Topological Quantum Phase Transition Research Articles

A Weyl-Z2 semimetal from holography

We present effective field theories for the weakly coupled Weyl-Z2 semimetal, as well as the holographic realization for the strongly coupled case. In both cases, the anomalous systems have both the chiral anomaly and the Z2 anomaly and possess topological quantum phase transitions from the Weyl-Z2 semimetal phases to partly or fully topological trivial phases. We find that the topological phase transition is characterized by the anomalous transport parameters, i.e. the anomalous Hall conductivity and the Z2 anomalous Hall conductivity. These two parameters are nonzero at the Weyl-Z2 semimetal phase and vanish at the topologically trivial phases. In the holographic case, the different behavior between the two anomalous transport coefficients is discussed. Our work reveals the novel phase structure of strongly interacting Weyl-Z2 semimetal with two pairs of nodes.

Dynamical piezomagnetic effect in time-reversal-invariant Weyl semimetals with axionic charge density waves

Charge density waves (CDWs) in Weyl semimetals (WSMs) have been shown to induce an exotic axionic insulating phase in which the sliding mode (phason) of the CDW acts as a dynamical axion field, giving rise to a large positive magnetoconductance [Wang et al., Phys. Rev. B 87, 161107(R) (2013); Roy et al., Phys. Rev. B 92, 125141 (2015); J. Gooth et al., Nature (London) 575, 315 (2019)]. In this work, we predict that dynamical strain can induce a bulk orbital magnetization in time-reversal (TR)-invariant WSMs that are gapped by a CDW. We term this effect the ``dynamical piezomagnetic effect'' (DPME). Unlike in J. Gooth et al. [Nature (London) 575, 315 (2019)], the DPME introduced in this work occurs in a bulk-constant (i.e., static and spatially homogeneous in the bulk) CDW, and does not rely on fluctuations, such as a phason. By studying the low-energy effective theory and a minimal tight-binding (TB) model, we find that the DPME originates from an effective valley axion field that couples the electromagnetic gauge field with a strain-induced pseudogauge field. In particular, whereas the piezoelectric effects studied in previous works are characterized by 2D Berry curvature, the DPME represents the first example of a fundamentally 3D strain effect originating from the Chern-Simons 3-form. We further find that the DPME has a discontinuous change at a critical value of the phase of the CDW order parameter. We demonstrate that, when there is a jump in the DPME, the surface of the system undergoes a topological quantum phase transition (TQPT), while the bulk remains gapped. Hence, the DPME provides a bulk signature of the boundary TQPT in a TR-invariant Weyl CDW.

Multipartite quantum nonlocality and Bell-type inequalities in a spin-1/2 model with topological quantum phase transitions

Multipartite quantum nonlocality and Bell-type inequalities are used to characterize quantum correlations in an infinite-size bond-alternating spin-$\frac{1}{2}$ Heisenberg chain with next-nearest-neighbor interactions. With the help of powerful tensor-network algorithms, both zero and finite temperatures are considered. First, at zero temperature, both in the even-Haldane phase and in the odd-Haldane phase, a high hierarchy of multipartite nonlocality is observed. Nevertheless, in the two phases, the spread of the multipartite nonlocality among the lattice is different. Thereby, the nonlocality measures are relatively large in one phase and vanish in the other phase, and provide quite sharp signals for the topological quantum phase transitions (QPTs) between these two phases. The influence of the next-nearest-neighbor coupling $\ensuremath{\alpha}$ upon the multipartite nonlocality in the model is also discussed. Second, we find that the footprints of the QPTs survive at low temperatures. Third, based upon the scaling behavior of the finite-temperature nonlocality measure, we propose a quantity $\mathcal{K}$ to characterize the finite-temperature nonlocality in the large-$n$ limit. We find that in high-temperature regions, $\mathcal{K}$ is reduced linearly as the temperature rises.

Atomic Scale Control and Visualization of Topological Quantum Phase Transition in π‐Conjugated Polymers Driven by Their Length (Adv. Mater. 44/2021)

Quantum Phase Transitions As reported by Pavel Jelinek and co-workers in article number 2104495, length control of π-conjugated pentacene polymers leads to the observation of a topological quantum phase transition. The transition is marked by the emergence of a zero-energy in-gap edge state and a pseudo Jahn–Teller effect is identified as the driving mechanism.

Electrodynamics of Topologically Ordered Quantum Phases in Dirac Materials.

First-principles calculations of the electronic ground state in tantalum arsenide are combined with tight-binding calculations of the field dependence of its transport model equivalent on the graphene monolayer to study the emergence of topologically ordered quantum states, and to obtain topological phase diagrams. Our calculations include the degrees of freedom for nuclear, electronic, and photonic interactions explicitly within the quasistatic approximation to the time-propagation-dependent density functional theory. This field-theoretic approach allows us to determine the non-linear response of the ground state density matrix to the applied electromagnetic field at distinct quantum phase transition points. Our results suggest the existence of a facile electronic switch between trivial and topologically ordered quantum states that may be realizable through the application of a perpendicular electric or magnetic field alongside a staggered-sublattice potential in the underlying lattice. Signatures of the near field electrodynamics in nanoclusters show the formation of a quantum fluid phase at the topological quantum phase transition points. The emergent carrier density wave transport phase is discussed to show that transmission through the collective excitation mode in multilayer heterostructures is a unique possibility in plasmonic, optoelectronic, and photonic applications when atomic clusters of Dirac materials are integrated within nanostructures, as patterned or continuous surfaces.

Quantized Goos-Hänchen shifts on the surface of hybridized topological insulator thin films

We study the Goos-Hänchen (GH) shift from the surface of a hybridized topological insulator (TI) thin film in the presence of a static magnetic field. We impinge a circularly polarized Gaussian beam on TI thin film substrate and calculate the lateral and angular GH shifts under partial reflection conditions. We show that magnetic field modulated giant positive and negative quantized spatial and angular beam shifts can be obtained by tuning the angle of incidence in the vicinity of Brewster angle and frequency in the terahertz regime. We also investigate the GH shifts in different topological phases of the TI thin film by driving the system through several topological quantum phase transitions (TQPTs), i.e., from topologically nontrivial to a semi metallic state and further to a band insulating state by manipulating the interplay between Zeeman and hybridization interactions. Furthermore, we investigate the effects of chemical potential on the GH shifts. Our results show that the sign of these shifts changes from negative to positive values as the chemical potential is changed from n-type to p-type. The work in this paper sheds important light on controlling GH shifts in different phases of a TI.

Atomic Scale Control and Visualization of Topological Quantum Phase Transition in π‐Conjugated Polymers Driven by Their Length

AbstractQuantum phase transitions (QPTs) driven by quantum fluctuations are transitions between distinct quantum phases of matter. At present, they are poorly understood and not readily controlled. Here, scanning tunneling microscopy (STM) and noncontact atomic force microscopy (nc‐AFM) are used to explore atomic scale control over quantum phase transitions between two different topological quantum states of a well‐defined π‐conjugated polymer. The phase transition is driven by a pseudo Jahn–Teller effect that is activated above a certain polymer chain length. In addition, theoretical calculations indicate the presence of long‐lasting coherent fluctuations between the polymer's two quantum phases near the phase transition, at finite temperature. This work thus presents a new way of exploring atomic‐scale control over QPTs and indicates that emerging quantum criticality in the vicinity of a QPT can give rise to new states of organic matter.

Topological quantum phase transitions on the breathing kagomé lattice

We explore extensively topological quantum phase transitions (TQPTs) of the breathing kagomé lattice model in the presence of staggered fluxes. We obtain rich topological phases, including the Chern insulator (CI) and the second-order topological insulator (SOTI) phases, by tuning the dimerized hopping parameter t 1′ and the staggered-flux parameter ϕ. The CI phases can be identified on the basis of the chiral edge states and the non-zero Chern numbers. However, in sharp contrast to the CI phases, the SOTI phases are characterized by the robust corner states and the quantized polarizations. In addition, we explore the TQPTs considering the next-nearest-neighbor hopping parameter t 2. We demonstrate the existence of two-dimensional SOTIs with broken time-reversal symmetry and reveal the TQPTs between the CIs and the SOTIs.

Lifting the Spin‐Momentum Locking in Ultra‐Thin Topological Insulator Films

Abstract3D topological insulators are known to carry 2D Dirac‐like topological surface states in which spin‐momentum locking prohibits backscattering. When thinned down to a few nanometers, the hybridization between the topological surface states at the top and bottom surfaces results in a topological quantum phase transition, which can lead to the emergence of a quantum spin Hall phase. Here, the thickness‐dependent transport properties across the quantum phase transition are studied on the example of (Bi0.16Sb0.84.)2Te3 films, with a four‐tip scanning tunneling microscope. The findings reveal an exponential drop of the conductivity below the critical thickness. The steepness of this drop indicates the presence of spin‐conserving backscattering between the top and bottom surface states, effectively lifting the spin‐momentum locking and resulting in the opening of a gap at the Dirac point. The experiments provide a crucial step toward the detection of quantum spin Hall states in transport measurements.

Momentum relaxation in a holographic Weyl semimetal

We study the effects of momentum relaxation on the holographic Weyl semimetal which exhibits a topological quantum phase transition between the Weyl semimetal phase and a topological trivial phase. The conservation of momentum in the field theory is broken by the axion fields in holography. The topological Weyl semimetal phase is characterized by a nontrivial anomalous Hall conductivity. We find that the critical value of the phase transition decreases when we increase the momentum relaxation strength up to a special value, above which it goes to zero. This indicates that the Weyl semimetal phase shrinks and finally disappears as the momentum relaxation strength is increased, which is consistent with the weakly coupled field theory predictions. We also study the behavior of transverse and longitudinal conductivities and low-temperature dependence of the dc resistivities with respect to momentum relaxation strength.

Topological quantum phase transitions and criticality in a longer-range Kitaev chain

In an attempt to theoretically investigate the quantum phase transition and criticality in topological models, we study Kitaev chain with longer-range couplings (finite number of neighbors) as well as truly long-range couplings (infinite number of neighbors). We carry out an extensive topological characterization of the momentum space to explore the possibility of obtaining higher order winding numbers and analyze the nature of their stability in the model. The occurrences of phase transitions from even-to-even and odd-to-odd winding numbers are observed with decreasing longer-rangeness in the system. We derive topological quantum critical lines and study them to understand the behavior of criticality. A suppression of higher order winding numbers is observed with decreasing longer-rangeness in the model. We show that the mechanism behind such phenomena is due to the superposition and vanishing of the topological quantum critical lines associated with the higher winding number. Through the study of Berry connection we show the possible different behaviors of critical lines when they undergo superposition along with the corresponding critical exponents. We analyze the behavior of the long-range models through the momentum space characterization. We also provide exact solution for the problem and discuss the experimental aspects of the work.

Deconfined quantum phase transition of a higher-order symmetry-protected topological state

A higher-order (HO) symmetry-protected topological (SPT) state can be realized in a plaquette-modulated square lattice antiferromagnet, which hosts a spin-$1/2$ degenerate mode on each corner of the lattice with open boundaries. In this work, we show with the field-theoretic analysis and quantum Monte Carlo simulations that the plaquette modulation can drive a direct topological quantum phase transition from the HOSPT to a trivial disordered phase across the deconfined quantum critical point (DQCP) between the antiferromagnetic (AF) order and the valence bond solid (VBS) order, thus the DQCP is a multicritical point bridging both the AF-VBS transition and the topological transition of the HOSPT phase. Our work thus reveals the ubiquitous duality between topological transitions of SPT phases and DQCPs.

Anomalous Floquet Chiral Topological Superconductivity in a Topological Insulator Sandwich Structure.

We show that Floquet chiral topological superconductivity arises naturally in Josephson junctions made of magnetic topological insulator-superconductor sandwich structures. The Josephson phase modulation associated with an applied bias voltage across the junction drives the system into the anomalous Floquet chiral topological superconductor hosting chiral Majorana edge modes in the quasienergy spectrum, with the bulk Floquet bands carrying zero Chern numbers. The bias voltage acts as a tuning parameter enabling novel Floquet topological quantum phase transitions driving the system into a myriad of exotic Majorana-carrying Floquet topological superconducting phases. Our theory establishes a new paradigm for realizing Floquet chiral topological superconductivity in solid-state systems, which should be experimentally directly accessible.

Finite-temperature topological phase transitions of spin- j systems in Uhlmann processes: General formalism and experimental protocols

The Uhlmann process is built on the density matrix of a mixed quantum state and offers a way to characterize topological properties at finite temperatures. We analyze an ideal spin-j quantum paramagnet in a magnetic field undergoing an Uhlmann process and derive general formulae of the Uhlmann phase and Loschmidt amplitude for arbitrary j as the system traverses a great circle in the parameter space. A quantized jump of the Uhlmann phase signifies a topological quantum phase transition (TQPT) of the underlying process, which is accompanied by a zero of the Loschmidt amplitude. The exact results of j=1/2 and j=1 systems show topological regimes that only survive at finite temperatures but not at zero temperature, and the number of TQPTs is associated with the winding number in the parameter space. Our results pave the way for future studies on finite-temperature topological properties, and possible experimental protocols and implications for atomic simulators and digital simulations are discussed.

Pressure-induced topological quantum phase transition in the magnetic topological insulator MnBi2Te4

In this paper, topological quantum phase transition was reported in the magnetic topological insulator MnBi2Te4 under pressure strain. Electronic and topological properties of the bulk anti-ferromagnetic MnBi2Te4 were investigated by first-principles calculations. We found that the band structure of MnBi2Te4 changes with the strain, resulting in a phase transition between metal and insulator. From the variation of charge-density distribution with strain, it was found that hydrostatic tensile strain is beneficial for increasing the interlayer spacing, thereby reducing the anti-ferromagnetic interaction between layers. On the contrary, the compressive strain promotes the strengthening of the bonding between the Te and Bi atomic layers. It was worth noting that the phase transition occurs at 2.12% strain when the band crossing is observed at Γ point, suggesting that the band gap has just closed. In addition, through the calculation of surface states, it is observed that, after the action of 2.12% strain, the bulk band gap of the system closes with the surface band gap reopens, achieving an intrinsic mechanism of strain modulation of the MnBi2Te4 antiferromagnetic bulk structure to undergoes a topological quantum phase transition. Our results provide feasible guidance not only for pressure-strain engineering of MnBi2Te4 experimentally but also for developing a meaningful strain-control mechanism for the electronic structures of other potential intrinsic magnetic insulators.

Multipartite quantum nonlocality and topological quantum phase transitions in a spin-1/2 two-leg Kitaev ladder

Multipartite quantum nonlocality and topological quantum phase transitions in a spin-1/2 two-leg Kitaev ladder

Non-Hermitian topological phases and dynamical quantum phase transitions: a generic connection

The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena—topological phases and dynamical quantum phase transitions (DQPTs)—in non-Hermitian systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs following the quench from a trivial to a non-Hermitian topological phase. Moreover, the critical momenta and critical time of the DQPTs are found to be directly related to the topological invariants of the non-Hermitian system. We further demonstrate our theory in three prototypical non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with next-nearest-neighbor hoppings, and the nonreciprocal Su–Schrieffer–Heeger model. Finally, we suggest a proposal to experimentally verify the found connection by a nitrogen-vacancy center in diamond.

PhotoinducedWeyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator* *Project supported by the National Natural Science Foundation of China (Grant No. 11804070) and Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ19A040007).

Motivated by the fact that Weyl fermions can emerge in a three-dimensional topological insulator on breaking either time-reversal or inversion symmetries, we propose that a topological quantum phase transition to a Weyl semimetal phase occurs under the off-resonant circularly polarized light, in a three-dimensional topological insulator, when the intensity of the incident light exceeds a critical value. The circularly polarized light effectively generates a Zeeman exchange field and a renormalized Dirac mass, which are highly controllable. The phase transition can be exactly characterized by the first Chern number. A tunable anomalous Hall conductivity emerges, which is fully determined by the location of the Weyl nodes in momentum space, even in the doping regime. Our predictions are experimentally realizable through pump-probe angle-resolved photoemission spectroscopy and raise a new way for realizing Weyl semimetals and quantum anomalous Hall effects.

Dynamical topological quantum phase transitions at criticality

The nonequilibrium dynamics of two-dimensional Su-Schrieffer-Heeger model, in the presence of staggered chemical potential, is investigated using the notion of dynamical quantum phase transition. We contribute to expanding the systematic understanding of the interrelation between the equilibrium quantum phase transition and the dynamical quantum phase transition (DQPT). Specifically, we find that dynamical quantum phase transition relies on the existence of massless propagating quasiparticles as signaled by their impact on the Loschmidt overlap. These massless excitations are a subset of all gapless modes, which leads to quantum phase transitions. The underlying two-dimensional model reveals gapless modes, which do not couple to the dynamical quantum phase transitions, while relevant massless quasiparticles present periodic nonanalytic signatures on the Loschmidt amplitude. The topological nature of DQPT is verified by the quantized integer values of the topological order parameter, which gets even values. Moreover, we have shown that the dynamical topological order parameter truly captures the topological phase transition on the zero Berry curvature line, where the Chern number is zero and the two-dimensional Zak phase is not the proper indicator.

Valley and spin polarized quantized spin dependent photonic shifts in topological silicene

In this article we report the magneto-optical (MO) and electro-optical (EO) modulation, in the terahertz regime, of the photonic spin Hall effect (PSHE) of reflected light from the surface of the topological silicene-substrate quantum systems subjected to external electric and magnetic fields. The prominent feature of these 2D materials is the tunable band gap that can be controlled by an external electric field or by irradiating circular polarized light beam. We demonstrate that the in-plane and transverse spatial spin dependent shifts are quantized due to the Landau level (LL) quantization of the MO conductivities. By controlling the staggered electric potential, we can drive the system through several topological quantum phase transitions. The magnitude of the giant PSHE in these materials is several times larger than the incident Gaussian beam wavelength. Furthermore, the PSHE shifts are extremely sensitive to the spin and valley indices of the Dirac fermions in these materials promising potential in the design of surface sensors, spin-dependent beam splitters, precision meteorology and quantum information processing.