Nontrivial Berry Phase Research Articles

Berry phases in the generalized Rabi model with dispersive-type interaction

Motivated by J. Larson’s work (Crespi et al., 2012), in which vacuum induced non-trivial Berry phases for Jaynes–Cummings (JC) model were considered to be the results from the application of rotating wave approximation (RWA) and become vanishing in the quantum Rabi model without RWA. Besides a counterpart relation between the trivialness or non-trivialness of Berry phases and the existence of conical intersections (CIs) of adiabatic potentials is illustrated by introducing semi-classical energy surface. We argue that there exist no definite connections between the trivialness or not of Berry phase and the CIs of adiabatic potentials because the CIs are fully controllable for the generalized JC and Rabi models discussed in this text by adjusting the dispersive non-linear interacting parameter.

Measuring outcome correlation for Bell cat state and geometric phase induced spin parity effect

In terms of quantum probability statistics, the Bell inequality (BI) and its violation are extended to spin-[Formula: see text] entangled Schrödinger cat state (called the Bell cat state) with both parallel and antiparallel spin-polarizations. Except the spin-1/2, the BI is never ever violated by the Bell cat states with the measuring outcomes including entire Hilbert space. If, on the other hand, measuring outcomes are restricted in the subspace of spin coherent state (SCS), a universal Bell-type inequality (UBI), [Formula: see text], is formulated in terms of the local realistic model. We observe a spin parity effect that the UBI can be violated only by the Bell cat states of half-integer but not the integer spins. The violation of UBI is seen to be a direct result of nontrivial Berry phase between the SCSs of south- and north-pole gauges for half-integer spin, while the geometric phase is trivial for the integer spins. A maximum violation bound of UBI is found as [Formula: see text], which is valid for arbitrary half-integer spin-[Formula: see text] states.

Electronic Transport Evidence for Topological Nodal-Line Semimetals of ZrGeSe Single Crystals

Although the band topology of ZrGeSe has been studied via magnetic torque technique, the electronic transport behaviors related to the relativistic Fermions in ZrGeSe are still unknown. Here, we first report systematic electronic transport properties of high-quality ZrGeSe single crystals under magnetic fields up to 14 T. Resistivity plateaus of temperature dependent resistivity curves both in the presence and absence of magnetic fields as well as large, non-saturating magnetoresistance in low-temperature region were observed. By analyzing the temperature- and angular-dependent Shubnikov-de Haas oscillations and fitting it via the Lifshitz-Kosevich (LK) formula with the Berry phase being taken into account, we proved that Dirac fermions dominate the electronic transport behaviors of ZrGeSe and the presence of non-trivial Berry phase. First principles calculations demonstrate that ZrGeSe possesses Dirac bands and normal bands near Fermi surface, resulting in the observed magnetotransport phenomena. These results demonstrate that ZrGeSe is a topological nodal-line semimetal, which provides a fundamentally important platform to study the quantum physics of topological semimetals.

Anomalous quantum oscillations and evidence for a non-trivial Berry phase in SmSb

Topologically non-trivial electronic structures can give rise to a range of unusual physical phenomena, and the interplay of band topology with other effects such as electronic correlations and magnetism requires further exploration. The rare earth monopnictides X(Sb,Bi) (X = lanthanide) are a large family of semimetals where these different effects may be tuned by the substitution of rare-earth elements. Here we observe anomalous behavior in the quantum oscillations of one member of this family, antiferromagnetic SmSb. The analysis of Shubnikov-de Haas (SdH) oscillations provides evidence for a non-zero Berry phase, indicating a non-trivial topology of the α-band. Furthermore, striking differences are found between the temperature dependence of the amplitudes of de Haas-van Alphen effect oscillations, which are well fitted by the Lifshitz-Kosevich (LK) formula across the measured temperature range, and those from SdH measurements which show a significant disagreement with LK behavior at low temperatures. Our findings of unusual quantum oscillations in an antiferromagnetic, mixed valence semimetal with a possible non-trivial band topology can provide an opportunity for studying the interplay between topology, electronic correlations and magnetism.

Emergence of intrinsic superconductivity below 1.178 K in the topologically non-trivial semimetal state of CaSn3

Topological materials which are also superconducting are of great current interest, since they may exhibit a non-trivial topologically-mediated superconducting phase. Although there have been many reports of pressure-tuned or chemical-doping-induced superconductivity in a variety of topological materials, there have been few examples of intrinsic, ambient pressure superconductivity in a topological system having a stoichiometric composition. Here, we report that the pure intermetallic CaSn3 not only exhibits topological fermion properties, but also has a superconducting phase at ~1.178 K under ambient pressure. The topological fermion properties, including the nearly zero quasi-particle mass and the non-trivial Berry phase accumulated in cyclotron motions, were revealed from the de Haas–van Alphen (dHvA) quantum oscillation studies of this material. Although CaSn3 was previously reported to be superconducting with Tc = 4.2 K, our studies show that the Tc = 4.2 K superconductivity is extrinsic and caused by Sn on the degraded surface, whereas its intrinsic bulk superconducting transition occurs at 1.178 K. These findings make CaSn3 a promising candidate for exploring new exotic states arising from the interplay between non-trivial band topology and superconductivity, e.g. topological superconductivity (TSC).

Shubnikov–de Haas and de Haas–van Alphen oscillations in the topological semimetal CaAl4

We report the magneto-transport properties of CaAl$_4$ single crystals with $C2/m$ structure at low temperature. CaAl$_4$ exhibits large unsaturated magnetoresistance $\sim$3000$\%$ at 2.5 K and 14 T. The nonlinear Hall resistivity is observed, which indicates the multi-band feature. The first-principles calculations show the electron-hole compensation and the complex Fermi surface in CaAl$_4$, to which the two-band model with over-simplified carrier mobility can't completely apply. Evident quantum oscillations have been observed with B//c and B//ab configurations, from which the nontrivial Berry phase is extracted by the multi-band Lifshitz-Kosevich formula fitting. An electron-type quasi-2D Fermi surface is found by the angle-dependent Shubnikov-de Haas oscillations, de Haas-van Alphen oscillations and the first-principles calculations. The calculations also elucidate that CaAl$_4$ owns a Dirac nodal line type band structure around the $\Gamma$ point in the $Z$-$\Gamma$-$L$ plane, which is protected by the mirror symmetry as well as the space inversion and time reversal symmetries. Once the spin-orbit coupling is included, the crossed nodal line opens a negligible gap (less than 3 meV). The open-orbit topology is also found in the electron-type Fermi surfaces, which is believed to help enhance the magnetoresistance observed.

Chiral anomaly and nontrivial Berry phase in the topological nodal-line semimetal SrAs3

We report the systematic measurement of the magnetoresistance (MR) properties and Hall resistivity of the topological nodal-line semimetal $\mathrm{SrA}{\mathrm{s}}_{3}$ single crystals. We observed large unsaturated MR accompanied by pronounced Shubnikov-de Hass (SdH) oscillations. Analysis of the SdH oscillations reveals two small frequencies of 1.6 T ($\ensuremath{\alpha}$ pocket) and 5.8 T ($\ensuremath{\beta}$ pocket). The $\ensuremath{\alpha}$ pocket has a nontrivial Berry phase and a small effective mass of $\ensuremath{\sim}0.034{m}_{0}$, while the $\ensuremath{\beta}$ pocket has a trivial Berry phase with an effective mass of $\ensuremath{\sim}0.11{m}_{0}$. Hall resistivity measurement reveals the coexistence of a low-concentration hole $({n}_{h}=6.45\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{4pt}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$) with high mobility ($1.68\ifmmode\times\else\texttimes\fi{}{10}^{5}$ $\mathrm{c}{\mathrm{m}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$) and a high-concentration electron $({n}_{e}=2.34\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{4pt}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$) with lower mobility ($9.50\ifmmode\times\else\texttimes\fi{}{10}^{3}$ $\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$) at 2 K. Furthermore, we observed robust large negative MR in the presence of parallel magnetic and electric fields induced by the chiral magnetic effect.

Magnetotransport Properties of a Nodal Line Semimetal TiSi**Supported by the National Key Research Program of China under Grant Nos 2016YFA0401000 and 2016YFA0300604, the National Basic Research Program of China under Grant No 2015CB921303, the Strategic Priority Research Program (B) of Chinese Academy of Sciences under Grant No XDB07020100, and the National Natural Science Foundation of China under Grant No 11874417.

We report the magnetoresistance (MR), de Haas-van Alphen (dHvA) effect and Hall effect measurements on a single crystal of TiSi, which is predicted to be a nodal line semimetal. With application of a magnetic field, a metal-to-insulator-like transition in ρ(T) and a nonsaturating MR are observed at low temperatures. The dHvA oscillations reveal a small Fermi-surface pocket with a nontrivial Berry phase. The analysis of the nonlinear Hall resistivity shows that TiSi is a multiband system with low carrier densities and high mobilities. All these results unambiguously prove the existence of Dirac fermions in TiSi.

Topological bosonic states on ribbons of a honeycomb lattice

The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of edge states. We provide intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topological edge states are robust against weak interactions beyond the hardcore repulsion. Our results can be simulated by using bosonic cold atoms trapped in designed optical lattices.

Localization physics in graphene moiré superlattices

Non-trivial Berry phase of graphene leads to unusual quantum correction to the conductivity. Berry phase of pi in single layer graphene (SLG) and 2pi in bi-layer graphene (BLG) is expected to reveal weak anti-localization (WAL) and weak localization (WL), respectively. However, experimentally both WAL and WL have been observed in graphene devices depending on the strength of different scattering mechanisms. Graphene superlattice having multiple Dirac cones is expected to exhibit pi to 2pi Berry phase transition from primary Dirac cone (PDC) to cloned Dirac cone (CDC). However, its effect on localization physics has not been explored yet. In this letter we present the magneto-conductance study in a hexagonal Boron-nitride (hBN)-graphene moire superlattice. Our results reveal a transition from WAL at PDC to WL at CDC in a single device by tuning the Fermi energy. The transition is supported by the quantum oscillation measurements showing a shift of pi phase from PDC to CDC and corresponding theoretical calculation capturing the Berry phase transition. Thus, our studies on localization physics in graphene superlattice pave the way to understand the carrier dynamics at multiple Dirac cones.

Berry phase theory of planar Hall effect in topological insulators

The appearance of negative longitudinal magnetoresistance (LMR) in topological semimetals such as Weyl and Dirac semimetals is understood as an effect of chiral anomaly, whereas such an anomaly is not well-defined in topological insulators. Nevertheless, it has been shown recently in both theory and experiments that nontrivial Berry phase effects can give rise to negative LMR in topological insulators even in the absence of chiral anomaly. In this paper, we present a quasi-classical theory of another intriguing phenomenon in topological insulators – also ascribed to chiral anomaly in Weyl and Dirac semimetals– the so-called planar Hall effect (PHE). PHE implies the appearance of a transverse voltage in the plane of applied non-parallel electric and magnetic fields, in a configuration in which the conventional Hall effect vanishes. Starting from Boltzmann transport equations we derive the expressions for PHE and LMR in topological insulators in the bulk conduction limit, and show the important role played by orbital magnetic moment. Our theoretical results for magnetoconductance with non-parallel electric and magnetic fields predict detailed experimental signatures in topological insulators – specifically of planar Hall effect – that can be observed in experiments.

Quantitative evaluation of Dirac physics in PbTe

The magnetic field dependence of electronic transport, magnetic, and elastic properties in single crystals of PbTe were investigated in high magnetic fields up to 55 T. The magnetoresistance, magnetization, ultrasonic attenuation, and sound velocity showed clear quantum oscillations with pronounced Zeeman-splitting, which causes a large second harmonic in the frequency spectra. The ratio of the Zeeman to the cyclotron energy, which is regarded as an index of `Diracness' [H. Hayasaka and Y. Fuseya, J. Phys.: Condens. Matter \textbf{28,} 31LT01 (2016).], was determined to be 0.52 and 0.57 in samples with different carrier densities. We also pointed out that the effect of Zeeman-splitting seriously affects the Landau-level fan diagram analysis, which is widely used to extract the nontrivial Berry's phase from the quantum oscillations.

Giant planar Hall effect in the Dirac semimetal ZrTe5−δ

Recently, giant planar Hall effect originating from chiral anomaly has been predicted in nonmagnetic Dirac/Weyl semimetals. ZrTe5 is considered to be an intriguing Dirac semimetal at the boundary of weak topological insulators and strong topological insulators, though this claim still remains controversial. Here, we report the observation in ZrTe5 of the giant planar Hall resistivity that shows two different magnetic-field dependences as predicted by theory and a maximum at the Lifshitz transition temperature. We found that the giant planar Hall resistivity fades out with decreasing the thickness of ZrTe5 nanoplates, which may be ascribed to the vanishing of the 3D nature of the samples. In addition, we have observed a nontrivial Berry phase, chiral-anomaly-induced negative longitudinal magnetoresistance, and a giant in-plane anisotropic magnetoresistance in these ZrTe5 nanoplates. All the experimental observations demonstrated coherently that ZrTe5 is a Dirac semimetal.

Large magnetoresistance and superconductivity in \u03b1-gallium single crystals

Topological metals, including Dirac and Weyl semimetals, represent a wide class of quantum materials with non-trivial electronic band structures. The essential properties of Dirac or Weyl fermions, including light effective mass and high mobility, have been observed in a number of semimetal compounds, which in turn exhibit large positive magnetoresistances. Here, we report an unexpected observation of all these properties in α-gallium (α-Ga) single crystals, a pure metal that is in the liquid phase at room temperature and ambient pressure. Based on systematical transport measurements, α-Ga single crystal is found to exhibit large magnetoresistance, reaching about 1.66 × 106 per cent at 2 K in a magnetic field of 9 T. At low temperatures the de Haas–van Alphen and Shubinikov de Hass quantum oscillations show ultrahigh mobility and very small cyclotron effective mass for charge carriers, together with a non-trivial Berry phase. Combined with first-principle band structure calculations, these properties demonstrate α-Ga as a rare topological pure metal. Furthermore, superconductivity with Tc of ~0.9 K is confirmed by both specific heat and resistivity measurements. These findings suggest that α-Ga is a unique pure metal displaying both non-trivial topological and superconducting properties.

Vanishing quantum oscillations in Dirac semimetal ZrTe5

One of the characteristics of topological materials is their nontrivial Berry phase. Experimental determination of this phase largely relies on a phase analysis of quantum oscillations. We study the angular dependence of the oscillations in a Dirac material [Formula: see text] and observe a striking spin-zero effect (i.e., vanishing oscillations accompanied with a phase inversion). This indicates that the Berry phase in [Formula: see text] remains nontrivial for arbitrary field direction, in contrast with previous reports. The Zeeman splitting is found to be proportional to the magnetic field based on the condition for the spin-zero effect in a Dirac band. Moreover, it is suggested that the Dirac band in [Formula: see text] is likely transformed into a line node other than Weyl points for the field directions at which the spin zero occurs. The results underline a largely overlooked spin factor when determining the Berry phase from quantum oscillations.

Anisotropic angular magnetoresistance and Fermi surface topology of the candidate novel topological metal Pd3Pb

Pd${}_{3}$Pb has recently been predicted to host topological features consisting of a combination of triple nodal points, Dirac points, and open Fermi arcs. Authors' magnetotransport measurements show that Pd${}_{3}$Pb shares many features with other topological semimetals, including a highly anisotropic Fermi surface, large transverse magnetoresistance, and pronounced Shubnikov-de Hass oscillations. The quantum oscillations indicate that its electronic structure imparts a non-trivial Berry phase to Pd${}_{3}$Pb, potentially associated with the complex topological features predicted theoretically.

Multiple topologically nontrivial bands in noncentrosymmetric YSn2

The square lattices formed by main-group elements such as Bi, Sb, Sn, and Si in layered materials have attracted a lot of interest, since they can create rich topological phases. In this paper, we report the slightly distorted square lattice of Sn in a noncentrosymmetric compound ${\mathrm{YSn}}_{2}$ generates multiple topologically nontrivial bands, one of which likely hosts a nodal line and tunable Weyl semimetal state induced by the Rashba spin-orbit coupling and proper external magnetic field. The quasiparticles described as relativistic fermions from these bands are manifested by nearly zero mass and nontrivial Berry phases probed in de Haas-van Alphen (dHvA) oscillations. The dHvA study also reveals ${\mathrm{YSn}}_{2}$ has a complicated Fermi surface, consisting of several three-dimensional (3D) and one 2D pocket. Our first-principles calculations show the pointlike 3D pocket at Y point on the Brillouin zone boundary hosts the possible Weyl state. Our findings establish ${\mathrm{YSn}}_{2}$ as a new interesting platform for observing novel topological phases and studying their underlying physics.

Multi-carrier transport in ZrTe5 film**Project supported by Guangdong Innovative and Entrepreneurial Research Team Program (Grant No. 2016ZT06D348) and Shenzhen Peacock Program (Grant No. KQTD2016022619565991).

Single-layered zirconium pentatelluride (ZrTe5) has been predicted to be a large-gap two-dimensional (2D) topological insulator, which has attracted particular attention in topological phase transitions and potential device applications. Herein, we investigated the transport properties in ZrTe5 films as a function of thickness, ranging from a few nm to several hundred nm. We determined that the temperature of the resistivity anomaly peak (Tp) tends to increase as the thickness decreases. Moreover, at a critical thickness of ∼40 nm, the dominating carriers in the films change from n-type to p-type. A comprehensive investigation of Shubnikov–de Hass (SdH) oscillations and Hall resistance at variable temperatures revealed a multi-carrier transport tendency in the thin films. We determined the carrier densities and mobilities of two majority carriers using the simplified two-carrier model. The electron carriers can be attributed to the Dirac band with a non-trivial Berry phase π, while the hole carriers may originate from surface chemical reaction or unintentional doping during the microfabrication process. It is necessary to encapsulate the ZrTe5 film in an inert or vacuum environment to potentially achieve a substantial improvement in device quality.

Topological Type-II Dirac Fermions Approaching the Fermi Level in a Transition Metal Dichalcogenide NiTe2

Type-II Dirac/Weyl semimetals are characterized by strongly tilted Dirac cones such that the Dirac/Weyl node emerges at the boundary of electron and hole pockets as a new state of quantum matter, distinct from the standard Dirac/Weyl points with a point-like Fermi surface which are referred to as type-I nodes. The type-II Dirac fermions were recently predicted by theory and have since been confirmed in experiments in the PtSe2-class of transition metal dichal-cogenides. However, the Dirac nodes observed in PtSe2, PdTe2 and PtTe2 candidates are quite far away from the Fermi level, making the signature of topological fermions obscure as the physical properties are still dominated by the non-Dirac quasiparticles. Here we report the synthesis of a new type-II Dirac semimetal NiTe2 in which a pair of type-II Dirac nodes are located very close to the Fermi level. The quantum oscillations in this material reveal a nontrivial Berry's phase associated with these Dirac fermions. Our first principles calculations further unveil a topological Dirac cone in its surface states. Therefore, NiTe2 may not only represent an improved system to formulate the theoretical understanding of the exotic consequences of type-II Dirac fermions, it also facilitates possible applications based on these topological carriers.

Rotor spectra and Berry phases in the chiral limit of QCD on a torus

We consider the finite-volume spectra of QCD in the chiral limit of massless up and down quarks and massive strange quarks in the baryon number sectors $B = 0$ and $B = 1$ for different values of the isospin. Spontaneous symmetry breaking gives rise to rotor spectra, as the chiral order parameter precesses through the vacuum manifold. Baryons of different isospin influence the motion of the order parameter through non-trivial Berry phases and associated abstract monopole fields. Our investigation provides detailed insights into the dynamics of spontaneous chiral symmetry breaking in QCD on a torus. It also sheds new light on Berry phases in the context of quantum field theory. Interestingly, the Berry gauge field resulting from QCD solves a Yang-Mills-Chern-Simons equation of motion on the vacuum manifold $SU(2) = S^3$.