Grüneisen ratio quest for self-duality of quantum criticality in a spin-1/2 XY chain with Dzyaloshinskii–Moriya interaction

The quantum phase transition(QPT) and quantum criticality of an anisotropic spin-1/2 XY chain under the interplay of magnetic field and Dzyaloshinskii–Moriya(DM) interaction, which is interpreted as an electric field, are investigated, wherein the anisotropic parameter plays a similar role as the superconducting pairing gap in the interacting Kitaev topological superconductor model that protects the topological order. It is shown that the thermal Drude weight is a good quantity to characterize the gapped(D_(th) = 0) and gapless(D_(th) 0) ground states. The continuous QPT is marked by a quantum critical point(QCP) associated with entropy accumulation, which is manifested by a characteristic Güneisen ratio(GR) with or without selfduality symmetry. It is shown that at a self-dual QCP, the GR keeps a finite value as T→0,while at a general QCP without self-duality symmetry, it displays a power-law temperature dependent divergence: Γ(T,r_c)～±T~(-1),which provides a novel thermodynamic means for probing QPT.     

Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction.     

Contrasting different scenarios for the quantum critical point

Competing scenarios for quantum critical points (QCPs) of strongly interacting Fermi systems signaled by a divergent density of states at zero temperature are contrasted. The conventional scenario, which enlists critical fluctuations of a collective mode and attributes the divergence to a coincident vanishing of the quasi-particle strength z, is shown to be incompatible with identities arising from conservation laws prevailing in the fermionic medium. An alternative scenario, in which the topology of the Fermi surface is altered at the QCP, is found to explain the non-Fermi-liquid thermodynamic behavior observed experimentally in Yb-based compounds close to the QCP. It is suggested that combination of the topological scenario with the theory of quantum phase transitions will provide a proper foundation for analysis of the extended QCP region.     

Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction. The text was submitted by the author in English.     

Majorana modes in time-reversal invariant s-wave topological superconductors

We present a time-reversal invariant s-wave superconductor supporting Majorana edge modes. The multiband character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the s-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.     

Overview of phases and phase transitions

We provide an overview of some modern developments in the theory of phases and phase transitions in classical and quantum systems. We show the link between non-ergodicity and fidelity in quantum systems and discuss topological phase transitions. We show that the quantum phase transitions are associated with qualitative changes in some properties of the quantum wavefunctions across the phase transition. We discuss the topological phase transition associated with p-wave superconductor since it is a topic of wide interest because of the possible observation of Majorana fermions.     

Magnetic-field control of quantum critical points of valence transition

We study the mechanism of how critical end points of first-order valence transitions are controlled by a magnetic field. We show that the critical temperature is suppressed to be a quantum critical point (QCP) by a magnetic field, and unexpectedly, the QCP exhibits nonmonotonic field dependence in the ground-state phase diagram, giving rise to the emergence of metamagnetism even in the intermediate valence-crossover regime. The driving force of the field-induced QCP is clarified to be cooperative phenomena of the Zeeman and Kondo effects, which create a distinct energy scale from the Kondo temperature. This mechanism explains the peculiar magnetic response in CeIrIn(5) and the metamagnetic transition in YbXCu(4) for X=In as well as the sharp contrast between X=Ag and Cd.     

Adaptation of the Landau-Migdal quasiparticle pattern to strongly correlated Fermi systems

A quasiparticle pattern advanced in Landau’s first article on Fermi-liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi-Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exceptional state whose spectrum of single-particle excitations exhibits a completely flat portion at zero temperature. Analysis of the evolution of the temperature dependence of the single-particle spectrum yields results that provide a natural explanation of classical behavior of this class of Fermi systems in the QCP region.     

Understanding the heavy fermion phenomenology from a microscopic model

We solve the 3D periodic Anderson model using a two impurity cluster dynamical mean field theory. We obtain the temperature versus hybridization phase diagram. Approaching the quantum critical point (QCP) both the Néel and lattice Kondo temperatures decrease and they do not cross at the lowest temperature we reached. While strong ferromagnetic spin fluctuation on the Kondo side is observed, our result suggests the critical static spin susceptibility is local in space at the QCP. We observe in the crossover region a logarithmic temperature dependence in the specific heat coefficient and spin susceptibility.     

Quantum phase transitions and vortex dynamics in superconducting networks

Josephson-junction arrays are ideal model systems to study a variety of phenomena such as phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on the quantum dynamical properties of low-capacitance Josephson-junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated with the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy needed to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single-electron effects with the Josephson effect. They give rise to (quantum) superconductor–insulator phase transitions that occur when the ratio between the coupling constants is varied or when the external fields are varied. We describe the dependence of the various control parameters on the phase diagram and the transport properties close to the quantum critical points. On the superconducting side of the transition, vortices are the topological excitations. In low-capacitance junction arrays these vortices behave as massive particles that exhibit quantum behavior. We review the various quantum–vortex experiments and theoretical treatments of their quantum dynamics.     

铁基超导体的量子临界行为

铁基超导体呈现丰富的电子相图, 各种有序态相互交叠. 本文主要介绍利用核磁共振手段在空穴型和电子型掺杂的BaFe₂As₂以及LaFeAsO_1-xF_x这三种具有代表性的铁基超导体中探测到的反铁磁序与超导序的微观共存、量子临界点和量子临界行为. 实验发现, 无论在空穴型还是电子型掺杂的铁基超导体中, 反铁磁相变温度都随着掺杂被抑制, 并最终在某个掺杂量降到零温而形成量子临界点. 在反铁磁转变温度之上存在结构相变, 其转变温度也随着掺杂而降低. 核磁共振谱证实结构相变也形成一个量子临界点. 本文介绍核磁共振及输运测量揭示的这两种量子临界点附近存在的量子临界行为, 共存态下奇异的超导性质等.     

Quantum critical scaling and the origin of non-fermi-liquid behavior in Sc1-xUxPd3

We used inelastic neutron scattering to study magnetic excitations of Sc1-xUxPd3 for U concentrations (x=0.25, 0.35) near the spin glass quantum critical point (QCP). The excitations are spatially incoherent, broad in energy (E=variant Planck's over 2piomega), and follow omega/T scaling at all wave vectors investigated. Since similar omega/T scaling has been observed for UCu5-xPdx and CeCu6-xAux near the antiferromagnetic QCP, we argue that the observed non-Fermi-liquid behavior in these f-electron materials arises from the critical phenomena near a T=0 K phase transition, irrespective of the nature of the transition.     

Search for Majorana fermions in multiband semiconducting nanowires

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor. We show that, when an odd number of subbands are occupied, the system realizes a nontrivial topological state supporting Majorana modes. We study the topological quantum phase transition in this system and calculate the phase diagram as a function of the chemical potential and magnetic field. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality but also allows one to have higher carrier density in the nanowire, and as such multisubband nanowires are better suited for observing the Majorana particle. We study the robustness of the topological phase by including the effects of the short- and long-range disorder. We show that there is an optimal regime in the phase diagram ("sweet spot") where the topological state is to a large extent insensitive to the presence of disorder.     

Testable signatures of quantum nonlocality in a two-dimensional chiral p-wave superconductor

A class of topological excitations-the odd-winding number vortices-in a spinless 2D chiral p-wave (px+ipy) superconductor traps Majorana fermion states in the vortex cores. For a dilute gas of such vortices, the lowest energy fermionic eigenstates are intrinsically nonlocal. We predict two testable signatures of this unusual quantum nonlocality in quasiparticle tunneling experiments. We discuss why the associated teleportationlike phenomenon does not imply the violation of causality.     

一维化学势调制的p波超导体中的拓扑量子相变

本文研究了一维公度势和非公度势调制下的p波超导量子线系统的拓扑相变.在公度势调制下,通过计算Z2拓扑不变量确定系统的相图,指出系统的拓扑相变强烈地依赖于调制参数α和相移δ.在非公度势调制下,以α=(√5-1)/2,δ=0为例,计算系统的低能激发谱、Z2拓扑不变量以及逆参与率等,发现p波配对强度△∈(0,0.33)时,系统存在拓扑非平庸超导相,拓扑平庸超导相和拓扑平庸局域相的转变.而当p波配对强度△>0.33时,系统存在拓扑非平庸超导相和拓扑平庸局域相的转变.     

Evidence for the strain critical point in high Tc superconductors

We report experimental evidence for the phase diagram of doped cuprate superconductors as a function of the micro-strain of the planar Cu-O bond length, measured by Cu K-edge EXAFS, and hole doping . The local lattice distortions are measured by EXAFS and the charge ordering is measured by synchrotron radiation diffuse X-ray diffraction. This phase diagram shows a QCP at P() where for charge-orbital-spin stripes and free carriers co-exist. The superconducting phase occurs in the region of critical fluctuations around this QCP. The function of two variables shows its maximum at the strain QCP. The critical fluctuations near this strain QCP give the self-organization of a metallic superlattice of quantum wires “superstripes" that favors the amplification of the critical temperature. Received 25 September 2000     

Gauge theories of Josephson junction arrays

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetric Kalb-Ramond gauge field.     

Evolution of edge states in topological superfluids during the quantum phase transition

The quantum phase transition between topological and nontopological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing spin-triplet superfluid ³He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where the Green’s function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green’s function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.     

Properties of holons in the quantum dimer model

I introduce a doped two-dimensional quantum dimer model describing a doped Mott insulator and retaining the original Fermi statistics of the electrons. This model shows a rich phase diagram including a d-wave hole-pair unconventional superconductor at small enough doping and a bosonic superfluid at large doping. The hole kinetic energy is shown to favor binding of topological defects to the bare fermionic holons turning them into bosons, in agreement with arguments based on resonating valence bond wave function. Results are discussed in the context of cuprate superconductors.     

Field-induced quantum critical point in CeCoIn5

The resistivity of the heavy-fermion superconductor CeCoIn5 was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho approximately T, and the development of a Fermi liquid state, with its characteristic rho=rho(0)+AT2 dependence. The field dependence of the T2 coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occurring at a critical field which coincides, within experimental accuracy, with the superconducting critical field H(c2). We discuss the relation of this field-tuned QCP to a change in the magnetic state, seen as a change in magnetoresistance from positive to negative, at a crossover line that has a common border with the superconducting region below approximately 1 K.