One-dimensional Electron Systems Research Articles

Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state

Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires and graphene. Recently, a new method has emerged with the recognition that symmetry-protected topological (SPT) phases, which occur in systems with an energy gap to quasiparticle excitations (such as insulators or superconductors), can host robust surface states that remain gapless as long as the relevant global symmetry remains unbroken. The nature of the charge carriers in SPT surface states is intimately tied to the symmetry of the bulk, resulting in one- and two-dimensional electronic systems with novel properties. For example, time reversal symmetry endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, fixing the orientation of their spin relative to their momentum. Weakly breaking this symmetry generates a gap on the surface, resulting in charge carriers with finite effective mass and exotic spin textures. Analogous manipulations have yet to be demonstrated in two-dimensional topological insulators, where the primary example of a SPT phase is the quantum spin Hall state. Here we demonstrate experimentally that charge-neutral monolayer graphene has a quantum spin Hall state when it is subjected to a very large magnetic field angled with respect to the graphene plane. In contrast to time-reversal-symmetric systems, this state is protected by a symmetry of planar spin rotations that emerges as electron spins in a half-filled Landau level are polarized by the large magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability, which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with a tunable bandgap and an associated spin texture.

Realization of pristine and locally tunable one-dimensional electron systems in carbon nanotubes

The ability to tune local parameters of quantum Hamiltonians has been demonstrated in experimental systems including ultracold atoms, trapped ions, superconducting circuits and photonic crystals. Such systems possess negligible disorder, enabling local tunability. Conversely, in condensed-matter systems, electrons are subject to disorder, which often destroys delicate correlated phases and precludes local tunability. The realization of a disorder-free and locally-tunable condensed-matter system thus remains an outstanding challenge. Here, we demonstrate a new technique for deterministic creation of locally-tunable, ultralow-disorder electron systems in carbon nanotubes suspended over complex electronic circuits. Using transport experiments we show that electrons can be localized at any position along the nanotube and that the confinement potential can be smoothly moved from location to location. The high mirror symmetry of transport characteristics about the nanotube centre establishes the negligible effects of electronic disorder, thus allowing experiments in precision-engineered one-dimensional potentials. We further demonstrate the ability to position multiple nanotubes at chosen separations, generalizing these devices to coupled one-dimensional systems. These capabilities could enable many novel experiments on electronics, mechanics and spins in one dimension.

Pristine quantum devices on demand

A technique combining direct nanotube transfer with scanning probe microscopy can be used to create ultraclean one-dimensional electron systems in suspended carbon nanotubes.

Thermal transport and quench relaxation in nonlinear Luttinger liquids

One-dimensional electrons with a linearized dispersion relation are equivalent to a collection of harmonic plasmon modes, which represent long wavelength density oscillations. An immediate consequence of this Luttinger model of one-dimensional electron systems is the absence of inelastic scattering processes responsible for the relaxation of nonequilibrium states. In a generic nonlinear Luttinger liquid plasmons may decay and thus acquire a finite lifetime. We show that equilibration of plasmons is hierarchical and has profound implications for the dynamics after a thermal quench. We also develop a thermal transport theory and compute thermal conductance of the nonlinear Luttinger liquid by treating the collision integral of plasmons in a manifestly nonperturbative way.

Dynamics of waves in one-dimensional electron systems: Density oscillations driven by population inversion

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.

Collapse of Charge Ordering Due to Disorder in Quasi One-Dimensional Electron Systems

Effects of disorder on charge ordering (CO) is investigated for one-dimensional (1D) and quasi 1D extended Hubbard model with infinite on-site repulsion at quarter filling. Only the forward scattering due to disorder is taken into account. In the 1D model, the resistivity due to Umklapp scattering that is an origin of CO is shown to be suppressed by the forward scattering. In addition, we obtain that the CO transition temperature TCO for quasi 1D model becomes smaller with increasing strength of the forward scattering.

Coulomb drag between ballistic quantum wires

We develop a kinetic equation description of Coulomb drag between ballistic one-dimensional electron systems, which enables us to demonstrate that equilibration processes between right- and left-moving electrons are crucially important for establishing dc drag. In one-dimensional geometry, this type of equilibration requires either backscattering near the Fermi level or scattering with small-momentum transfer near the bottom of the electron spectrum. Importantly, pairwise forward scattering in the vicinity of the Fermi surface alone is not sufficient to produce a nonzero dc drag resistivity ${\ensuremath{\rho}}_{\mathrm{D}}$, in contrast to a number of works that have studied Coulomb drag due to this mechanism of scattering before. We show that slow equilibration between two subsystems of electrons of opposite chirality, ``bottlenecked'' by inelastic collisions involving cold electrons near the bottom of the conduction band, leads to a strong suppression of Coulomb drag, which results in an activation dependence of ${\ensuremath{\rho}}_{\mathrm{D}}$ on temperature, instead of the conventional power law. We demonstrate the emergence of a drag regime in which ${\ensuremath{\rho}}_{\mathrm{D}}$ does not depend on the strength of interwire interactions, while depending strongly on the strength of interactions inside the wires.

Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Interacting one-dimensional electron systems are generally referred to as ``Luttinger liquids,'' after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The ``spin-incoherent Luttinger liquid'' describes a finite-temperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. Similar physics can take place in the ground state, when a Luttinger liquid is coupled to a spin bath, which effectively introduces a ``spin temperature'' through its entanglement with the spin degree of freedom. We show that the spin-incoherent state can be written as a factorized wave function, with a spin wave function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled $t\ensuremath{-}J$ chains, but also for the $t\ensuremath{-}J$-Kondo chain with strongly interacting conduction electrons. We argue that this theory is quite universal and may describe a family of problems that could be dubbed ``spin incoherent.''

Heat flow in InAs/InP heterostructure nanowires

The transfer of heat between electrons and phonons plays a key role for thermal management in future nanowire-based devices, but only a few experimental measurements of electron-phonon (e-ph) coupling in nanowires are available. Here, we combine experimental temperature measurements on an InAs/InP heterostructure nanowire system with finite element modeling to extract information on heat flow mediated by e-ph coupling. We find that the electron and phonon temperatures in our system are highly coupled even at temperatures as low as 2 K. Additionally, we find evidence that the usual power-law temperature dependence of electron-phonon coupling may not correctly describe the coupling in nanowires and show that this result is consistent with previous research on similar one-dimensional electron systems. We also compare the strength of the observed e-ph coupling to a theoretical analysis of e-ph interaction in InAs nanowires, which predicts a significantly weaker coupling strength than observed experimentally.

Gate controlled spin-density wave and chiral FFLO superconducting phases in interacting helical liquids

We explore the phases exhibited by an interacting helical liquid in the presence of finite chemical potential (applied gate voltage) and spin imbalance (applied magnetic field). We find that the helical nature gives rise to quantum orders that are expected to be absent in nonchiral one-dimensional electronic systems. For repulsive interactions, the ordered state has an oscillatory spin texture whose ordering wave vector is controlled by the chemical potential. We analyze the manner in which a magnetic impurity provides signatures of such oscillations. We find that finite spin imbalance favors a finite current carrying ground state that is not condensed in the absence of interactions and is superconducting for attractive interactions. This state is characterized by Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type oscillations where the Cooper pairs obtain a finite center-of-mass momentum. These phases can be realized on the edge of two-dimensional systems exhibiting the quantum spin Hall effect or on dislocation lines in weak topological insulators.

Nonuniversal conductance quantization observed in a gate-defined 1D wire

A new method of fabricating a one-dimensional (1D) electron system using a conventional GaAs/AlGaAs heterostructure with metallic gates has been demonstrated. The transport properties of 1D wires with various lengths up to 6400 nm have been studied. A clear conductance quantization, which has never before been observed in a gate-defined 1D wire system, was observed. This confirms that the 1D wire is indeed clean without a significant local resonant state in the conduction channel. Also, the conductance step height was found to be less than 2e2/h for wires longer 3200 nm. Such nonuniversal conductance quantization is regarded as a fingerprint of a Luttinger liquid. The result confirms that a 1D electron system can be fabricated by using a conventional method.

Quantum phase transition in a resonant level coupled to interacting leads

A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the 'conventional' Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.

Microwave-induced nonequilibrium temperature in a suspended carbon nanotube

Antenna-coupled suspended single carbon nanotubes exposed to 108 GHz microwave radiation are shown to be selectively heated with respect to their metal contacts. This leads to an increase in the conductance as well as to the development of a power-dependent DC voltage. The increased conductance stems from the temperature dependence of tunneling into a one-dimensional electron system. The DC voltage is interpreted as a thermovoltage, due to the increased temperature of the electron liquid compared to the equilibrium temperature in the leads.

Manifestations of electron interactions in photogalvanic effect in chiral nanotubes

Carbon nanotubes provide one of the most accessible experimental realizations of one-dimensional electron systems. In the experimentally relevant regime of low doping, the Luttinger liquid formed by electrons may be approximated by a Wigner crystal. The crystal-like electronic order suggests that nanotubes exhibit effects similar to the M\"ossbauer effect where the momentum of an emitted photon is absorbed by the whole crystal. We show that the circular photovoltaic effect in chiral nanotubes is of the same nature. We obtain the frequency dependence of the photovoltage and characterize its singularities in a broad frequency range where the electron correlations are essential. Our predictions provide a basis for using the photogalvanic effect as a new experimental probe of electron correlations in nanotubes.

Spectral properties of one-dimensional spiral spin density wave states

We provide a full characterization of the spectral properties of spiral spin density wave (SSDW) states which emerge in one-dimensional electron systems coupled to localized magnetic moments or quantum wires with spin-orbit interactions. We derive analytic results for the spectral function, local density of states and optical conductivity in the low-energy limit by using field theory techniques. We identify various collective modes and show that the spectrum strongly depends on the interaction strength between the electrons. The results provide characteristic signatures for an experimental detection of SSDW states.

Anomalous localization and dual role of correlation in one-dimensional electronic systems with long-range correlated disorder

The localization behaviors of electronic states and the role of long-range correlation (LRC) in a one-dimensional tight-binding Anderson model with long-range correlated diagonal disorder were numerically studied at the band center by using the transfer matrix method. Two different kinds of localized states with anomalous properties were found in two special localized regimes: regime I with both weak correlation and weak disorder and regime II with both strong correlation and strong disorder. Further calculations show that the LRC plays inverse role in these two regimes: by increasing the degree of LRC, the localization is suppressed in regime I while the localization is enhanced in regime II.

Ultrafast optical excitation of coherent phonons in a one-dimensional metal at the photoinduced insulator-metal transition

Photoinduced insulator-metal transition from the charge-density wave (CDW) ground state in a one-dimensional electron system is studied within the nonadiabatic theory of electron-phonon coupling. Ultrafast melting and partial recovery of the CDW and its critical slowing down are found to accompany the cooperative lattice response by an electron-phonon energy transfer on the subpicosecond time scale, which is read out by the nonadiabatic depopulation and repopulation of coherent phonons. Further, electron correlation is described in a self-consistent mean-field theory. In the strong electron correlation, the spin-density wave competes with the CDW and the photoinduced responses of the lattice is found to undergo the nonadiabatic-adiabatic transition.

What lurks below the last plateau: experimental studies of the 0.7 × 2e2/h conductance anomaly in one-dimensional systems

The integer quantised conductance of one-dimensional electron systems is a well-understood effect of quantum confinement. A number of fractionally quantised plateaus are also commonly observed. They are attributed to many-body effects, but their precise origin is still a matter of debate, having attracted considerable interest over the past 15 years. This review reports on experimental studies of fractionally quantised plateaus in semiconductor quantum point contacts and quantum wires, focusing on the 0.7 × 2e2/h conductance anomaly, its analogues at higher conductances and the zero-bias peak observed in the dc source–drain bias for conductances less than 2e2/h.

Equilibration of Luttinger Liquid and Conductance of Quantum Wires

Luttinger liquid theory describes one-dimensional electron systems in terms of noninteracting bosonic excitations. In this approximation thermal excitations are decoupled from the current flowing through a quantum wire, and the conductance is quantized. We show that relaxation processes not captured by the Luttinger liquid theory lead to equilibration of the excitations with the current and give rise to a temperature-dependent correction to the conductance. In long wires, the magnitude of the correction is expressed in terms of the velocities of bosonic excitations. In shorter wires it is controlled by the relaxation rate.

Majorana Edge States in Interacting One-Dimensional Systems

We show that one-dimensional electron systems in the proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime in which the Majorana edge states persist. We present strategies of how this regime can be reached.