arXiv subjects

Yan He

Publications and source records attributed to Yan He.

At least 109 records · Page 6Linked to original sources

arXiv2016

Analytic Solution of the Ornstein-Zernike Relation for Inhomogeneous Liquids

The properties of a classical simple liquid can be strongly affected by application of an external potential that supports inhomogeneity. To understand the nature of these property changes the equilibrium particle distribution functions of the liquid have, typically, been evaluated individually as functions of system control parameters, such as the packing fraction of a hard sphere liquid. In this study we focus attention on two distribution functions that characterize the inhomogeneous liquid: the pair direct correlation function $c(\mathbf{r}_1,\mathbf{r}_2)$ and the pair correlation function $g(\mathbf{r}_1,\mathbf{r}_2)$. We solve the Ornstein-Zernike equation for the inhomogeneous liquid to obtain $c(\mathbf{r}_1,\mathbf{r}_2)$ as an explicit function of $g(\mathbf{r}_1,\mathbf{r}_2)$, with the latter considered to be an experimental observable, using information about the well studied and resolved $g^0(\mathbf{r}_1-\mathbf{r}_2)$ and $c^0(\mathbf{r}_1-\mathbf{r}_2)$ for the parent homogeneous ($^0$) system. The result obtained with our formulation is tested against the exact solutions for the correlation and distribution functions of a one-dimensional inhomogeneous hard rod liquid. Following the success of that test the formalism is extended to obtain $c(\mathbf{r}_1,\mathbf{r}_2)$ as an explicit function of $g(\mathbf{r}_1,\mathbf{r}_2)$ in a three dimensional liquid.

cond-mat.soft↗

arXiv2016

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

By using Bogoliubov transformations to construct the ground states of fermionic Bardeen-Cooper-Schrieffer (BCS) superfluids and weakly-interacting Bose gases supporting Bose Einstein Condensation (BEC), their algebraic structures and implications can be analyzed in detail. Both ground states are generalized squeezed coherent states saturating a generalized Heisenberg uncertainty relation, and they acquire quantized Berry phases when the corresponding systems are transported along a closed path in their parameter spaces. While the Berry phase of the BCS ground state depends on the total particle number, the Berry phase of the BEC ground state depends only on the particles outside the BEC. The Berry phases are associated with magnetic monopoles in the parameter spaces and we found that the Dirac quantization condition is satisfied. Moreover, both ground states are entangled states of the fermion or boson quanta and we found the entanglement entropy quantifying the internal correlations. A fixed particle-number approach of fermionic superfluids does not saturate the generalized uncertainty relation, exhibits internal entanglement, and gives corresponding Berry phase. In addition, the algebraic structures of the ground states can be classified by the $q$-deformed Hopf algebra, $\bigoplus_{\mathbf{k}}h_{q_{\mathbf{k}}}(1)$ for bosons and $q$-deformed Hopf superalgebra $\bigoplus_{\mathbf{k}}h_{q_{\mathbf{k}}}(1|1)$ for fermions, respectively.

cond-mat.quant-gas↗

arXiv2016

Boundary-induced dynamics in 1D topological systems and memory effects of edge modes

Dynamics induced by a change of boundary conditions reveals rate-dependent signatures associated with topological properties in one-dimensional Kitaev chain and SSH model. While the perturbation from a change of the boundary propagates into the bulk, the density of topological edge modes in the case of transforming to open boundary condition reaches steady states. The steady-state density depends on the transformation rate of the boundary and serves as an illustration of quantum memory effects in topological systems. Moreover, while a link is physically broken as the boundary condition changes, some correlation functions can remain finite across the broken link and keep a record of the initial condition. By testing those phenomena in the non-topological regimes of the two models, none of the interesting signatures of memory effects can be observed. Our results thus contrast the importance of topological properties in boundary-induced dynamics.

cond-mat.mes-hall↗

arXiv2015

BCS-BEC crossover of Spin Polarized Fermi Gases with Rashba Spin-Orbit Coupling

We study the BCS-Bose Einstein Condensation (BEC) crossover of a three dimensional spin polarized Fermi gas with Rashba spin-orbital-coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the $G_0G$ pair fluctuation theory. These fluctuations generate a pseudogap even persistent above $T_c$. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting $T_c$ curves show that the enhancement of pairing due to the SOC roughly cancels out the suppression of pairing due to the population imbalance. Thus we observed that in a large portion of the parameter space, the polarized superfluid state are stabilized by the SOC.

cond-mat.quant-gas↗

arXiv2015

Establishing the Gauge Invariant Linear Response of Fermionic Superfluids with Pair Fluctuations: A Diagrammatic approach

We present a manifestly gauge invariant linear response theory for ultra-cold Fermi gases undergoing BCS-Bose-Einstein Condensation (BEC) crossover with pair fluctuation effect included, especially in the superfluid phase, by introducing an effective external electromagnetic (EM) field. For pure BCS-type superfluids, the gauge invariance of the linear response theory can be maintained by constructing a full external EM vertex by including the fluctuation of the order parameters in the same way as the the self-energy effect is included in the quasi-particle, therefore the Ward identity (WI) is satisfied. While for the Fermionic superfluids with pairing fluctuation effect included in the quasi-particle self-energy, the construction of a gauge invariant vertex is non-trivial, since in the broken symmetry phase the effect of Nambu-Goldstone modes (collective modes) intertwines with that of the pairing fluctuation. In this paper, we find that under a suitable diagrammatic representation, the construction of such vertex is greatly simplified, which allow us to build a WI-maintaining vertex with pseudogap effects included in the superfluid phase. We focus on the $G_0G$ $t$-matrix approach to the pair fluctuations, although our formalism should also works equally well for the $G_0G_0$ $t$-matrix theory.

cond-mat.quant-gas↗

arXiv2014

Conserving Approximation of Pairing theories in Fermionic superfluid phase

Respecting the conservation laws of momentum and energy in a many body theory is very important for understanding the transport phenomena. The previous conserving approximation requires that the self-energy of a single particle can be written as a functional derivative of a full dressed Green's function. This condition can not be satisfied in the $G_0G$ t-matrix or pair fluctuation theory which emphasizes the fermion pairing with a stronger than the Bardeen-Cooper-Schrieffer (BCS) attraction. In the previous work\cite{stressWI}, we have shown that when the temperature is above the superfluid transition temperature $T_c$, the $G_0G$ t-matrix theory can be put into a form that satisfies the stress tensor Ward identity (WI) or local form of conservation laws by introducing a new type of vertex correction. In this paper, we will extend the above conservation approximation to the superfluid phase in the BCS mean field level. To establish the stress tensor WI, we have to include the fluctuation of the order parameter or the contribution from the Goldstone mode. The result will be useful for understanding the transport properties such as the behavior of the viscosity of Fermionic gases in the superfluid phases.

cond-mat.quant-gas↗

arXiv2014

Gauge Invariant Linear Response Theories for Ultracold Fermi Gases with Pseudogap

Recent experimental progresses allow for exploring some important physical quantities of ultracold Fermi gases, such as the compressibility, spin susceptibility, viscosity, optical conductivity and spin diffusivity. Theoretically, these quantities can be evaluated from suitable linear response theories. For BCS superfluid, it has been found that the gauge invariant linear response theories can be fully consistent with some stringent consistency constraints. When the theory is generalized to stronger-than-BCS regime, one may meet serious difficulties to satisfy the gauge invariance conditions. In this paper, we try to construct density and spin linear response theories which are formally gauge invariant for a Fermi gas undergoing BCS-Bose-Einstein Condensation (BEC) crossover, especially below the superfluid transition temperature $T_c$. We adapt a particular $t$-matrix approach which is close to the $G_0G$ formalism to incorporate non-condensed pairing in the normal state. We explicitly show that the fundamental constraints imposed by the Ward identities, $Q$-limit Ward identity are indeed satisfied.

cond-mat.quant-gas↗

arXiv2014

Intrinsic Anomalous Hall Effect in Magneto-Chiral States

We show that a finite Hall effect in zero applied magnetic field occurs for partially filled bands in certain time-reversal violating states with zero net flux per unit-cell. These states are the Magneto-chiral states with parameters in the effective one-particle Hamiltonian such that they do not satisfy the Haldane-type constraints for topological electronic states. The results extend an earlier discussion of the Kerr effect observed in the cuprates but may be applicable to other experimental situations.

cond-mat.str-el↗

arXiv2014

The $Z_2$ Classification of Dimensional Reduced Hopf Insulators

The Hopf insulators are characterized by a topological invariant called Hopf index which classifies maps from three-sphere to two-sphere, instead of a Chern number or a Chern parity. In contrast to topological insulator, the Hopf insulator is not protected by any kind of symmetry. By dimensional reduction, we argue that there exists a new type of $\mathbb{Z}_2$ index for 2D Hamiltonian with vanishing Chern number. Specific model Hamiltonian with this nontrivial $\mathbb{Z}_2$ index is constructed. We also numerically calculate the topological protected edge modes of this dimensional reduced Hopf insulator and show that they are consistent with the $\mathbb{Z}_2$ classification.

cond-mat.mes-hall↗

arXiv2014

Unified treatment of Fermi pockets and arcs scenarios for the cuprates: Sum rule consistent response functions of the pseudogap

Essential to understanding the cuprate pseudogap phase is a study of the charge (and spin) response functions, which we address here via a consistent approach to the Fermi arcs and the Fermi pockets scenario of Yang, Rice and Zhang (YRZ). The two schemes are demonstrated to be formally similar, and to share a common physics platform; we use this consolidation to address the inclusion of vertex corrections which have been omitted in YRZ applications. We show vertex corrections can be easily implemented in a fashion analytically consistent with sum rules and that they yield important contributions to most observables. A study of the charge ordering susceptibility of the YRZ scenario makes their simple physics evident: they represent the inclusion of charged bosonic, spin singlet degrees of freedom, and are found to lead to a double peak structure.

cond-mat.supr-con↗

arXiv2014

Topological Soliton with Nonzero Hopf Invariant in Yang-Mills-Higgs Model

We propose a topological soliton or instanton solution with nonzero Hopf invariant to the 3+1D non-Abelian gauge theory coupled with scalar fields. This solution, which we call Hopf soliton, represents a spacetime event that makes a $2π$ rotation of the monopole. Although the action of this Hopf soliton is logarithmically divergent, it may still give relevant contributions in a finite-sized system. Since the Chern-Simons term for the unbroken $U(1)$ gauge field may appear in the low energy effective theory, the Hopf soliton may possibly generate fractional statistics for the monopoles.

math-ph↗

arXiv2013

Density and Spin Linear Response of Atomic Fermi Superfluids with Population Imbalance in BCS-BEC Crossover

We present a theoretical study of the density and spin (representing the two components) linear response of Fermi superfluids with tunable attractive interactions and population imbalance. In both linear response theories, we find that the fluctuations of the order parameter must be treated on equal footing with the gauge transformations associated with the symmetries of the Hamiltonian so that important constraints including various sum rules can be satisfied. Both theories can be applied to the whole BCS-Bose-Einstein condensation crossover. The spin linear responses are qualitatively different with and without population imbalance because collective-mode effects from the fluctuations of the order parameter survive in the presence of population imbalance, even though the associated symmetry is not broken by the order parameter. Since a polarized superfluid becomes unstable at low temperatures in the weak and intermediate coupling regimes, we found that the density and spin susceptibilities diverge as the system approaches the unstable regime, but the emergence of phase separation preempts the divergence.

cond-mat.quant-gas↗

arXiv2013

Quantum oscillations in non-Fermi liquids: Implications for high-temperature superconductors

We address quantum oscillation experiments in high Tc superconductors and the evidence from these experiments for a pseudogap versus a Fermi liquid phase at high magnetic fields. As a concrete alternative to a Fermi liquid phase, the pseudogap state we consider derives from earlier work within a Gor'kov-based Landau level approach. Here the normal state pairing gap in the presence of high fields is spatially non-uniform, incorporating small gap values. These, in addition to d-wave gap nodes, are responsible for the persistence of quantum oscillations. Important here are methodologies for distinguishing different scenarios. To this end we examine the temperature dependence of the oscillations. Detailed quantitative analysis of this temperature dependence demonstrates that a high field pseudogap state in the cuprates may well "masquerade" as a Fermi liquid.

cond-mat.supr-con↗

arXiv2013

Establishing Conservation Laws in Pair Correlated Many Body theories: T matrix Approaches

We address conservation laws associated with current, momentum and energy and show how they can be satisfied within many body theories which focus on pair correlations. Of interest are two well known t-matrix theories which represent many body theories which incorporate pairing in the normal state. The first of these is associated with Nozieres Schmitt-Rink theory, while the second involves the t-matrix of a BCS-Leggett like state as identified by Kadanoff and Martin. T-matrix theories begin with an ansatz for the single particle self energy and are to be distinguished from $Φ$-derivable theories which introduce an ansatz for a particular contribution to the thermodynamical potential. Conservation laws are equivalent to Ward identities which we address in some detail here. Although $Φ$-derivable theories are often referred to as "conserving theories", a consequence of this work is the demonstration that these two t-matrix approaches similarly can be made to obey all conservation laws. Moreover, simplifying approximations in $Φ$-derivable theories, frequently lead to results which are incompatible with conservation.

cond-mat.quant-gas↗

arXiv2013

The Compressibility in Strongly Correlated Superconductors and Superfluids: From BCS to BEC

We present a theoretical study of the compressibility, $κ$, in a Fermi gas with attractive contact interactions, providing predictions for the strongly-attractive regime and the superfluid phase. Our work emphasizes the compressibility sum rule and gauge invariance as constraints on $κ$ and we show how within a particular $t$-matrix approach, these can be satisfied in the normal phase when no approximations are made. For tractability, approximations must be introduced, and it is believed that thermodynamical approaches to $κ$ are more reliable, than correlation function based schemes. Contrasting with other studies in the literature, we present thermodynamic calculations of $κ$; these yield semi-quantitative agreement with experiment and provide physical insight into similar results obtained via quantum Monte Carlo simulations.

cond-mat.quant-gas↗

arXiv2013

Fundamental Constraints on Linear Response Theories of Fermi Superfluids Above and Below $T_c$

We present fundamental constraints required for a consistent linear response theory of fermionic superfluids and address temperatures both above and below the transition temperature $T_c$. We emphasize two independent constraints, one associated with gauge invariance (and the related Ward identity) and another associated with the compressibility sum rule, both of which are satisfied in strict BCS theory. However, we point out that it is the rare many body theory which satisfies both of these. Indeed, well studied quantum Hall systems and random-phase approximations to the electron gas are found to have difficulties with meeting these constraints. We summarize two distinct theoretical approaches which are, however, demonstrably compatible with gauge invariance and the compressibility sum rule. The first of these involves an extension of BCS theory to a mean field description of the BCS-Bose Einstein condensation crossover. The second is the simplest Nozieres Schmitt- Rink (NSR) treatment of pairing correlations in the normal state. As a point of comparison we focus on the compressibility $κ$ of each and contrast the predictions above $T_c$. We note here that despite the compliance with sum rules, this NSR based scheme leads to an unphysical divergence in $κ$ at the transition. Because of the delicacy of the various consistency requirements, the results of this paper suggest that avoiding this divergence may repair one problem while at the same time introducing others.

cond-mat.quant-gas↗

arXiv2013

Theory of Fluctuating Charge Ordering in the Pseudogap Phase of the Cuprates Via A Preformed Pair Approach

We study the static and dynamic behavior of charge ordering within a d-wave pair pseudogap (pg) scenario. This is addressed using a density-density correlation function derived from the standard pg self energy, $Σ$ and compatible with the longitudinal and transverse sum rules. The broadening factor $γ$ in $Σ$ reflects the breaking of pairs into constituent fermions. We apply this form for $Σ$ (derived elsewhere for high fields) to demonstrate the existence of quantum oscillations in a non-Fermi liquid pg state. Our conclusion is that the pseudogap-induced pairbreaking, via $γ$, allows the underlying fermiology to be revealed; in YBCO, finite $ω$ and $γ$ enable antinodal fluctuations, despite the competition with a d-wave gap in the static and superconducting limits.

cond-mat.supr-con↗

arXiv2013

Magneto-Chiral Kerr effect with application to the cuprates

Rotation of polarization of light on transmission and reflection at materials with time-reversal breaking (Faraday and Kerr effects, respectively) have been studied for over a hundred years. We add to such phenomena by studying optical properties of magneto-chiral states which are loop currents with topological Hall effect. These break time-reversal and are chiral but the product of chirality and time-reversal is preserved. Qualitatively new features arise in reflection and transmission through such a state. This state is shown to be induced in underdoped cuprates given the observed magneto-electric loop-current order in cuprates and certain other specified condition. These results explain the observation of Kerr effects with unusual properties in the underdoped cuprates and help further confirm the nature of the symmetry breaking in underdoped cuprates.

cond-mat.str-el↗