arXiv subjects

B. Q. Song

Publications and source records attributed to B. Q. Song.

13 recordsLinked to original sources

arXiv2026

Quantum Formulation of Chiral Vortical Effect in Weyl Semi-metals

The chiral vortical effect (CVE) is the generation of an axial current in a rotating Weyl fermion; its description is presently based on semiclassical frameworks. In this work, we develop a fully quantum formulation for CVE, solving the exact evolution of microscopic spinful wavefunctions, which enables a bottom-up quantitative test of semi-classical theories and postulated distributions $f_{\text{CVE}}$ in different reference frames. Notably, it shows that $f_{\text{CVE}}$ is over a ground-state-free Floquet spectrum, qualitatively distinct from a thermal equilibrium distribution (i.e., fermi form $f_F$), underscoring CVE as a non-equilibrium phenomenon, distinguished from other chiral transports. The $f_F$ only approximately holds when three conditions are simultaneously fulfilled: (1) slow rotation $\omega R/v_F\ll 1$, (2) high chemical potential $\mu/(\hbar v_F R)\gg 1$, (3) isotropic symmetry, where $R$ is the size, $v_F$ is fermi velocity. In these conditions, the theory recovers established semiclassical results, including the current-response coefficients and the magnetization contribution; otherwise, it uncovers quantum phenomena such as ``void states", deviation from the semiclassical formula $j_{\text{CVE}} \sim \mu^2$, a $v_F$-independent charge pumping. The theory is based on semimetals, providing more experimentally accessible detection than fundamental Weyl particles.

cond-mat.str-el↗

arXiv2026

Chiral vortical effect and boundary-induced vortical pumping in finite Weyl systems

The chiral vortical effect (CVE) -- an axial current driven by rotation in chiral matter -- appears in systems ranging from relativistic fluids to Weyl semimetals. We present an exact quantum solution of a rotating Weyl fermion in a finite cylinder. We recover the exact current density on the rotation axis obtained by Vilenkin and show that its cross-sectional average vanishes in the thermodynamic limit, establishing that the bulk vortical response is purely a magnetization current. For spin-polarized boundary conditions, we uncover an additional effect beyond the known CVE: a robust family of chiral modes that transport axial charge, $\Delta Q=\chi N^2,\Delta\theta/4\pi$, under rotation by angle $\Delta\theta$, where $\chi$ is the Weyl node chirality and $N$ is the number of chiral modes. The pump is independent of temperature, Fermi level, and Weyl velocities, but depends on the UV-sensitive number $N$. These results clarify the quantum structure of the bulk CVE and reveal a boundary-enforced chiral spectral structure underlying vortical response in Weyl systems.

cond-mat.str-el↗

arXiv2025

Geometric origin of supercurrents in Berry phase: Formula for computing currents from wavefunctions with correlation and particle number variation

The complexity of itinerant and many-body nature in Bardeen-Cooper-Schrieffer (BCS) wavefunctions has traditionally led to the use of coarse-grained order parameters for describing currents in superconductors (SC), rather than directly utilizing wavefunctions. In this work, we introduce a phase-based formula that enables the direct computation of currents from microscopic wavefunctions, accounting for correlation and particle number variations. Interestingly, the formulation draws parallels with insulators, suggesting a unified framework for understanding (intra-band) charge transport across two extremes of conductivity. A group velocity current $J_{band}{\propto}\frac{1}{\hbar}{\partial}_kE(k)$ is derived from Berry phase, independent of wave package dynamics, robust against correlation. Additionally, we identify a correlation-driven contribution, $J_{corr}$, which reveals that the pairing correlations ${\langle}c_kc_{-k}{\rangle}$ among dancing partners provide a current component beyond the velocity operator.

cond-mat.supr-con↗

arXiv2024

Type-II pumping beyond resonance principle: From energetic to geometric rules

Conventionally, pumping relies on energetic resonance: energy quanta ${\hbar}ω$ matches the gap $Δ$. Under linear approximation, this is known as the Fermi golden rule (FGR). However, this principle becomes challenging to apply in the "0/0" limit, where $ω,Δ{\rightarrow}0$ simultaneously. In "0/0" scenarios, such as topological phase transition (TPT), a type-II pumping, geometric pumping (GP), is recognized subject to geometric rules, distinguished from type-I dictated by FGR. Type-I features an "arrow of energy", sending particles higher in energy, reflected by FGR's dependence on Fermi distribution $f_v-f_c$ (probabilities of valence and conduction bands). While GP is non-directional, its probability relies on $f_v+f_c-2f_v f_c$ instead, a key signature for detection. In this work, we address: (1) the concept of GP; (2) its features of fractionality, irreversibility, and dependence on TPT; (3) experimental detection with ultra-fast spectrum in coherent phonon driving of ZrTe$_5$.

quant-ph↗

arXiv2024

Quantum geometry embedded in unitarity of evolution: revealing its impacts as geometric oscillation and dephasing in spin resonance and crystal bands

Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader concept. We show how geometry emerges in quantum as an intrinsic consequence of unitary evolution, composing a frame work compatible with quantum metric and independent of specific details or approximations, suggesting quantum geometry may have widespread applicability. Indeed, we exemplify geometric observables, such as oscillation, dephasing, in spin and band scenarios. Anomalies, supported by both analytic and numerical solutions, underscore the advantages of adopting a geometric perspective, potentially yielding distinguishable experimental signatures.

quant-ph↗

arXiv2024

Quantum Liouville's theorem based on Haar measure

Liouville theorem (LT) reveals robust incompressibility of distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., LT is only conditionally true (e.g., for perfect Harmonic potential). We develop quantum Liouville theorem (rigorous incompressibility) for arbitrary potentials (interacting or not) in Hamiltonians. Haar measure, instead of symplectic measure dp^dq used in Wigner's scheme, plays a central role. The argument is based on general measure theory, independent of specific spaces or coordinates. Comparison of classical and quantum is made: for instance, we address why Haar measure and metric preservation do not work in the classical case. Applications of theorems in statistics, topological phase transition, ergodic theory, etc. are discussed.

quant-ph↗

arXiv2024

Position operators in terms of converging finite-dimensional matrices: Exploring their interplay with geometry, transport, and gauge theory

Position operator $\hat{r}$ appears as $i{\partial_p}$ in wave mechanics, while its matrix form is well known diverging in diagonals, causing serious difficulties in basis transformation, observable yielding, etc. We aim to find a convergent $r$-matrix (CRM) to improve the existing divergent $r$-matrix (DRM), and investigate its influence at both the conceptual and the application levels. Unlike the spin matrix, which affords a Lie algebra representation as the solution of $[s_i,s_j]={\epsilon}_{i,j,k}s_k$, the $r$-matrix cannot be a solution for $[\hat{r},p]=i\hbar$, namely Weyl algebra. Indeed: matrix representations of Weyl algebras prove not existing; thus, neither CRM nor DRM would afford a representation. Instead, the CRM should be viewed as a procedure of encoding $\hat{r}$ using matrices of arbitrary finite dimensions. Deriving CRM recognizes that the limited understanding about Weyl algebra has led to the divergence. A key modification is increasing the 1-st Weyl algebra (the familiar substitution $\hat{r}{\rightarrow}i{\partial_p}$) to the $N$-th Weyl algebra. Resolving the divergence makes $r$-matrix rigorously defined, and we are able to show $r$-matrix is distinct from a spin matrix in terms of its defining principles, transformation behavior, and the observable it yields. At the conceptual level, the CRM fills the logical gap between the $r$-matrix and the Berry connection; and helps to show that Bloch space $\mathcal{H}_B$ is incomplete for $\hat{r}$. At the application level, we focus on transport, and discover that the Hermitian matrix is not identical with the associative Hermitian operator, i.e., $r_{m,n}=r_{n,m}^*{\nLeftrightarrow}\hat{r}=\hat{r}^{\dagger}$. We also discuss how such a non-representation CRM can contribute to building a unified transport theory.

quant-ph↗

arXiv2022

Geometric pumping and dephasing at topological phase transition

A measure-preserving formalism (MPF) is constructed and applied to spin/band models, which yield observations about pumping. It occurs at topological phase transition (TPT), i.e., a $Z_2$-flip, suggesting that $Z_2$ can imply bulk effects. The model's asymptotic behavior is analytically solved via MPF. The pumping probability is geometric, fractional, and has a ceiling of $\frac{1}{2}$. Intriguingly, theorems are proved about occurrence conditions, which are linked to the system's dimension and the distinction between rational and irrational numbers. Experimental detection is discussed.

math-ph↗

arXiv2021

Construction of $A$-$B$ hetero-layer intermetallic crystals: case studies of the 1144-phase TM-phosphides \textit{AB}(TM)$_4$P$_4$ (TM=Fe, Ru, Co, Ni

The discovery of the 1144-phase, e.g. CaKFe$_4$As$_4$, creates opportunities to build novel intermetallics with alternative stacking of two parent compounds. Here we formalize the idea by defining a class of bulk crystalline solids with $A$-$B$ stacking (including 1144-phases and beyond), which is a generalization of hetero-structures from few-layer or thin-film semi-conductors to bulk intermetallics. Theoretically, four families of phosphides \textit{AB}(TM)$_4$P$_4$ (TM=Fe, Ru, Co, Ni) are investigated by first-principles calculations, wherein configurational, vibrational and electronic degrees of freedom are considered. It predicts a variety of stable 1144-phases (especially Ru- and Fe-phosphides). Stability rules are found and structural/electronic properties are discussed. Experimentally, we synthesize high-purity CaKRu$_4$P$_4$ as a proof of principle example. The synthetic method is simple and easily applied. Moreover, it alludes to a strategy to explore complex multi-component compounds, facilitated by a phase diagram coordinated by collective descriptors.

cond-mat.mtrl-sci↗

arXiv2021

Competing superconductivity and charge-density wave in Kagome metal CsV3Sb5: evidence from their evolutions with sample thickness

Recently superconductivity and topological charge-density wave (CDW) were discovered in the Kagome metals $A$V$_3$Sb$_5$ ($A$ = Cs, Rb, and K), which have an ideal Kagome lattice of vanadium. Here we report resistance measurements on thin flakes of CsV$_3$Sb$_5$ to investigate the evolution of superconductivity and CDW with sample thickness. The CDW transition temperature ${\it T}_{\rm CDW}$ decreases from 94 K in bulk to a minimum of 82 K at thickness of 60 nm, then increases to 120 K as the thickness is reduced further to 4.8 nm (about five monolayers). Since the CDW order in CsV$_3$Sb$_5$ is quite three-dimensional (3D) in the bulk sample, the non-monotonic evolution of ${\it T}_{\rm CDW}$ with reducing sample thickness can be explained by a 3D to 2D crossover around 60 nm. Strikingly, the superconducting transition temperature ${\it T}_{\rm c}$ shows an exactly opposite evolution, increasing from 3.64 K in the bulk to a maximum of 4.28 K at thickness of 60 nm, then decreasing to 0.76 K at 4.8 nm. Such exactly opposite evolutions provide strong evidence for competing superconductivity and CDW, which helps us to understand these exotic phases in $A$V$_3$Sb$_5$ Kagome metals.

cond-mat.supr-con↗

arXiv2021

Double-dome superconductivity under pressure in the V-based Kagome metals AV3Sb5 (A = Rb and K)

We present high-pressure electrical transport measurements on the newly discovered V-based superconductors $A$V$_3$Sb$_5$ ($A$ = Rb and K), which have an ideal Kagome lattice of vanadium. Two superconducting domes under pressure are observed in both compounds, as previously observed in their sister compound CsV$_3$Sb$_5$. For RbV$_3$Sb$_5$, the $T_c$ increases from 0.93 K at ambient pressure to the maximum of 4.15 K at 0.38 GPa in the first dome. The second superconducting dome has the highest $T_c$ of 1.57 K at 28.8 GPa. KV$_3$Sb$_5$ displays a similar double-dome phase diagram, however, its two maximum $T_c$s are lower, and the $T_c$ drops faster in the second dome than RbV$_3$Sb$_5$. An integrated temperature-pressure phase diagram of $A$V$_3$Sb$_5$ ($A$ = Cs, Rb and K) is constructed, showing that the ionic radius of the intercalated alkali-metal atoms has a significant effect. Our work demonstrates that double-dome superconductivity under pressure is a common feature of these V-based Kagome metals.

cond-mat.supr-con↗

arXiv2018

Whether it is possible to stabilize the 1144-phase pnictides with tri-valence cations?

The 1144 iron arsenide (e.g. CaKFe4As4) has recently been discovered and inspired a tide of search for superconductors. Such far, the discovered compounds are confined to iron arsenides (ABFe4As4), where A and B are either alkali metals or alkaline earth elements. In this work, we propose two directions in searching 1144 structures: (i) using tri-valence cations for A; (ii) substituting the transition metal, e.g. replacing Fe by Co. Following the two directions, we employ density functional theory to study stability and electronic structures of 1144 pnictides of various tri-valence cations (La, Y, In, Tl, Sm and Gd), as well as cobalt arsenides. For LaAFe4As4, the 1144 phase can be stabilized in three systems: LaKFe4As4, LaRbFe4As4 and LaCsFe4As4, which show quasi-two-dimensional semi-metal features similar to the iron pnictide superconductors: hole-type Fermi surface at Gama point and electron-type Fermi surface at M point in B.Z. In addition, LaKFe4As4 feature an extra bubble shaped Fermi surface sheets, distinct from the other two peers. Y does not support any 1144 phase within our search. For In and Tl, substitute Fe by Co and two unknown compounds of the 122 phase are stabilized: InCo2As2 and TlCo2As2. The two cobalt arsenides have Fermi surfaces of similar topology as iron arsenides, but the Fermi surfaces are all electron-type, showing potentials to be undiscovered superconductors. Stable 1144 phases are also found in InKCo4As4 and InRbCo4As4. For Sm and Gd, most 1144 and 122 iron arsenides are found unstable.

cond-mat.supr-con↗

arXiv2012

Possible Manipulation of Kondo Effect by Transition between Antiferromagnetic and Ferromagnetic s-d Coupling

Kondo effect originates from antiferromagnetic (AFM) s-d coupling between magnetic impurity and the conduction electron, while it will be totally quenched in ferromagnetic (FM) regime due to malfunction of spin-flip. We investigate the possibility of switching on/off Kondo effect by transition of AFM/FM s-d coupling using 3d-metal phthalocyanine molecule (MPc) on Au(111) as a model system. A Hamiltonian model is constructed based on the feature of MPc molecule to show the condition for AFM/FM s-d coupling. The AFM s-d coupling could transform to FM s-d coupling if the spin state of the lowest unoccupied orbital changes.

cond-mat.str-el↗