arXiv subjects

Lianyi He

Publications and source records attributed to Lianyi He.

At least 73 records · Page 4Linked to original sources

arXiv2013

Non-Galilean response of Rashba coupled Fermi gases

We consider the effect of a momentum kick on the ground state of a non-interacting two-dimensional Fermi gas subject to Rashba spin-orbit coupling. Although the total momentum is a constant of motion, the gas does not obey the rules of Galilean relativity. Upon imprinting a small overall velocity to the non-interacting gas, we find that the Fermi sea is deformed in a non-trivial way. We also consider a weakly repulsive Fermi gas, and find, from its Hartree shift, that the total ground state of the system may change into a deformed, finite momentum ground state as the repulsion is increased beyond a critical value, without the need of any external Zeeman fields. We also discuss possible experimental signatures of these effects.

cond-mat.quant-gas↗

arXiv2013

Pairing fluctuation effects in a strongly coupled color superfluid/superconductor

We investigate the effects of pairing fluctuations in fermionic superfluids/superconductors where pairing occurs among three species (colors) of fermions. Such color superfluids/superconductors can be realized in three-component atomic Fermi gases and in dense quark matter. The superfluidity/superconductivity is characterized by a three-component order parameter which denotes the pairing among the three colors of fermions. Due to the SU$(3)$ symmetry of the Hamiltonian, one color does not participate pairing. This branch of fermionic excitation is gapless in the naive BCS mean-field description. In this paper, we adopt a pairing-fluctuation theory to investigate the pairing fluctuation effects on the unpaired color in strongly coupled atomic color superfluids and quark color superconductors. At low temperature, a large pairing gap of the paired colors suppresses the pairing fluctuation effects for the unpaired color, and the spectral density of the unpaired color shows a single Fermi-liquid peak, which indicates the naive mean-field picture remains valid. As the temperature is increased, the spectral density of the unpaired color generally exhibits a three-peak structure: the Fermi-liquid peak remains but get suppressed, and two pseudogap-like peaks appears. At and above the superfluid transition temperature, the Fermi-liquid peak disappears completely and the all three colors exhibits pseudogap-like spectral density. The coexistence of Fermi liquid and pseudogap behavior is generic for both atomic color superfluids and quark color superconductors.

nucl-th↗

arXiv2013

Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential

QCD at finite isospin chemical potential $μ_{\text I}$ possesses a positively definite fermion determinant and the lattice simulation can be successfully performed. While the two-flavor effective models may be sufficient to describe the phenomenon of pion condensation, it is interesting to study the roles of the strangeness degree of freedom and the U$_{\rm A}(1)$ anomaly. In this paper, we present a systematic study of the three-flavor Nambu--Jona-Lasinio model with a Kobayashi-Maskawa-'t Hooft (KMT) term that mimics the U$_{\rm A}(1)$ anomaly at finite isospin chemical potential. In the mean-field approximation, the model predicts a phase transition from the vacuum to the pion superfluid phase, which takes place at $μ_{\rm I}$ equal to the pion mass $m_π$. Due to the U$_{\rm A}(1)$ anomaly, the strangeness degree of freedom couples to the light quark degrees of freedom and the strange quark effective mass depends on the pion condensate. However, the strange quark condensate and the strange quark effective mass change slightly in the pion superfluid phase, which verifies the validity of the two-flavor models. The effective four-fermion interaction of the Kobayashi-Maskawa-'t Hooft term in the presence of the pion condensation is constructed. Due to the U$_{\rm A}(1)$ anomaly, the pion condensation generally induces scalar-pseudoscalar interaction. The Bethe-Salpeter equation for the mesonic excitations is established and the meson mass spectra are obtained at finite isospin chemical potential and temperature. Finally, the general expression for the topological susceptibility $χ$ at finite isospin chemical potential $μ_{\rm I}$ is derived. In contrast to the finite temperature effect which suppresses $χ$, the isospin density effect leads to an enhancement of $χ$.

hep-ph↗

arXiv2013

Superfluidity and collective modes in Rashba spin-orbit coupled Fermi gases

We present a theoretical study of the superfluidity and the corresponding collective modes in two-component atomic Fermi gases with s-wave attraction and synthetic Rashba spin-orbit coupling. The general effective action for the collective modes is derived from the functional path integral formalism. By tuning the spin-orbit coupling from weak to strong, the system undergoes a crossover from an ordinary BCS/BEC superfluid to a Bose-Einstein condensate of rashbons. We show that the properties of the superfluid density and the Anderson-Bogoliubov mode manifest this crossover. At large spin-orbit coupling, the superfluid density and the sound velocity become independent of the strength of the s-wave attraction. The two-body interaction among the rashbons is also determined. When a Zeeman field is turned on, the system undergoes quantum phase transitions to some exotic superfluid phases which are topologically nontrivial. For the two-dimensional system, the nonanalyticities of the thermodynamic functions and the sound velocity across the phase transition are related to the bulk gapless fermionic excitation which causes infrared singularities. The superfluid density and the sound velocity behave nonmonotonically: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The three-dimensional system is also studied.

cond-mat.quant-gas↗

arXiv2013

BCS-BEC crossover at finite temperature in spin-orbit coupled Fermi gases

By adopting a $T$-matrix-based method within the $G_0G$ approximation for the pair susceptibility, we study the effects of the pairing fluctuation on the three-dimensional spin-orbit coupled Fermi gases at finite temperature. The critical temperatures of the superfluid/normal phase transition are determined for three different types of spin-orbit coupling (SOC): (1) the extreme oblate (EO) or Rashba SOC, (2) the extreme prolate (EP) or equal Rashba-Dresselhaus SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence of the critical temperature signals a crossover from BCS to BEC state; at strong SOC limit, the critical temperature recover those of ideal BEC of rashbons. The pairing fluctuation induces a pseudogap in the fermionic excitation spectrum in both superfluid and normal phases. We find that, for EO- and S-type SOC, even at weak coupling, sufficiently strong SOC can induce sizable pseudogap. Our research suggests that the spin-orbit coupled Fermi gases may open new means to the study of the pseudogap formation in fermionic systems.

cond-mat.quant-gas↗

arXiv2013

BCS-BEC quantum phase transition and collective excitations in two-dimensional Fermi gases with p- and d-wave pairings

It is generally believed that the BCS-BEC evolution in fermionic systems with s-wave pairing is a smooth crossover. However, for nonzero orbital-angular-momentum pairing such as p- or d-wave pairing, the system undergoes a quantum phase transition at the point where the chemical potential $μ$ vanishes. In this paper, we study the BCS-BEC quantum phase transition and the collective excitations associated with the order-parameter fluctuations in two-dimensional fermionic systems with p- and d-wave pairings. We show that the quantum phase transition in such systems can be generically traced back to the infrared behavior of the fermionic excitation at $μ=0$: $E_{\bf k}\sim k^l$, where $l=1,2$ is the quantum number of the orbital angular momentum. The nonanalyticity of the thermodynamic quantities is due to the infrared divergence caused by the fermionic excitation at $μ=0$. As a result, the evolution of the Anderson-Bogoliubov mode is not smooth: Its velocity is nonanalytical across the quantum phase transition.

cond-mat.quant-gas↗

arXiv2012

Unusual Zeeman-field effects in two-dimensional spin-orbit-coupled Fermi superfluids

We investigate the Zeeman field effects on the bulk superfluid properties and the collective modes in two-dimensional (2D) attractive atomic Fermi gases with Rashba-type spin-orbit coupling. In the presence of a large spin-orbit coupling, the system undergoes a quantum phase transition to a topological superfluid state at a critical Zeeman field. We show that the nonanalyticities of the thermodynamic functions as well as other physical quantities at the quantum phase transition originate from the infrared singularities caused by the gapless fermionic spectrum. The same argument applies also to the BCS-BEC evolution in 2D fermionic superfluids with $p$- or d-wave pairing. The superfluid density $n_s$ and the velocity of the Goldstone sound mode $c_s$ behave oppositely in the normal and the topological superfluid phases: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The velocity of the Goldstone sound mode also shows nonanalyticity at the quantum phase transition. For large Zeeman field, we find $n_s\rightarrow n$ and $c_s\rightarrow \upsilon_{\rm F}$, where $n$ is the total fermion density and $\upsilon_{\rm F}$ is the Fermi velocity of noninteracting system. The unusual behavior of the superfluid density and the collective modes can be understood by the fact that the spin-orbit-coupled superfluid state at large Zeeman field can be mapped to the $p_x+ip_y$ superfluid state of spinless fermions.

cond-mat.quant-gas↗

arXiv2012

BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling

We present a systematic theoretical study of the BCS-BEC crossover problem in three-dimensional atomic Fermi gases at zero temperature with a spherical spin-orbit coupling which can be generated by a synthetic non-Abelian gauge field coupled to neutral fermions. Our investigations are based on the path integral formalism which is a powerful theoretical scheme for the study of the properties of the bound state, the superfluid ground state, and the collective excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system enters the BEC state of a novel type of bound state (referred to as rashbon) which possesses a non-trivial effective mass. Analytical results and interesting universal behaviors for various physical quantities at large spin-orbit coupling are obtained. Our theoretical predictions can be tested in future experiments of cold Fermi gases with three-dimensional spherical spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2012

Nonperturbative Effects on the Ferromagnetic Transition in Repulsive Fermi Gases

It is generally believed that a dilute spin-1/2 Fermi gas with repulsive interactions can undergo a ferromagnetic phase transition to a spin-polarized state at a critical gas parameter $(k_{\rm F}a)_c$. Previous theoretical predictions of the ferromagnetic phase transition have been based on the perturbation theory, which treats the gas parameter as a small number. On the other hand, Belitz, Kirkpatrick, and Vojta (BKV) have argued that the phase transition in clean itinerant ferromagnets is generically of first order at low temperatures, due to the correlation effects that lead to a nonanalytic term in the free energy. The second-order perturbation theory predicts a first-order phase transition at $(k_{\rm F}a)_c=1.054$, consistent with the BKV argument. However, since the critical gas parameter is expected to be of order O(1), perturbative predictions may be unreliable. In this paper we study the nonperturbative effects on the ferromagnetic phase transition by summing the particle-particle ladder diagrams to all orders in the gas parameter. We consider a universal repulsive Fermi gas where the effective range effects can be neglected, which can be realized in a two-component Fermi gas of $^6$Li atoms by using a nonadiabatic field switch to the upper branch of a Feshbach resonance with a positive s-wave scattering length. Our theory predicts a second-order phase transition, which indicates that ferromagnetic transition in dilute Fermi gases is possibly a counterexample to the BKV argument. The predicted critical gas parameter $(k_{\rm F}a)_c=0.858$ is in good agreement with the recent quantum Monte Carlo result $(k_{\rm F}a)_c=0.86$ for a nearly zero-range potential [S. Pilati, \emph{et al}., Phys. Rev. Lett. {\bf 105}, 030405 (2010)]. We also compare the spin susceptibility with the quantum Monte Carlo result and find good agreement.

cond-mat.stat-mech↗

arXiv2012

BCS-BEC Crossover in 2D Fermi Gases with Rashba Spin-Orbit Coupling

We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy $E_{\text B}$ and effective mass $m_{\text B}$ of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable to the Fermi momentum. The ground-state properties and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature are studied, and analytical results are obtained in various limits. For large SOC, the BKT transition temperature recovers that for a Bose gas with an effective mass $m_{\text B}$. We find that the condensate and superfluid densities have distinct behaviors in the presence of SOC: the condensate density is generally enhanced by the SOC due to the increase of the molecule binding, the superfluid density is suppressed because of the non-trivial molecule effective mass $m_{\text B}$.

cond-mat.quant-gas↗

arXiv2011

Critical Zeeman Splitting of a Unitary Fermi Superfluid

We determine the critical Zeeman energy splitting of a homogeneous Fermi superfluid at unitary in terms of the Fermi energy $ε_{\text F}$ according to recent experimental results in LKB-Lhomond. Based on the universal equations of state for the superfluid and normal phases, we show that there exist two critical fields $H_{c1}$ and $H_{c2}$, between which a superfluid-normal mixed phase is energetically favored. Universal formulae for the critical fields and the critical population imbalance $P_c$ are derived. We have found a universal relation between the critical fields and the critical imbalances: $H_{c1}=γξε_{\text F}$ and $H_{c2}=(1+γP_c)^{2/3}H_{c1}$ where $ξ$ is the universal constant and $γ$ is the critical value of the chemical potential imbalance in the grand canonical ensemble. Since $ξ$, $γ$ and $P_c$ have been measured in the experiments, we can determine the critical Zeeman fields without the detail information of the equation of state for the polarized normal phase. Using the experimental data from LKB-Lhomond, we have found $H_{c1}\simeq0.37ε_{\text F}$ and $H_{c2}\simeq0.44ε_{\text F}$. Our result of the polarization $P$ as a function of the Zeeman field $H/ε_{\text F}$ is in good agreement with the data extracted from the experiments. We also give an estimation of the critical magnetic field for dilute neutron matter at which the matter gets spin polarized, assuming the properties of the dilute neutron matter are close to those of the unitary Fermi gas.

nucl-th↗

arXiv2010

Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories

QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential $μ_{\text B}$ and the lattice simulation can be successfully performed. While the chiral perturbation theories are sufficient to describe the Bose condensate at low density, to describe the crossover from Bose-Einstein condensation (BEC) to BCS superfluidity at moderate density we should use some fermionic effective model of QCD, such as the Nambu-Jona-Lasinio model. In this paper, using two-color two-flavor QCD as an example, we examine how the Nambu-Jona-Lasinio model describes the weakly interacting Bose condensate at low density and the BEC-BCS crossover at moderate density. Near the quantum phase transition point $μ_{\text B}=m_π$ ($m_π$ is the mass of pion/diquark multiplet), the Ginzburg-Landau free energy at the mean-field level can be reduced to the Gross-Pitaevskii free energy describing a weakly repulsive Bose condensate with a diquark-diquark scattering length identical to that predicted by the chiral perturbation theories. The Goldstone mode recovers the Bogoliubov excitation in weakly interacting Bose condensates. The results of in-medium chiral and diquark condensates predicted by chiral perturbation theories are analytically recovered. The BEC-BCS crossover and meson Mott transition at moderate baryon chemical potential as well as the beyond-mean-field corrections are studied. Part of our results can also be applied to real QCD at finite baryon or isospin chemical potential.

hep-ph↗

arXiv2010

Neutral Color Superconductivity Including Inhomogeneous Phases at Finite Temperature

We investigate neutral quark matter with homogeneous and inhomogeneous color condensates at finite temperature in the frame of an extended NJL model. By calculating the Meissner masses squared and gap susceptibility, the uniform color superconductor is stable only in a temperature window close to the critical temperature and becomes unstable against LOFF phase, mixed phase and gluonic phase at low temperatures. The introduction of the inhomogeneous phases leads to disappearance of the strange intermediate temperature 2SC/g2SC and changes the phase diagram of neutral dense quark matter significantly.

hep-ph↗

arXiv2009

Pion Superfluidity and Meson Properties at Finite Isospin Density

We investigate pion superfluidity and its effect on meson properties and equation of state at finite temperature and isospin and baryon densities in the frame of standard flavor SU(2) NJL model. In mean field approximation to quarks and random phase approximation to mesons, the critical isospin chemical potential for pion superfluidity is exactly the pion mass in the vacuum, and corresponding to the isospin symmetry spontaneous breaking, there is in the pion superfluidity phase a Goldstone mode which is the linear combination of the normal sigma and charged pion modes. We calculate numerically the gap equations for the chiral and pion condensates, the phase diagrams, the meson spectra, and the equation of state, and compare them with that obtained in other effective models. The competitions between pion superfluidity and color superconductivity at finite baryon density and between pion and kaon superfluidity at finite strangeness density in flavor SU(3) NJL model are briefly discussed.

hep-ph↗

arXiv2009

Critical Zeeman Splitting of Fermi Superfluidity at Infinite Scattering Length

We determine the critical Zeeman energy splitting for Fermi superfluidity at infinite s-wave scattering length according to the Monte Carlo and experimental results of the equations of state. Based on the universality hypothesis, we show that there exist two critical fields $H_{c1}$ and $H_{c2}$, between which a superfluid-normal mixed phase is energetically favored, and model-independent formulae for $H_{c1}$, $H_{c2}$ and the critical population imbalance $P_c$ are derived. Using recent Monte Carlo and experimental results of $P_c$, $H_{c1}$ and $H_{c2}$ are determined. It is found $H_{c1}=0.41ε_{\text F}$ and $H_{c2}=0.50ε_{\text F}$, with $ε_{\text F}$ being the Fermi energy of non-interacting gas.

cond-mat.supr-con↗

arXiv2009

Quark and Gluon Condensates in Isospin Matter

Applying the Hellmann-Feynman theorem to a charged pion gas, the quark and gluon condensates at low isospin density are determined by precise pion properties. At intermediate density around $ f_π^2m_π$, from both the estimation for the dilute pion gas and the calculation with Nambu--Jona-Lasinio model, the quark condensate is strongly and monotonously suppressed, while the gluon condensate is enhanced and can be larger than its vacuum value. This unusual behavior of the gluon condensate is universal for Bose condensed matter of mesons. Our results can be tested by lattice calculations at finite isospin density.

nucl-th↗

arXiv2009

Stable Sarma State in Two-band Fermi Systems

We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gapless Fermi surfaces which is always unstable in single-band systems, can be the stable ground state in two-band systems. To realize a visible mismatch window for the stable Sarma state, two conditions should be satisfied: a nonzero inter-band exchange interaction and a large asymmetry between the two bands.

cond-mat.supr-con↗

arXiv2008

BEC-BCS Crossover in the Nambu--Jona-Lasinio Model of QCD

The BEC-BCS crossover in QCD at finite baryon and isospin chemical potentials is investigated in the Nambu--Jona-Lasinio model. The diquark condensation in two color QCD and the pion condensation in real QCD would undergo a BEC-BCS crossover when the corresponding chemical potential increases. We determined the crossover chemical potential as well as the BEC and BCS regions. The crossover is not triggered by increasing the strength of attractive interaction among quarks but driven by changing the charge density. The chiral symmetry restoration at finite temperature and density plays an important role in the BEC-BCS crossover. For real QCD, strong couplings in diquark and vector meson channels can induce a diquark BEC-BCS crossover in color superconductor, and in the BEC region the chromomagnetic instability is fully cured and the ground state is a uniform phase.

hep-ph↗