Topological Quantum Phase Transition Research Articles

Quantum oscillations and electronic features in V1− δ Sb2 single crystals

Nonsymmorphic compounds have attracted much interest owing to their potential nontrivial electronic states. Here, we grew V1−δSb2 single crystal with a nonsymmorphic space group I4/mcm and studied their de Haas–van Alphen oscillations. Orientation-dependent magnetization showed quantum oscillations, allowing determination of the three-dimensional Fermi surface and Berry phase. Our theoretical calculation implied that VSb2's band structures manifest flat bands along the Γ–X path, Dirac band crossings near the P and N points, and in the Γ–Z direction, and nontrivial surface states along the Γ¯–Z¯ line. However, the inconsistencies in observed and calculated quantum oscillation frequencies suggest that VSb2's band structures cannot nicely account for these electronic properties of our samples. This study reveals the profound impact of V vacancies on VSb2's electronic states, implying the possible topological quantum phase transition via defect engineering.

Manipulating topological quantum phase transitions of Kitaev's quantum spin liquids with electric fields

Manipulating topological quantum phase transitions of Kitaev's quantum spin liquids with electric fields

Detecting Quantum Topologic Phase Transitions Through The C-Function

Topological Quantum Field Theory or TQFT is a quantum field theory that calculates topological invariance in measurement theory and mathematical physics. In recent years, several attempts have been made to find efficient observations to determine the TQFT of quasiparticle properties. In this paper, we propose a different and very effective way to detect the critical points of TQFT by considering the system functions. We suggest the C-Function as a novel probe that is accurate for detecting the location of critical points on topological quantum. The C-function uses a holographic model to show a topological quantum phase transition between a simple topological isolation phase and a gapless Weyl semimetal. The quantum tipping point displays a strong Lifshitz-like anisotropy in the spatial direction, and a quantum phase transition that does not follow the standard Landau paradigm. The C-function precisely shows the global features of quantum criticality and distinguishes very accurately between two separate zero-temperature phases. Considering the C-function relationship with entanglement entropy can detect quantum phase transitions and can be applied outside the holographic framework.
 Keywords: quantum topologic, phase transitions, c-function

Characterization of gapless topological quantum phase transition via magnetocaloric effect

It has attracted much attention on the interplay between topology and criticality in topological quantum systems, i.e., gapless topological quantum phase transition (TQPT) on critical lines. It is demonstrated that the magnetocaloric effect (MCE) is able to signal the gapless TQPT in an extended Kitaev chain, which is witnessed by the unusual critical behavior of joint effect of Grüneison ration (GR) and isothermal entropy change. We uncover the conventional TQPT between gapped phases showing high symmetry (HS) and non-HS critical points with self-duality, which is signaled by the finite value of GR as T → 0 and the largest inverse MCE with T-linear relation of isothermal entropy change. Two critical lines intersect at a multicritical point, at which there is a T−1 critical divergence of GR as well as T1/2 critical behavior of isothermal entropy change. It manifests a “weak” gapless TQPT on one critical line, demonstrated by the shifting zero-crossing of GR without the largest inverse MCE. On the other critical line, it shows a “strong” gapless TQPT, which is evidenced by the negative dip of GR together with the largest inverse MCE. Our work provides a novel thermodynamic perspective on gapless TQPT.

Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein Condensation in Two Dimensions: Crossovers and Topological Quantum Phase Transitions

We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.

Strain-driven topological quantum phase transition in (pseudo)cubic (mixed)-Cs/MA/FA halide perovskites

First-order topological phase transition in noncentrosymmetric FAPbI3.

Bloch oscillations probed quantum phases in HgTe quantum wells

The semiconductor quantum well based on mercury telluride is characterized by two distinct phases: conventional insulating phase and topological insulating phase with helical edge states. The system undergoes a topological quantum phase transition from one phase to the other, tuned by the critical geometric parameters of the quantum well. It is shown that the quantum states in each phase exhibit distinct flavors of Bloch oscillations, depending strongly on the geometric parameters and crystal momentum of the system. In particular, the group and Berry velocities and the real-space trajectories exhibit pronounced Bloch oscillations. Interestingly, the x- and y-components of the group velocity are interchanged by interchanging their corresponding components of the crystal momentum. In addition, a Gaussian wave packet undergoes distinct time evolution in each quantum phase of the HgTe quantum well. Moreover, the effects of applied in-plane electric and transverse magnetic fields are determined within the framework of Newtonian mechanics, leading to the geometric visualization of such an oscillatory motion. We find that in the presence of both applied in-plane electric and transverse magnetic fields simultaneously, the system undergoes a dynamic phase transition between confined and de-confined states, tuned by the relative strength of the fields. It is argued that the distinct Bloch oscillations originate from the peculiar band structure of HgTe quantum wells in each quantum phase. Furthermore, we find that the direct-current drift velocity in each quantum phase exhibits negative differential conductivity, a hallmark of the Bloch oscillation regime.

Pressure-Induced Superconductivity and Topological Quantum Phase Transitions in the Topological Semimetal ZrTe2.

Topological transition metal dichalcogenides (TMDCs) have attracted much attention due to their potential applications in spintronics and quantum computations. In this work, the structural and electronic properties of topological TMDCs candidate ZrTe2 are systematically investigated under high pressure. A pressure-induced Lifshitz transition is evidenced by the change of charge carrier type as well as the Fermi surface. Superconductivity is observed at around 8.3GPa without structural phase transition. A typical dome-shape phase diagram is obtained with the maximum Tc of 5.6K for ZrTe2 . Furthermore, the theoretical calculations suggest the presence of multiple pressure-induced topological quantum phase transitions, which coexists with emergence of superconductivity. The results demonstrate that ZrTe2 with nontrivial topology of electronic states displays new ground states upon compression.

Quantum phase transition in CeCoIn5: Experimental facts and theory

The condensed-matter community is involved in a hot debate on the nature of quantum critical points (QCP) governing the low-temperature properties of heavy fermion metals. The smeared jump-like behavior revealed both in the residual resistivity and the Hall resistivity R H , along with the violation of the time invariance symmetry and the charge invariance , include the violation of quasiparticle-hole symmetry, and provide vital clues on the origin of both the non-Fermi-liquid behavior and QCP. For the first time, based on a number of important experimental data, we show that these experimental observations point out unambiguously that QCP of is accompanied by the symmetry violation, and QCP itself is represented by the topological fermion-condensation quantum phase transition (FCQPT) connecting two Fermi surfaces of different topological charges.

Steered Quantum Coherence as a Signature of Topological Quantum Phase Transitions in the Extended XY Model

AbstractIn recent years, there has been a surge of interest in exploring coherence measures and correlation measures to characterize topological quantum phase transitions (TQPTs). Here, motivated by the continued push in this direction, the steered quantum coherence (SQC) in the extended XY model is studied to analyze its capability in characterizing TQPTs. It is shown that the first derivative of SQC succeeds in signaling different critical points of TQPTs. In particular, it is found that the SQC is a long‐range correlation and the first derivative of SQC can always accurately identify TQPTs for different site distance.

Entanglement entropy as an order parameter for strongly coupled nodal line semimetals

Topological semimetals are a class of many-body systems exhibiting novel macroscopic quantum phenomena at the interplay between high energy and condensed matter physics. They display a topological quantum phase transition (TQPT) which evades the standard Landau paradigm. In the case of Weyl semimetals, the anomalous Hall effect is a good non-local order parameter for the TQPT, as it is proportional to the separation between the Weyl nodes in momentum space. On the contrary, for nodal line semimetals (NLSM), the quest for an order parameter is still open. By taking advantage of a recently proposed holographic model for strongly-coupled NLSM, we explicitly show that entanglement entropy (EE) provides an optimal probe for nodal topology. We propose a generalized c-function, constructed from the EE, as an order parameter for the TQPT. Moreover, we find that the derivative of the renormalized EE with respect to the external coupling driving the TQPT diverges at the critical point, signaling the rise of non-local quantum correlations. Finally, we show that these quantum information quantities are able to characterize not only the critical point but also features of the quantum critical region at finite temperature.

Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators.

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. In this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t-J model on the six- and eight-leg cylinders, we identify a d+id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d-wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.

Topological quantum phase transition in a mixed-spin Heisenberg tetramer chain with alternating spin-1/2 and spin-5/2 dimers

We investigate magnetic quantum phases and the topological quantum phase transition between two distinct valence-bond solid (VBS) phases of a minimal interacting spin-chain model that captures a magnetic behavior of the novel low-dimensional quantum ferrimagnetic material Cu2Fe2Ge4O13. The studied mixed-spin Heisenberg tetramer chain consists of a 4-period array of spins involving two types of dimers sa−sa (sa=1/2) and Sb−Sb (Sb=5/2) under the assumption of unique intra- and inter-dimer coupling constants J1 and J2, respectively. Using the tensor-network formulation of the density-matrix renormalization group method, we have constructed the ground-state phase diagram in the parameter space magnetic field versus the interaction ratio J=J2/J1, whereby all ground states are in accordance with the Oshikawa–Yamanaka–Affleck theorem for a given period. In addition, we have implemented the recent tangential finite-size scaling method in order to characterize the critical behavior of the topological VBS transition through calculation of the critical point Jc and the critical exponent of the correlation length ν. Our results are consistent with the topological quantum phase transition from the SU(2) Wess–Zumino–Witten universality class with the critical exponent of correlation length ν=2/3 by assuming the proper logarithmic correction.

Parametrized quantum circuit for weight-adjustable quantum loop gas

Motivated by the recent success of realizing the topologically ordered ground state of the exactly solvable toric code model by a quantum circuit on the real quantum device [K. J. Satzinger {\it et al}., Science \textbf{374}, 1237 (2021)], here we propose a parametrized quantum circuit (PQC) with the same real-device-performable optimal structure to represent quantum loop gas states with adjustably weighted loop configurations. Combining such a PQC with the variational quantum eigensolver, we obtain the accurate quantum circuit representation for the toric code model in an external magnetic field with any field strength, where the system is not exactly solvable. The topological quantum phase transition in this system is further observed in the optimized circuits by measuring the magnetization and topological entanglement entropy.

Unveiling and Manipulating Hidden Symmetries in Graphene Nanoribbons.

Armchair graphene nanoribbons are a highly promising class of semiconductors for all-carbon nanocircuitry. Here, we present a new perspective on their electronic structure from simple model Hamiltonians and abinitio calculations. We focus on a specific set of nanoribbons of width n=3p+2, where n is the number of carbon atoms across the nanoribbon axis and p is a positive integer. We demonstrate that the energy-gap opening in these nanoribbons originates from the breaking of a previously unidentified hidden symmetry by long-ranged hopping of π electrons and structural distortions occurring at the edges. This hidden symmetry can be restored or manipulated through the application of in-plane lattice strain, which enables continuous energy-gap tuning, the emergence of Dirac points at the Fermi level, and topological quantum phase transitions. Our work establishes an original interpretation of the semiconducting character of armchair graphene nanoribbons and offers guidelines for rationally designing their electronic structure.

Quantized fields induced topological features in Harper-Hofstadter model

Classical magnetic fields might change the properties of topological insulators such as the time reversal symmetry protected topological edge states. This poses a question that whether quantized fields would change differently the feature of topological materials with respect to the classical one. In this paper, we propose a model to describe topological insulators (ultracold atoms in square optical lattices with magnetic field) coupled to a tunable single-mode quantized field, and discuss the topological features of the system. We find that the quantized field can induce topological quantum phase transitions in a different way. To be specific, for fixed gauge magnetic flux ratio, we calculate the energy bands for different coupling constants between the systems and the fields in both open and periodic boundary conditions. We find that the Hofstadter butterfly graph is divided into a pair for continuous gauge magnetic flux ratio, which is different from the one without single-mode quantized field. In addition, we plot topological phase diagrams characterized by Chern number as a function of the momentum of the single-mode quantized field and obtain a quantized structure with non-zero filling factor.

Quantum transport phenomena in magnetic topological insulators

In the past decade, magnetic topological insulators have been an important focus in condensed matter physics research. The intricate interplay between the nontrivial band topology and spin, orbit, charge, and dimensionality degrees of freedom can give rise to abundant exotic topological quantum states and topological phase transitions. Measuring the transport properties of magnetic topological insulators is a crucial approach to exploring their exotic properties, which is of significant scientific importance in deepening our understanding of topological quantum states. Simultaneously, it also holds substantial potential applications in the development of novel low-power electronic devices. In this work, experimental progress of transport researches of magnetic topological insulators is reviewed, including quantum anomalous Hall effect and topological quantum phase transitions in magnetically doped topological insulators, the quantum anomalous Hall phase, axion insulator phase and Chern insulator phase in intrinsic antiferromagnetic topological insulator MnBi<sub>2</sub>Te<sub>4</sub>, as well as the helical phase emerged from the Chern insulator in pulsed high magnetic fields. Finally, this work analyzes the future direction of development in magnetic topological insulators, and the transport phenomena that have not been understood in these systems, offering an insight into and perspectives on the potential breakthroughs to be achieved in this area of research.

Thermodynamic signature of topological quantum phase transition in a two-leg Kitaev ladder

We study the topological quantum phase transitions (QPTs) and quantum criticality of a two-leg Kitaev ladder. In the absence of superconducting phase difference, the thermal Drude weight portrays well the gapped topological quantum phases (Dth=0) and gapless quantum criticality (Dth>0), which is further manifested by the critical energy spectrum with different gapless linear relation modes. The self-dual quantum criticality is demonstrated by the Grüneisen ratio (GR) Γ= constant irrelevant of temperature. Tuning the superconducting phase difference Φ=π, the system undergoes a gapped topological nontrivial phase transition into a gapless trivial one, manifested by the quadratic contact point at the center of Brillouin zone. Meanwhile, it is identified by the temperature dependent power-law divergence: Γ∼±T−1 at low temperature, which is similar to the general QPT. In particular, with the chemical potential vanishing, one can obtain full flat bands, giving rise to the discontinuous topological QPT. Furthermore, it is worth noting that the scaling of GR provides a new thermodynamic means to check the order of topological QPTs, which falls on a universal curve or not, indicating the continuous or discontinuous transition.

Control of electronic topology in a strongly correlated electron system

It is becoming increasingly clear that breakthrough in quantum applications necessitates materials innovation. In high demand are conductors with robust topological states that can be manipulated at will. This is what we demonstrate in the present work. We discover that the pronounced topological response of a strongly correlated “Weyl-Kondo” semimetal can be genuinely manipulated—and ultimately fully suppressed—by magnetic fields. We understand this behavior as a Zeeman-driven motion of Weyl nodes in momentum space, up to the point where the nodes meet and annihilate in a topological quantum phase transition. The topologically trivial but correlated background remains unaffected across this transition, as is shown by our investigations up to much larger fields. Our work lays the ground for systematic explorations of electronic topology, and boosts the prospect for topological quantum devices.

Unusual thermodynamic signature of topological quantum criticality in two coupled Su-Schrieffer-Heeger chains

Symmetry breaking and topological quantum phase transitions (QPTs) are usually accompanied by a gap opening or closing. For the continuous QPT, it is marked by a quantum critical point. Herein, we study the topological feature of quantum phase boundary-quantum criticality of two coupled Su-Schrieffer-Heeger chains. Two topological nontrivial insulating phases and a trivial one are recapped with two different topological phase boundaries, which are termed as Dirac semimetals (DSMs) with one or two Dirac nodal points within considering spin degeneracy. Specially, a tricritical point holds the character of quadratic contact point semimetal (QCPSM) that is regarded as a parent phase of DSMs. Meanwhile, the QCPSM and DSMs are featured by the quantum critical scaling of thermal Drude weight and specific heat. Furthermore, the Grüneisen ratio serves as a superb tool for the diagnosis of topological semimetals, which is demonstrated with or without self-duality of quantum criticality explicitly.