Topological Quantum Phase Transition Research Articles

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.

Eigenspectrum, Chern numbers and phase diagrams of ultracold color-orbit-coupled SU(3) fermions in optical lattices

We study ultracold color fermions with three internal states Red, Green and Blue with ${\rm SU(3)}$ symmetry in optical lattices, when color-orbit coupling and color-flip fields are present. This system corresponds to a generalization of two-internal state fermions with ${\rm SU(2)}$ symmetry in the presence of spin-orbit coupling and spin-flipping Zeeman fields. We investigate the eigenspectrum and Chern numbers to describe different topological phases that emerge in the phase diagrams of color-orbit coupled fermions in optical lattices. We obtain the phases as a function of artificial magnetic, color-orbit and color-flip fields that can be independently controlled. For fixed artificial magnetic flux ratio, we identify topological quantum phases and phase transitions in the phase diagrams of chemical potential versus color-flip fields or color-orbit coupling, where the chirality and number of midgap edge states changes. The topologically non-trivial phases are classified in three groups: the first group has total non-zero chirality and exhibit only the quantum charge Hall effect; the second group has total non-zero chirality and exhibit both quantum charge and quantum color Hall effects; and the third group has total zero chirality, but exhibit the quantum color Hall effect. These phases are generalizations of the quantum Hall and quantum spin Hall phases for charged spin-$1/2$ fermions. Lastly, we also describe the color density of states and a staircase structure in the total and color filling factors versus chemical potential for fixed color-orbit, color-flip and magnetic flux ratio. We show the existence of incompressible states at rational filling factors precisely given by a gap-labelling theorem that relates the filling factors to the magnetic flux ratio and topological quantum numbers.

Quantum temporal steering in a noise channel with topological characterization

We explore quantum temporal steering, measured by temporal steering robustness $${\mathcal {R}}_\mathrm{TS}$$ , in a quantum channel $$\varLambda $$ described by a qubit coupling to an extended anisotropic XY spin chain associated with non-trivial topological characterization. When the environment channel undergoes a topological quantum phase transition (TQPT), driven by magnetic field $$\lambda $$ , we find that $${\mathcal {R}}_\mathrm{TS}$$ is remarkably depressed. Moreover, $${\mathcal {R}}_\mathrm{TS}$$ exhibits a finite-size scaling behavior in the vicinity of TQPT points. Meanwhile, by calculating the temporal steering robustness power $$P_{{\mathcal {R}}}$$ , we can get the environment channel’s phase diagram which is exactly similar with the one obtained by topological quantity, i.e., winding number $${\mathcal {N}}$$ . Additionally, we also analyze the behaviors of $${\mathcal {R}}_\mathrm{TS}$$ when the environment channel is driven by other parameters (i.e., anisotropy of nearest-neighbor interaction $$\gamma $$ , three-site interactions $$\alpha $$ and anisotropy of three-site interactions $$\delta $$ ). The results show that $${\mathcal {R}}_\mathrm{TS}$$ approaches to zero quickly in a short time t at all the TQPT points and $$P_{{\mathcal {R}}}$$ can also highlight these points exactly for all driving parameters.

Three-terminal nonlocal conductance in Majorana nanowires: Distinguishing topological and trivial in realistic systems with disorder and inhomogeneous potential

We develop a theory for the three-terminal nonlocal conductance in Majorana nanowires as existing in the superconductor-semiconductor hybrid structures in the presence of superconducting proximity, spin-orbit coupling, and Zeeman splitting. The key question addressed is whether such nonlocal conductance can decisively distinguish between trivial and topological Majorana scenarios in the presence of chemical potential inhomogeneity and random impurity disorder. We calculate the local electrical as well as nonlocal electrical and thermal conductance of the pristine nanowire (good zero-bias conductance peaks), the nanowire in the presence of quantum dots and inhomogeneous potential (bad zero-bias conductance peaks), and the nanowire in the presence of large disorder (ugly zero-bias conductance peaks). The local conductance by itself is incapable of distinguishing the trivial states from the topological states since zero-bias conductance peaks are generic in the presence of disorder and inhomogeneous potential. The nonlocal conductance, which in principle is capable of providing the bulk gap closing and reopening information at the topological quantum phase transition, is found to be far too weak in magnitude to be particularly useful in the presence of disorder and inhomogeneous potential. Therefore, we focus on the question of whether the combination of the local, nonlocal electrical, and thermal conductance can separate the good, bad, and ugly zero-bias conductance peaks in finite-length wires. Our paper aims to provide a guide to future experiments, and we conclude that a combination of all three measurements would be necessary for a decisive demonstration of topological Majorana zero modes in nanowires---positive signals corresponding to just one kind of measurements are likely to be false positives arising from disorder and inhomogeneous potential.

Multi-critical topological transition at quantum criticality

The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.