Field-induced polarization of Dirac valleys in bismuth

Zhu, Zengwei; Collaudin, Aurélie; Fauqué, Benoît; Kang, W.; Behnia, Kamran

doi:10.1038/nphys2111

Cited by 269 publications

(262 citation statements)

References 29 publications

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“…The existence of three anisotropic valleys offers electrons an additional degree of freedom, a subject of recent attention [2]. Here, we map the Landau spectrum by angle-resolved magnetostriction, and quantify the carrier number in each valley: while the electron valleys keep identical spectra, they substantially differ in their density of states at the Fermi level.…”

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confidence: 99%

“…Still the unexpected hysteresis seen in the torque measurements [10], reminiscent of a first-order phase transition, remained unexplained. However, subsequent torque magnetometry studies [30] failed to reproduce this hysteresis and found no evidence of the suspected high-field phase transition.Most recently, a new experiment by Zhu et al refueled the suspicions of possible interaction effects in bismuth: the magnetoconductivity tensor in bismuth was shown to spontaneously lose the threefold rotational symmetry of the underlying lattice at low temperature and high magnetic field [2]. This behavior, which is not related to the previously reported hysteresis, is again unexpected in the non-interacting picture and suggests a type of electronic order involving the valley degree of freedom and favored by electron-electron interactions.…”

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confidence: 99%

“…Most recently, a new experiment by Zhu et al refueled the suspicions of possible interaction effects in bismuth: the magnetoconductivity tensor in bismuth was shown to spontaneously lose the threefold rotational symmetry of the underlying lattice at low temperature and high magnetic field [2]. This behavior, which is not related to the previously reported hysteresis, is again unexpected in the non-interacting picture and suggests a type of electronic order involving the valley degree of freedom and favored by electron-electron interactions.…”

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Thermodynamic evidence for valley-dependent density of states in bulk bismuth

et al. 2014

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Electron-like carriers in bismuth are described by the Dirac Hamiltonian, with a band mass becoming a thousandth of the bare electron mass along one crystalline axis [1]. The existence of three anisotropic valleys offers electrons an additional degree of freedom, a subject of recent attention [2]. Here, we map the Landau spectrum by angle-resolved magnetostriction, and quantify the carrier number in each valley: while the electron valleys keep identical spectra, they substantially differ in their density of states at the Fermi level. Thus, the electron fluid does not keep the rotational symmetry of the lattice at low temperature and high magnetic field, even in the absence of internal strain. This effect, reminiscent of the Coulomb pseudo-gap in localized electronic states, affects only electrons in the immediate vicinity of the Fermi level. It presents the most striking departure from the non-interacting picture of electrons in bulk bismuth.A naturally occurring element known since ancient times [3,4], the semi-metal bismuth has played an important role in the history of solid state physics [5]. Over the last five years, bismuth has attracted new attention focused on its unusual properties in the presence of a strong magnetic field. More than 120 years after the first discovery of the Nernst-Ettingshausen effect (NE) in the very same material [6], giant NE oscillations were observed in the vicinity of the quantum limit [7]. This limit is attained when the magnetic field is strong enough to confine carriers to their lowest Landau level(s). With currently available magnetic fields, it is only accessible in solids with a carrier concentration as low as in bismuth. Theory expects a prominent role for electron interactions beyond this limit [8]. NE measurements extended to 33 T, well above the quantum limit [9], found features unexpected in the single-particle picture. Torque magnetometry studies by Li et al. [10] up to 31 T showed a structure in magnetization with hysteresis suggesting a correlation-induced phase transition.These results inspired new theoretical studies of the Landau spectrum in bismuth [11,12], which is remarkably complex because the electron dispersion is Diraclike, with an additional anisotropic Zeeman term [13,14]. In particular, in the vicinity of the high-symmetry axis known as the trigonal axis, the magnetic field at which an electron Landau level is depleted rapidly changes with the field orientation. Recently, the angle-resolved Landau spectrum was determined by NE measurements for the whole solid angle [15,16], and found to be in good agreement with theoretical calculations by Fuseya [15], based on an earlier model by Vecchi and co-workers [13]. Thus the non-interacting picture can successfully explain most features of the high-field phase diagram, including those previously attributed to electron interaction [9,10]. Still the unexpected hysteresis seen in the torque measurements [10], reminiscent of a first-order phase transition, remained unexplained. However, subsequent torque magneto...

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Thermodynamic evidence for valley-dependent density of states in bulk bismuth

et al. 2014

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“…Recently, the emergence of atomically thin two-dimensional (2D) crystals such as graphene and transition metal dichalcogenides (TMDC) have offered new playgrounds to explore novel electronic device concepts [4][5][6][7][8][9][10] . In addition to spin, two types of internal indices of electrons have been investigated as information carriers, namely the layer [11][12][13][14] and valley [15][16][17][18][19] degrees of freedom.…”

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Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers

et al. 2013

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In monolayer group-VI transition metal dichalcogenides, charge carriers have spin and valley degrees of freedom, both associated with magnetic moments. On the other hand, the layer degree of freedom in multilayers is associated with electrical polarization. Here we show that transition metal dichalcogenide bilayers offer an unprecedented platform to realize a strong coupling between the spin, valley and layer pseudospin of holes. Such coupling gives rise to the spin Hall effect and spin-dependent selection rule for optical transitions in inversion symmetric bilayer and leads to a variety of magnetoelectric effects permitting quantum manipulation of these electronic degrees of freedom. Oscillating electric and magnetic fields can both drive the hole spin resonance where the two fields have valley-dependent interference, making an interplay between the spin and valley as information carriers possible for potential valley-spintronic applications. We show how to realize quantum gates on the spin qubit controlled by the valley bit.

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“…Valleytronics is an emerging device concept [1][2][3] based on the manipulation of valley degree of freedom in certain condensed matter systems such as semiconductor quantum well [4], silicon [5], bismuth [6], diamond [7], carbon nanotube [8], graphene [9], Dirac semimetal [10], and transition-metal dichalcogenide (TMD) monolayer [11]. In these materials, electrons can populate multiple low-energy states that are well separated in momentum space, known as valley.…”

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confidence: 99%

Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve, and universal reversible logic gate

et al. 2017

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Despite much anticipation of valleytronics as a candidate to replace the aging complementary metal-oxidesemiconductor (CMOS) based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all electrically in an electrostatic setting. Here, we propose a class of all-electric-controlled valley filter, valve, and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration mismatches that of a gate-controlled scattering region. The valley polarization can be abruptly switched into different states and remains stable over semi-infinite gate-voltage windows. Colossal tunneling valleypseudomagnetoresistance ratio of over 10000% can be achieved in a valley-valve setup. We further propose a valleytronic-based logic gate capable of covering all 16 types of two-input Boolean logics. Remarkably, the valley degree of freedom can be harnessed to resurrect logical reversibility in two-input universal Boolean gate. The (2+1) polarization states (two distinct valleys plus a null polarization) reestablish one-to-one inputto-output mapping, a crucial requirement for logical reversibility, and significantly reduce the complexity of reversible circuits. Our results suggest that the synergy of valleytronics and digital logics may provide new paradigms for valleytronic-based information processing and reversible computing. Despite much anticipation of valleytronics as a candidate to replace the aging complementary metal-oxidesemiconductor (CMOS) based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all electrically in an electrostatic setting. Here, we propose a class of all-electric-controlled valley filter, valve, and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration mismatches that of a gate-controlled scattering region. The valley polarization can be abruptly switched into different states and remains stable over semi-infinite gate-voltage windows. Colossal tunneling valley-pseudomagnetoresistance ratio of over 10 000% can be achieved in a valley-valve setup. We further propose a valleytronic-based logic gate capable of covering all 16 types of two-input Boolean logics. Remarkably, the valley degree of freedom can be harnessed to resurrect logical reversibility in two-input universal Boolean gate. The (2 + 1) polarization states (two distinct valleys plus a null polarization) reestablish one-to-one input-to-output mapping, a crucial requirement for logical reversibility, and significantly reduce the complexity of reversible circuits. Our results suggest that the synergy of va...

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Field-induced polarization of Dirac valleys in bismuth

Cited by 269 publications

References 29 publications

Thermodynamic evidence for valley-dependent density of states in bulk bismuth

Thermodynamic evidence for valley-dependent density of states in bulk bismuth

Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers

Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve, and universal reversible logic gate

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