stron…
We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half-filling where the electron-phonon coupling $g$ controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique. The dynamical effects induce distinct features such as absenceof the dispersion back-bending of Bogoliubov quasi-particles, non-monotonous coupling dependence of the pairing gap, and the soft phonon spectrum due to the Goldstone mode of local pair phase fluctuations. Also int…
We study the character change of the pionic condensation at finite isospin chemical potential μ_\mathrm{I} by adopting the linear sigma model as a non-local interaction between quarks. At low |μ_\mathrm{I}| the condensation is purely bosonic, then the Cooper pairing around the Fermi surface grows gradually as |μ_\mathrm{I}| increases. This q-\bar q pairing is weakly coupled in comparison with the case of the q-q pairing that leads to color superconductivity.
The pairing of interacting fermions leading to superfluidity has two limiting regimes: the Bardeen-Cooper-Schrieffer (BCS) scheme for weakly interacting degenerate fermions and the Bose-Einstein condensation (BEC) of bosonic pairs of strongly interacting fermions. While the superconductivity that emerges in most metallic systems is the BCS-like electron pairing, strongly correlated electrons with poor Fermi liquidity can condense into the unconventional BEC-like pairs. Quantum spin liquids harbor extraordinary spin correlation free from order and the superconductivity that possibly emerges by …
One of the major themes in the physics of condensed matter is unconventional superconductivity in correlated electronic systems. The symmetry structure of Cooper pairs is thought to be the key to the understanding of the pairing mechanism of their superconductivity. In iron pnictide superconductors, the precise symmetry of the order parameter as well its evolution with doping remains highly controversial. There is no general consensus on the nature of pairing in iron-based superconductors leaving the perspectives ranging from $s^{++}$ wave, to $s^{\pm}$, and $d$ wave. Here we show that doping …
Strongly correlated Fermi systems with pairing interactions become superfluid below a critical temperature $T_c$. The extent to which such pairing correlations alter the behavior of the liquid at temperatures $T > T_c$ is a subtle issue that remains an area of debate, in particular regarding the appearance of the so-called pseudogap in the BCS-BEC crossover of unpolarized spin-$1/2$ nonrelativistic matter. To shed light on this, we extract several quantities of crucial importance at and around the unitary limit, namely: the odd-even staggering of the total energy, the spin susceptibility, the …
