Bulk Quantum Hall Effect Research Articles

Novel Bulk Quantum Hall Effect in Nanostructured TaP Macroscopic Crystals.

Bulk quantum Hall effect (QHE), the natural extension of the two-dimensional (2D) QHE, is one of the representative phenomena of coherent electron transport. However, bulk QHE has rarely been reported in real materials with macroscopic sizes. Here, we report a novel bulk QHE in macroscopic millimeter-sized and nanostructured TaP crystals consisting of nanometer-scale lamellae. Specifically, the simultaneous quantum plateaus were observed in both transverse resistivity ρxy and vertical resistivity ρzz. The bulk QHE is attributable to synergetic action between Landau cyclotron movement under magnetic field B and periodically modulated potential due to the nanometer-scaled lamellae. This mechanism would form the fixed number of edge states along B-perpendicular and B-parallel directions respectively, equivalent to stacked 2D-QHE layers, leading to quantized ρxy and ρzz. Our work verifies that microstructure engineering could result in the coherent transport of electrons and generate new quantum phenomena in bulk materials.

High-field Studies on Layered Magnetic and Polar Dirac Metals: Novel Quantum Transport Phenomena Coupled with Spin-valley Degrees of Freedom

Recently, the interplay between the Dirac/Weyl fermion and various bulk properties, such as magnetism, has attracted considerable attention, since unconventional transport and optical phenomena were discovered. However, the design principles for such materials have not been established well. Here, we propose that the layered material $A$Mn$X_2$ ($A$: alkaline and rare-earth ions, $X$: Sb, Bi) is a promising platform for systematically exploring strongly correlated Dirac metals, which consists of the alternative stack of the $X^-$ square net layer hosting a 2D Dirac fermion and the $A^{2+}$-Mn$^{2+}$-$X^{3-}$ magnetic block layer. In this article, we shall review recent high-field studies on this series of materials to demonstrate that various types of Dirac fermions are realized by designing the block layer. First, we give an overview of the Dirac fermion coupled with the magnetic order in EuMnBi$_2$ ($A$=Eu). This material exhibits large magnetoresistance by the field-induced change in the magnetic order of Eu layers, which is associated with the strong exchange interaction between the Dirac fermion and the local Eu moment. Second, we review the Dirac fermion coupled with the lattice polarization in BaMn$X_2$ ($A$=Ba). There, spin-valley coupling manifests itself owing to the Zeeman-type spin-orbit interaction, which is experimentally evidenced by the bulk quantum Hall effect observed at high fields.

Magnetic field-induced non-linear transport in HfTe5.

The interplay of electron correlations and topological phases gives rise to various exotic phenomena including fractionalization, excitonic instability and axionic excitation. Recently discovered transition-metal pentatellurides can reach the ultra-quantum limit in low magnetic fields and serve as good candidates for achieving such a combination. Here, we report evidence of density wave and metal-insulator transition in HfTe5 induced by intense magnetic fields. Using the non-linear transport technique, we detect a distinct non-linear conduction behavior in the longitudinal resistivity within the a-c plane, corresponding to the formation of a density wave induced by magnetic fields. In high fields, the onset of non-linear conduction in the Hall resistivity indicates an impurity-pinned magnetic freeze-out as the possible origin of the insulating behavior. These frozen electrons can be gradually reactivated into mobile states above a threshold of electric field. This experimental evidence calls for further investigation into the underlying mechanism of the bulk quantum Hall effect and field-induced phase transitions in pentatellurides.

Two-dimensional transport and strong spin–orbit interaction in SrMnSb2**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0303302) and the National Natural Science Foundation of China (Grant Nos. 61322407, 11474058, and 61674040).

We have carried out magneto-transport measurements for single crystal SrMnSb2. Clear Shubnikov–de Haas oscillations were resolved at relatively low magnetic field around 4 T, revealing a quasi-2D Fermi surface. We observed a development of quantized plateaus in Hall resistance at high pulsed fields up to 60 T. Due to the strong 2D confinement and layered properties of the samples, we interpreted the observation as bulk quantum Hall effect that is contributed by the parallel 2D conduction channels. Moreover, the spin degeneracy was lifted leading to Landau level splitting. The presence of anisotropic g factor and the formation of the oscillation beating pattern reveal a strong spin–orbit interaction in the SrMnSb2 system.

Observation of quasi-two-dimensional Dirac fermions in ZrTe5

Since the discovery of graphene, layered materials have attracted extensive interest owing to their unique electronic and optical characteristics. Among them, Dirac semimetals, one of the most appealing categories, have been a long-sought objective in layered systems beyond graphene. Recently, layered pentatelluride ZrTe5 was found to host signatures of a Dirac semimetal. However, the low Fermi level in ZrTe5 strongly hinders a comprehensive understanding of the whole picture of electronic states through photoemission measurements, especially in the conduction band. Here, we report the observation of Dirac fermions in ZrTe5 through magneto-optics and magneto-transport. By applying a magnetic field, we observe a dependence of the inter-Landau-level resonance and Shubnikov–de Haas (SdH) oscillations with a nontrivial Berry phase, both of which are hallmarks of Dirac fermions. The angle-dependent SdH oscillations show a clear quasi-two-dimensional feature with a highly anisotropic Fermi surface and band topology, in stark contrast to the three-dimensional (3D) Dirac semimetal such as Cd3As2. This is further confirmed by the angle-dependent Berry phase measurements and the observation of bulk quantum Hall effect (QHE) plateaus. The unique band dispersion is theoretically understood: the system is at the critical point between a 3D Dirac semimetal and a topological insulator phase. With the confined interlayer dispersion and reducible dimensionality, our work establishes ZrTe5 as an ideal platform for exploring the exotic physical phenomena of Dirac fermions. The presence of fast, effectively massless electrons in layered zirconium pentatelluride (ZrTe5) crystals has been confirmed. The one-atom-thick structure of graphene enables its electrons to travel much faster than typical materials, and device designers are hunting for other layered crystals that have similar ‘Dirac fermions’. By performing magneto-optical and magneto-transport measurements, Faxian Xiu from Fudan University in China and co-workers have uncovered key signatures of electrons moving at relativistic speeds in the intriguing thermoelectric material ZrTe5. Because previous investigations of this phenomenon were hampered by ZrTe5's hard-to-access Fermi level, the team used magnetic fields to induce characteristic resonance and oscillation signals. These experiments revealed that these Dirac fermions had quasi-two-dimensional behaviour and unusual interlayer characteristics, which merit further theoretical studies and exploration of possible device applications. ZrTe5 has attracted intensive research interests because of the potential topological property. Here based on the transports and optic experiments, we observe unusual Landau quantization, non-trivial Berry phase and highly anisotropic carrier mass, which reveals quasi-two-dimensional Dirac fermions in bulk ZrTe5. The system is understood as locating at the critical point between a three-dimensional (3D) Dirac semimetal and a topological insulator. New physics or device application can be possibly realized in this quasi-2D ultra-relativistic system beyond graphene.

Structural and electronic properties of highly doped topological insulator Bi2Se3 crystals

Abstractmagnified imageWe present a study of the structural and electronic properties of highly doped topological insulator Bi2Se3 single crystals synthesized by the Bridgman method. Lattice structural characterizations by X‐ray diffraction, scanning tunneling microscopy, and Raman spectroscopy confirmed the high quality of the as‐grown single crystals. The topological surface states in the electronic band structure were directly re‐ vealed by angle‐resolved photoemission spectroscopy. Transport measurements showed that the conduction was dominated by the bulk carriers and confirmed a previously observed bulk quantum Hall effect in such highly doped Bi2Se3 samples. We briefly discuss several possible strategies of reducing bulk conductance. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Topological Aspects of Quantum Hall Effect in Graphene

We study the recently observed quantum Hall effect (QHE) in graphene from a theoretical viewpoint of topological nature of the QHE to pose questions: (i) The zero-mass Dirac dispersion, which is the origin of the anomalous QHE, exists only around the zero gap, so a natural question is what happens to the QHE topological numbers over the entire energy spectrum. (ii) How the property that the bulk QHE topological number is equal to the edge QHE topological number, shown for the ordinary QHE, applies to the honeycomb lattice. We have shown that (a) the anomalous QHE ∝ (2N + 1) persists, surprisingly, all the way up to the van-Hove singularities, at which the normal behaviour abruptly takes over. (b) The edge-bulk correspondence persists as shown from the result for finite systems. All these properties hold for the entire sequence of lattice Hamiltonians that interpolate between square↔honeycomb↔ π-flux lattices, so the anomalous QHE is on a quantum critical line.

Mapping of the anomalous magnetotransport regime in theα−(BEDT−TTF)2MHg(SCN)4(M=K,Tl)organic conductors

We present a comprehensive set of pulsed-magnetic-field measurements of the quasi-two-dimensional organic conductors $\ensuremath{\alpha}\ensuremath{-}(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF}{)}_{2}M\mathrm{Hg}(\mathrm{SCN}{)}_{4}$ $(M=\mathrm{K},\mathrm{Tl})$ to map out the boundaries of a high-field regime that was recently associated with the presence of the bulk quantum Hall effect. The phase inversion effect observed in the interplane magnetoresistivity and the behavior of quantum oscillations in the Hall potential are used to investigate the high-field region as a function of magnetic field, temperature, rotation angle, sweep rate, sample quality, and the anion of the charge-transfer salt. The inversion of the phase of the oscillations in ${\ensuremath{\rho}}_{\mathrm{zz}}$ is found to be directly related to the quality of the sample, and is suggested to be an intrinsic property of $\ensuremath{\alpha}\ensuremath{-}(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF}{)}_{2}M\mathrm{Hg}(\mathrm{SCN}{)}_{4}$ $(M=\mathrm{K},\mathrm{Tl}).$ A detailed mapping of the phase-inverted region indicates that its boundaries agree qualitatively with those of the recently proposed low-temperature--high-field state.

Anisotropic behavior of electrical conductivity and collective motion of charge density wave in quasi-two-dimensional conductor η-Mo 4O 11

Unique quasi-two-dimensional conductor η-Mo 4O 11 exhibits two charge density wave (CDW) transitions at T c1 =105 K and T c2 =35 K , and a bulk quantum Hall effect under both low temperature and high magnetic field. In the high-temperature CDW phase ( T c2< T< T c1), the in-plane anisotropy of carrier conduction is enhanced dramatically and the CDW current flows along the CDW nesting vector similar to quasi-one-dimensional conductors.

A new type of bulk quantum Hall effect in Bi 2− xSn xTe 3 crystals

We have found a new type of bulk quantum Hall effect (b-QHE) in layered crystals of Bi 2Te 3 and Bi 2− x Sn x Te 3 ( x=0.005, and 0.0075), whose Hall resistivities exhibit clear Hall plateaus at odd- and even-filling factors, respectively, and the corresponding resistivity minima appear not at the center but at the onset of the Hall plateaus. The charge transfer from the lower valence band in the former or Sn-induced impurity band (IB) in the latter to the upper valence band is found to be the key point for b-QHE.

Possibility of chiral-surface-state originated bulk quantum hall effect in η-mo 4o 11 crystal

Magnetotransport properties have been measured for quasi-two-dimensional oxide η-Mo 4O 11 at low temperatures 0.3–4.2 K in magnetic fields up to 10 T using both bulk contacts and edge contacts methods. In the former case, normal Shubnikov-de Haas oscillations are observed. In the latter case, the Hall resistivity ρ H and transverse magnetoresistance along the c-axis exhibits clear plateaus and minima, respectively, while the longitudinal magnetoresistance along the a *-axis shows a profound peak around 9 T. At the plateaus ρ H is quantized as, ρ H( v)/ρ H( v=2) = 2/ v( v: filling facter), which suggests that a 2D chiral-surface-state appears near the bulky crystal edge.

Bulk quantum Hall effect inη−Mo4O11

We report the observation of a bulk quantum Hall effect in the quasi-two-dimensional conductor $\ensuremath{\eta}\ensuremath{-}{\mathrm{Mo}}_{4}{\mathrm{O}}_{11}.$ The Hall resistance exhibits well-defined quantized plateaus, coincident with pronounced minima in the diagonal resistance. We propose a model involving (i) tiny quasi-two-dimensional electron and hole pockets, left over from an imperfectly nested charge-density wave, and (ii) the exchange of carriers between these mobile states and the localized charge-density-wave condensate. Together with a magnetic field, these factors result in well-separated bands of mobile states superimposed on a background continuum of localized states---the key ingredients for a quantum Hall effect. We also discuss the implications of these findings in the light of recent predictions concerning chiral metallic surface states in bulk quantum Hall systems.

Transport of surface states in the bulk quantum Hall effect

The two-dimensional surface of a coupled multilayer integer quantum Hall system consists of an anisotropic chiral metal. This unusual metal is characterized by ballistic motion transverse and diffusive motion parallel (\hat{z}) to the magnetic field. Employing a network model, we calculate numerically the phase coherent two-terminal z-axis conductance and its mesoscopic fluctuations. Quasi-1d localization effects are evident in the limit of many layers. We consider the role of inelastic de-phasing effects in modifying the transport of the chiral surface sheath, discussing their importance in the recent experiments of Druist et al.

Bulk quantum Hall effect: Evidence that surface states play a key role

It has been suggested recently that the \ensuremath{\alpha}-(BEDT-TTF${)}_{2}$MHg(SCN${)}_{4}$ salts (M=K and Tl) exhibit a bulk quantum Hall effect at high fields [Harrison et al., Phys. Rev. Lett. 77, 1576 (1996)]. We have examined experimentally predictions concerning the transport of current under such conditions. We find that the high field Shubnikov--de Haas oscillations exhibit a complicated temperature dependence, which is not evident in de Haas--van Alphen measurements on the same samples. These differences may be explained in terms of the competition between transport via the bulk and via the surface of the sample.

Bulk versus edge in the quantum Hall effect.

The manifestation of the bulk quantum Hall effect on edge is the chiral anomaly. The chiral anomaly {\it is} the underlying principle of the ``edge approach'' of quantum Hall effect. In that approach, $\sxy$ should not be taken as the conductance derived from the space-local current-current correlation function of the pure one-dimensional edge problem.

Chiral surface states in the bulk quantum Hall effect.

In layered samples which exhibit a bulk quantum Hall effect (QHE), a two-dimensional (2D) surface ``sheath'' of gapless excitations is expected. These excitations comprise a novel 2D chiral quantum liquid which should dominate the low temperature transport along the field ( $z$ axis). For the integer QHE, we show that localization effects are completely absent in the ``sheath,'' giving a metallic $z$-axis conductivity. For fractional filling $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3$, the sheath is a 2D non-Fermi-liquid, with incoherent $z$-axis transport and ${\ensuremath{\sigma}}_{\mathrm{zz}}\ensuremath{\sim}{T}^{3}$. Experimental implications for the Bechgaard salts are discussed.

Organic Conductors and Superconductors: New Directions in the Solid State

In single-crystal organic salts, we find a keen competition between superconducting, magnetic, insulating, and metallic states. The physics of these materials is further enriched by the sensitivity of these states to pressure, temperature, chemical formulation, and magnetic field. A growing international community of scientists have turned their attention to these materials, and are applying the techniques and theories of metal and semiconductor physics to probe these new systems. In this article we will explore these materials. We will discover that these materials have given us many new things: a renaissance in fermiology, new high-magnetic-field states of matter, a bulk quantum Hall effect, new challenges in the calculation of energy bands on a small energy scale, and elusive behavior which seems one step away from our present understanding of physics in low dimensions. Electron correlations probably play an important role in determining the phenomena, and should be considered in more microscopic theoretical treatments of these systems.

Magnetothermopower study of (TMTSF)2PF6 (where TMTSF is tetramethyltetraselenafulvalene).

We have performed a thermoelectric-power study of the organic conductor (TMTSF) 2 PF 6 which exhibits a type of bulk quantum Hall effect (QHE), resulting from a cascade of magnetic-field- induced spin-density-wave (FISDW) transitions. The FISDW are characterized by a sharp increase in thermopower as the temperature is lowered through the transition temperature, followed by an exponential decrease as temperature approaches zero. This suggest a temperature-dependent gap leading to collective QHE-like transport. Most surprising is the vanishing thermopower in the insulating n=0' state