Tunable discrete scale invariance in transition-metal pentatelluride flakes

AbstractLog-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials.

Download Full-text

Transport through several four-quantum-dot topological structures

Modern Physics Letters B ◽

10.1142/s0217984921503930 ◽

2021 ◽

pp. 2150393

Author(s):

Qingshuang Zhi ◽

Kongfa Chen ◽

Zelong He

Keyword(s):

Quantum Dot ◽

Coupling Strength ◽

Bound States ◽

Resonance Peak ◽

Coulomb Interactions ◽

Many Body ◽

Body Effect ◽

Topological Structures ◽

Resonance Band ◽

Interdot Coupling

In this paper, several four-quantum-dot topological structures are designed. The influence of the interdot coupling strength and intradot Coulomb interactions on the conductance is discussed. The location of the anti-resonance band can be manipulated by tuning the interdot coupling strength, which suggests a physical scheme of an effective quantum switch. The Fano anti-resonance peak may evolve into a resonance peak. For the particular value of the interdot coupling strength, two Fano anti-resonances collapse and bound states in the continuum are formed. Moreover, many-body effect makes the number of anti-resonance bands increase. This study provides a theoretical basis for the design of quantum computing devices.

Download Full-text

Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2002913117 ◽

2020 ◽

Vol 117 (21) ◽

pp. 11337-11343 ◽

Cited By ~ 2

Author(s):

Nan Zhang ◽

Gan Zhao ◽

Lin Li ◽

Pengdong Wang ◽

Lin Xie ◽

...

Keyword(s):

Scale Invariance ◽

Bound States ◽

Quantum Limit ◽

Periodic Oscillations ◽

Discrete Scale Invariance ◽

Topological Materials ◽

Elemental Semiconductor ◽

Physical Phenomena ◽

Discrete Scale ◽

Weyl Fermions

The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe5and HfTe5. The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop “Weyl semiconductors” provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.

Download Full-text

Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe5

National Science Review ◽

10.1093/nsr/nwz110 ◽

2019 ◽

Vol 6 (5) ◽

pp. 914-920 ◽

Cited By ~ 5

Author(s):

Huichao Wang ◽

Yanzhao Liu ◽

Yongjie Liu ◽

Chuanying Xi ◽

Junfeng Wang ◽

...

Keyword(s):

Scale Invariance ◽

Quantum Effect ◽

Transport Coefficients ◽

Resonant Scattering ◽

Hall Resistance ◽

Quantum Oscillations ◽

Discrete Scale Invariance ◽

Dirac Materials ◽

Theoretical Simulations ◽

Discrete Scale

Abstract Discrete-scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity that can be rarely observed in quantum systems. Here, we report the log-periodic quantum oscillations in the longitudinal magnetoresistivity (ρxx) and the Hall traces (ρyx) of HfTe5 crystals, which reveal the DSI in the transport-coefficients matrix. The oscillations in ρxx and ρyx show the consistent logB-periodicity with a phase shift. The finding of the logB oscillations in the Hall resistance supports the physical mechanism as a general quantum effect originating from the resonant scattering. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. This work evidences the universality of the DSI in the Dirac materials and provides indispensable information for a full understanding of this novel phenomenon.

Download Full-text

Evidence of Discrete Scale Invariance in DLA and Time-to-Failure by Canonical Averaging

International Journal of Modern Physics C ◽

10.1142/s0129183198000339 ◽

1998 ◽

Vol 09 (03) ◽

pp. 433-447 ◽

Cited By ~ 39

Author(s):

A. Johansen ◽

D. Sornette

Keyword(s):

Scale Invariance ◽

Time To Failure ◽

Laplacian Growth ◽

Ensemble Averaging ◽

Diffusion Limited Aggregation ◽

Discrete Scale Invariance ◽

Diffusion Limited ◽

Market Crashes ◽

Discrete Scale

Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0,l0λ,l0λ2,…, where λ is a preferred scaling ratio and l0 a microscopic cut-off. Signatures of discrete scale invariance have recently been found in a variety of systems ranging from rupture, earthquakes, Laplacian growth phenomena, "animals" in percolation to financial market crashes. We believe it to be a quite general, albeit subtle phenomenon. Indeed, the practical problem in uncovering an underlying discrete scale invariance is that standard ensemble averaging procedures destroy it as if it was pure noise. This is due to the fact, that while λ only depends on the underlying physics, l0 on the contrary is realization-dependent. Here, we adapt and implement a novel so-called "canonical" averaging scheme which re-sets the l0 of different realizations to approximately the same value. The method is based on the determination of a realization-dependent effective critical point obtained from, e.g., a maximum susceptibility criterion. We demonstrate the method on diffusion limited aggregation and a model of rupture.

Download Full-text

The potential model treatment of the scattering of electrons by atoms and the existence of negative ions

Zeitschrift für Naturforschung A ◽

10.1515/zna-1961-0507 ◽

1961 ◽

Vol 16 (5) ◽

pp. 492-500

Author(s):

F. B. Malik ◽

E. Trefftz

Keyword(s):

Bound States ◽

Negative Ions ◽

Potential Scattering ◽

Point Of View ◽

Neutral Atoms ◽

Many Body ◽

Scattered Electron ◽

Scattered Particle ◽

Potential Term ◽

The Many

The low energy scattering of electrons by different neutral atoms has been treated by assuming that the atomic wave functions remain unchanged even at the presence of the scattered particle and by neglecting the exchange between the scattered electron and the bound electrons. The potential term in the differential equation of the scattered particle is exactly the atomic potential of the neutral atom and is approximated by analytical expressions, yielding the potential scattering equation. The variational treatments of Hulthén, Kohn and a related one suggested by Malik, are applied to solve this equation for a Hartree atom with l=0. The scattering by He, C and N is treated explicitly and the results of He indicate that in this way one may get some good result without going into the great complexity of the many body problem. It is further pointed out that the study of scattering by neutral atoms near zero energy under this model may serve as a possible mean to investigate the existence of different negative ions and their number of bound states. It seems from this point of view that He-, C- and N- for this model may exist and have one bound s-state.

Download Full-text

N-boson spectrum from a discrete scale invariance

Physical Review A ◽

10.1103/physreva.90.032504 ◽

2014 ◽

Vol 90 (3) ◽

Cited By ~ 28

Author(s):

A. Kievsky ◽

N. K. Timofeyuk ◽

M. Gattobigio

Keyword(s):

Scale Invariance ◽

Discrete Scale Invariance ◽

Discrete Scale

Download Full-text

Photoemission Study of K Doping on a Monolayer of C60 on Clean Si(001)-(2 × 1) Surface

Surface Review and Letters ◽

10.1142/s0218625x98000219 ◽

1998 ◽

Vol 05 (01) ◽

pp. 101-104 ◽

Cited By ~ 6

Author(s):

Tun-Wen Pi ◽

Le-Hong Hong ◽

Rong-Tzong Wu ◽

Chiu-Ping Cheng ◽

May-Ho Ko

Keyword(s):

Binding Energy ◽

Work Function ◽

Valence Band ◽

Weak Interaction ◽

Silicon Surface ◽

Many Body ◽

Body Effect ◽

Charge Polarization ◽

The Many ◽

Photoemission Study

We present the first valence band photoemission study of a monolayer K x C 60 on a clean Si(001)-(2 × 1) surface. The monolayer C60 which shows weak interaction with the silicon surface reveals clear, but broadened, structures corresponding to bulk C 60. Upon K exposure, the work function drops rapidly due to charge polarization toward the Si surface, considerably affecting then the rate of the Lumo filling. Its centroid initially shown at 0.6 eV shifts to higher binding energy with higher concentration. Moreover, the LUMO always separates 1.5 ± 0.1 eV from the Homo. Features associated with the many-body effect do not appear in the spectra. The Fermi cutoff has never been observed, indicating the insulating nature of the K x C 60 surface.

Download Full-text