Snapshots of Dirac fermions near the Dirac point in topological insulators

Electron- versus Spin-Phonon Coupling Governs the Temperature-Dependent Carrier Dynamics in the Topological Insulator Bi2Te3

Ultrafast charge and spin dynamics have immense effects on the applications of topological insulators (TIs). By performing spin-adiabatic nonadiabatic molecular dynamics simulations in the presence of electron-phonon (e-ph) and spin-phonon couplings, we investigate temperature-dependent intra- and interband charge and spin relaxation dynamics via the bulk and surface paths in the three-dimensional TI Bi2Te3. The e-ph coupling dominates charge relaxation in the bulk path, and the relaxation rate is positively correlated with temperature due to the large energy gaps and weak spin polarization. Conversely, the relaxation dynamics exhibits an opposite temperature dependence in the surface path because of electron re-excitation and spin mismatching induced by spin-phonon coupling, which arises from small energy gaps and strong spin polarization. The two mechanisms rationalize the charge carriers being long-lived in the bulk and surface phases at low and room temperature, respectively. Additionally, strong thermal fluctuations of the topological states' magnetic moments destroy the spin-momentum locking and trigger backscattering at room temperature.

Two-photon IR pumped UV-Vis transient absorption spectroscopy of Dirac fermions in the topological insulator Bi2Se3

It is often taken for granted that in pump-probe experiments on the topological insulator (TI) Bi₂Se₃using IR pumping with a commercial Ti:sapphire laser [∼800 nm (1.55 eV photon energy)], the electrons are excited in the one-photon absorption regime, even when pumped with absorbed fluences in the mJ cm^-2range. Here, using UV-Vis transient absorption (TA) spectroscopy, we show that even at low-power Infrared (IR) pumping with absorbed fluences in theμJ cm^-2range, the TA spectra of the TI Bi₂Se₃extend across a part of the UV and the entire visible region. This observation suggests unambiguously that the two-photon pumping regime accompanies the usual one-photon pumping regime even at low laser powers applied. We attribute the high efficiency of two-photon pumping to the giant nonlinearity of Dirac fermions in the Dirac surface states (SS). On the contrary, one-photon pumping is associated with the excitation of bound valence electrons in the bulk into the conduction band. Two mechanisms of absorption bleaching were also revealed since they manifest themselves in different spectral regions of probing and cause the appearance of three different relaxation dynamics. These two mechanisms were attributed to the filling of the phase-space in the Dirac SS and bulk states, followed by the corresponding Pauli blocking.

Synthesis and characterization of a Sb2Te3/Bi2Te3 p-n junction heterostructure via electrodeposition in nanoporous membranes

Topological insulators (TIs) are bulk insulators with metallic surface states that can be described by a single Dirac cone. However, low-dimensional solids such as nanowires (NWs) are a challenge, due to the difficulty of separating surface contributions from bulk carriers. Fabrication of NWs with high surface-to-volume ratio can be realized by different methods such as chemical vapor transport, molecular beam epitaxy, and electrodeposition. The last method is used in the present work allowing the growth of structures such as p-n junctions, intercalation of magnetic or superconducting dots. We report the synthesis of high-quality TI NW: Bi₂Te₃, Sb₂Te₃ and p-n junction via electrodeposition. Structural, morphological, and nanostructure properties of NWs have been investigated by various characterization techniques. Interface structures and lateral heterojunctions (LHJ) in p-n junction NWs has also been made.

Dirac surface plasmons in photoexcited bismuth telluride nanowires: optical pump-terahertz probe spectroscopy

Collective excitation of Dirac plasmons in graphene and topological insulators has opened new possibilities of tunable plasmonic materials ranging from THz to mid-infrared regions. Using time resolved Optical Pump-Terahertz Probe (OPTP) spectroscopy, we demonstrate the presence of plasmonic oscillations in bismuth telluride nanowires (Bi₂Te₃ NWs) after photoexcitation using an 800 nm pump pulse. In the frequency domain, the differential conductivity (Δσ = σ_{pump on}-σ_{pump off}) spectrum shows a Lorentzian response where the resonance frequency (ω_p), attributed to surface plasmon oscillations, shifts with photogenerated carrier density (n) as . This dependence establishes the absorption of THz radiation by the Dirac surface plasmon oscillations of the charge carriers in the Topological Surface States (TSS) of Bi₂Te₃ NWs. Moreover, we obtain a modulation depth, tunable by pump fluence, of ∼40% over the spectral range of 0.5 to 2.5 THz. In addition, the time evolution of Δσ(t) represents a long relaxation channel lasting for more than 50 ps. We model the decay dynamics of Δσ(t) using coupled second order rate equations, highlighting the contributions from surface recombination as well as from trap mediated relaxation channels of the photoinjected carriers.

Ultrafast evolution of bulk, surface and surface resonance states in photoexcited [Formula: see text]

We use circular dichroism (CD) in time- and angle-resolved photoemission spectroscopy (trARPES) to measure the femtosecond charge dynamics in the topological insulator (TI) [Formula: see text]. We detect clear CD signatures from topological surface states (TSS) and surface resonance (SR) states. In time-resolved measurements, independently from the pump polarization or intensity, the CD shows a dynamics which provides access to the unexplored electronic evolution in unoccupied states of [Formula: see text]. In particular, we are able to disentangle the unpolarized electron dynamics in the bulk states from the spin-textured TSS and SR states on the femtosecond timescale. Our study demonstrates that photoexcitation mainly involves the bulk states and is followed by sub-picosecond transport to the surface. This provides essential details on intra- and interband scattering in the relaxation process of TSS and SR states. Our results reveal the significant role of SRs in the subtle ultrafast interaction between bulk and surface states of TIs.

Femtosecond time-evolution of mid-infrared spectral line shapes of Dirac fermions in topological insulators

Mid-infrared (MIR) light sources have much potential in the study of Dirac-fermions (DFs) in graphene and topological insulators (TIs) because they have a low photon energy. However, the topological surface state transitions (SSTs) in Dirac cones are veiled by the free carrier absorption (FCA) with same spectral line shape that is always seen in static MIR spectra. Therefore, it is difficult to distinguish the SST from the FCA, especially in TIs. Here, we disclose the abnormal MIR spectrum feature of transient reflectivity changes (ΔR/R) for the non-equilibrium states in TIs, and further distinguish FCA and spin-momentum locked SST using time-resolved and linearly polarized ultra-broadband MIR spectroscopy with no environmental perturbation. Although both effects produce similar features in the reflection spectra, they produce completely different variations in the ΔR/R to show their intrinsic ultrafast dynamics.

Single-component molecular conductor [Pt(dmdt)2]-a three-dimensional ambient-pressure molecular Dirac electron system

The single-component molecular conductor [Pt(dmdt)2] is a sought-after ambient-pressure molecular Dirac electron system, which exhibits a high temperature-insensitive conductivity and temperature-dependent magnetic susceptibility nearly vanishing below 120 K. First-principles DFT calculations reveal that Dirac cones emerge along the a* direction, and form Dirac nodal lines.

Nanoscale Near-Field Tomography of Surface States on (Bi0.5Sb0.5)2Te3

Three-dimensional topological insulators (TIs) have attracted tremendous interest for their possibility to host massless Dirac Fermions in topologically protected surface states (TSSs), which may enable new kinds of high-speed electronics. However, recent reports have outlined the importance of band bending effects within these materials, which results in an additional two-dimensional electron gas (2DEG) with finite mass at the surface. TI surfaces are also known to be highly inhomogeneous on the nanoscale, which is masked in conventional far-field studies. Here, we use near-field microscopy in the mid-infrared spectral range to probe the local surface properties of custom-tailored (Bi_0.5Sb_0.5)₂Te₃ structures with nanometer precision in all three spatial dimensions. Applying nanotomography and nanospectroscopy, we reveal a few-nanometer-thick layer of high surface conductivity and retrieve its local dielectric function without assuming any model for the spectral response. This allows us to directly distinguish between different types of surface states. An intersubband transition within the massive 2DEG formed by quantum confinement in the bent conduction band manifests itself as a sharp, surface-bound, Lorentzian-shaped resonance. An additional broadband background in the imaginary part of the dielectric function may be caused by the TSS. Tracing the intersubband resonance with nanometer spatial precision, we observe changes of its frequency, likely originating from local variations of doping or/and the mixing ratio between Bi and Sb. Our results highlight the importance of studying the surfaces of these novel materials on the nanoscale to directly access the local optical and electronic properties via the dielectric function.

Revealing Optical Transitions and Carrier Recombination Dynamics within the Bulk Band Structure of Bi2Se3

Bismuth selenide (Bi₂Se₃) is a prototypical 3D topological insulator whose Dirac surface states have been extensively studied theoretically and experimentally. Surprisingly little, however, is known about the energetics and dynamics of electrons and holes within the bulk band structure of the semiconductor. We use mid-infrared femtosecond transient reflectance measurements on a single nanoflake to study the ultrafast thermalization and recombination dynamics of photoexcited electrons and holes within the extended bulk band structure over a wide energy range (0.3 to 1.2 eV). Theoretical modeling of the reflectivity spectral line shapes at 10 K demonstrates that the electrons and holes are photoexcited within a dense and cold electron gas with a Fermi level positioned well above the bottom of the lowest conduction band. Direct optical transitions from the first and the second spin-orbit split valence bands to the Fermi level above the lowest conduction band minimum are identified. The photoexcited carriers thermalize rapidly to the lattice temperature within a couple of picoseconds due to optical phonon emission and scattering with the cold electron gas. The minority carrier holes recombine with the dense electron gas within 150 ps at 10 K and 50 ps at 300 K. Such knowledge of interaction of electrons and holes within the bulk band structure provides a foundation for understanding how such states interact dynamically with the topologically protected Dirac surface states.

Ultrafast Surface State Spin-Carrier Dynamics in the Topological Insulator Bi_{2}Te_{2}Se

Topological insulators are promising candidates for optically driven spintronic devices, because photoexcitation of spin polarized surface states is governed by angular momentum selection rules. We carry out femtosecond midinfrared spectroscopy on thin films of the topological insulator Bi_{2}Te_{2}Se, which has a higher surface state conductivity compared to conventionally studied Bi_{2}Se_{3} and Bi_{2}Te_{3}. Both charge and spin dynamics are probed utilizing circularly polarized light. With a sub-band-gap excitation, clear helicity-dependent dynamics is observed only in thin (<20  nm) flakes. On the other hand, such dependence is observed for both thin and thick flakes with above-band-gap excitation. The helicity dependence is attributed to asymmetric excitation of the Dirac-like surface states. The observed long-lasting asymmetry over 10 ps even at room temperature indicates low backscattering of surface state carriers which can be exploited for spintronic devices.

Control over Electron-Phonon Interaction by Dirac Plasmon Engineering in the Bi2Se3 Topological Insulator

Understanding the mutual interaction between electronic excitations and lattice vibrations is key for understanding electronic transport and optoelectronic phenomena. Dynamic manipulation of such interaction is elusive because it requires varying the material composition on the atomic level. In turn, recent studies on topological insulators (TIs) have revealed the coexistence of a strong phonon resonance and topologically protected Dirac plasmon, both in the terahertz (THz) frequency range. Here, using these intrinsic characteristics of TIs, we demonstrate a new methodology for controlling electron-phonon interaction by lithographically engineered Dirac surface plasmons in the Bi₂Se₃ TI. Through a series of time-domain and time-resolved ultrafast THz measurements, we show that, when the Dirac plasmon energy is less than the TI phonon energy, the electron-phonon coupling is trivial, exhibiting phonon broadening associated with Landau damping. In contrast, when the Dirac plasmon energy exceeds that of the phonon resonance, we observe suppressed electron-phonon interaction leading to unexpected phonon stiffening. Time-dependent analysis of the Dirac plasmon behavior, phonon broadening, and phonon stiffening reveals a transition between the distinct dynamics corresponding to the two regimes as the Dirac plasmon resonance moves across the TI phonon resonance, which demonstrates the capability of Dirac plasmon control. Our results suggest that the engineering of Dirac plasmons provides a new alternative for controlling the dynamic interaction between Dirac carriers and phonons.

Anti-site defect effect on the electronic structure of a Bi2Te3 topological insulator

Tuning the Fermi level (E_F) in Bi₂Te₃ topological-insulator (TI) films is demonstrated on controlling the temperature of growth with molecular-beam epitaxy (MBE).

Phase Separation of Dirac Electrons in Topological Insulators at the Spatial Limit

In this work we present unique signatures manifested by the local electronic properties of the topological surface state in Bi₂Te₃ nanostructures as the spatial limit is approached. We concentrate on the pure nanoscale limit (nanoplatelets) with spatial electronic resolution down to 1 nm. The highlights include strong dependencies on nanoplatelet size: (1) observation of a phase separation of Dirac electrons whose length scale decreases as the spatial limit is approached, and (2) the evolution from heavily n-type to lightly n-type surface doping as nanoplatelet thickness increases. Our results show a new approach to tune the Dirac point together with reduction of electronic disorder in topological insulator (TI) nanostructured systems. We expect our work will provide a new route for application of these nanostructured Dirac systems in electronic devices.

Ultrafast carrier dynamics in Ge by ultra-broadband mid-infrared probe spectroscopy

In this study, we carried out 800-nm pump and ultra-broadband mid-infrared (MIR) probe spectroscopy with high time-resolution (70 fs) in bulk Ge. By fitting the time-resolved difference reflection spectra [ΔR(ω)/R(ω)] with the Drude model in the 200–5000 cm⁻¹ region, the time-dependent plasma frequency and scattering rate have been obtained. Through the calculation, we can further get the time-dependent photoexcited carrier concentration and carrier mobility. The Auger recombination essentially dominates the fast relaxation of photoexcited carriers within 100 ps followed by slow relaxation due to diffusion. Additionally, a novel oscillation feature is clearly found in time-resolved difference reflection spectra around 2000 cm⁻¹ especially for high pump fluence, which is the Lorentz oscillation lasting for about 20 ps due to the Coulomb force exerted just after the excitation.

Enhancement of carrier lifetime by spin-orbit coupling in a topological insulator of an Sb2Te3 thin film

Electrons and phonons in chalcogenide-based materials are important factors in the performance of optical data-storage media and thermoelectric devices. However, the fundamental kinetics of carriers in chalcogenide materials remains controversial, and active debate continues over the mechanism responsible for carrier relaxation. In this study, we used optical-pump terahertz-probe spectroscopy, which permits the relationship between structural phase transition and optical property transitions to be examined, to investigate the ultrafast carrier dynamics in a multilayered [Sb(3 Å)/Te(9 Å)]_n thin film during the transition from the disordered to crystalline phase. Using terahertz time-domain spectroscopy and a contact-free optical technique, we demonstrated that the optical conductance and carrier concentration vary as functions of annealing temperature. Moreover, we observed that the topological surface state (TSS) affects the enhancement of the carrier lifetime, which is closely related to the degree of spin-orbit coupling (SOC). The combination of the optical technique and proposed carrier relaxation mechanism provides a powerful tool for monitoring TSS and SOC. Consequently, it was determined that the response of the disordered phase is dominated by an electron-phonon coupling effect, while that of the crystalline structure is controlled by a Dirac surface state and SOC effects. These results are important for understanding the fundamental physics of phase change materials and for optimizing and designing materials with better performance in optoelectronic devices.

Bandgap modulation in photoexcited topological insulator Bi2Te3 via atomic displacements

The atomic and electronic dynamics in the topological insulator (TI) Bi2Te3 under strong photoexcitation were characterized with time-resolved electron diffraction and time-resolved mid-infrared spectroscopy. Three-dimensional TIs characterized as bulk insulators with an electronic conduction surface band have shown a variety of exotic responses in terms of electronic transport when observed under conditions of applied pressure, magnetic field, or circularly polarized light. However, the atomic motions and their correlation between electronic systems in TIs under strong photoexcitation have not been explored. The artificial and transient modification of the electronic structures in TIs via photoinduced atomic motions represents a novel mechanism for providing a comparable level of bandgap control. The results of time-domain crystallography indicate that photoexcitation induces two-step atomic motions: first bismuth and then tellurium center-symmetric displacements. These atomic motions in Bi2Te3 trigger 10% bulk bandgap narrowing, which is consistent with the time-resolved mid-infrared spectroscopy results.

Unraveling Photoinduced Spin Dynamics in the Topological Insulator Bi(2)Se(3)

We report on a time-resolved ultrafast optical spectroscopy study of the topological insulator Bi_{2}Se_{3}. We unravel that a net spin polarization cannot only be generated using circularly polarized light via interband transitions between topological surface states (SSs), but also via transitions between SSs and bulk states. Our experiment demonstrates that tuning photon energy or temperature can essentially allow for photoexcitation of spin-polarized electrons to unoccupied topological SSs with two distinct spin relaxation times (∼25 and ∼300  fs), depending on the coupling between SSs and bulk states. The intrinsic mechanism leading to such distinctive spin dynamics is the scattering in SSs and bulk states which is dominated by E_{g}^{2} and A_{1g}^{1} phonon modes, respectively. These findings are suggestive of novel ways to manipulate the photoinduced coherent spins in topological insulators.

In-Situ Probing Plasmonic Energy Transfer in Cu(In, Ga)Se2 Solar Cells by Ultrabroadband Femtosecond Pump-Probe Spectroscopy

In this work, we demonstrated a viable experimental scheme for in-situ probing the effects of Au nanoparticles (NPs) incorporation on plasmonic energy transfer in Cu(In, Ga)Se2 (CIGS) solar cells by elaborately analyzing the lifetimes and zero moment for hot carrier relaxation with ultrabroadband femtosecond pump-probe spectroscopy. The signals of enhanced photobleach (PB) and waned photoinduced absorption (PIA) attributable to surface plasmon resonance (SPR) of Au NPs were in-situ probed in transient differential absorption spectra. The results suggested that substantial carriers can be excited from ground state to lower excitation energy levels, which can reach thermalization much faster with the existence of SPR. Thus, direct electron transfer (DET) could be implemented to enhance the photocurrent of CIGS solar cells. Furthermore, based on the extracted hot carrier lifetimes, it was confirmed that the improved electrical transport might have been resulted primarily from the reduction in the surface recombination of photoinduced carriers through enhanced local electromagnetic field (LEMF). Finally, theoretical calculation for resonant energy transfer (RET)-induced enhancement in the probability of exciting electron-hole pairs was conducted and the results agreed well with the enhanced PB peak of transient differential absorption in plasmonic CIGS film. These results indicate that plasmonic energy transfer is a viable approach to boost high-efficiency CIGS solar cells.

Electronic interference transport and its electron-phonon interaction in the Sb-doped Bi2Se3 nanoplates synthesized by a solvothermal method

Here we synthesized the antimony doped [Formula: see text] nanoplates by the solvothermal method. The angle-dependent magnetoconductance study was carried out and all the [Formula: see text] were found to be normalized to the perpendicular field, indicating a clear 2D electronic state. The features of weak antilocalization and universal conductance fluctuations were clearly identified in the magnetoresistance transport of the 4-probe nanodevices. The dephasing lengths are extracted respectively according to the Hikami-Larkin-Nagaoka theory. It is attributed to the involvement of the dynamic spin centers. The dephasing lengths are found to increase with the decreasing temperature following a [Formula: see text] law with [Formula: see text]. This reveals the additional dephasing source of electron-phonon interaction, which is often absent for pure 2D electronic systems.

Optically detecting the edge-state of a three-dimensional topological insulator under ambient conditions by ultrafast infrared photoluminescence spectroscopy

Ultrafast infrared photoluminescence spectroscopy was applied to a three-dimensional topological insulator TlBiSe2 under ambient conditions. The dynamics of the luminescence exhibited bulk-insulating and gapless characteristics bounded by the bulk band gap energy. The existence of the topologically protected surface state and the picosecond-order relaxation time of the surface carriers, which was distinguishable from the bulk response, were observed. Our results provide a practical method applicable to topological insulators under ambient conditions for device applications.

Ultra-high modulation depth exceeding 2,400% in optically controlled topological surface plasmons

Modulating light via coherent charge oscillations in solids is the subject of intense research topics in opto-plasmonics. Although a variety of methods are proposed to increase such modulation efficiency, one central challenge is to achieve a high modulation depth (defined by a ratio of extinction with/without light) under small photon-flux injection, which becomes a fundamental trade-off issue both in metals and semiconductors. Here, by fabricating simple micro-ribbon arrays of topological insulator Bi2Se3, we report an unprecedentedly large modulation depth of 2,400% at 1.5 THz with very low optical fluence of 45 μJ cm(-2). This was possible, first because the extinction spectrum is nearly zero due to the Fano-like plasmon-phonon-destructive interference, thereby contributing an extremely small denominator to the extinction ratio. Second, the numerator of the extinction ratio is markedly increased due to the photoinduced formation of massive two-dimensional electron gas below the topological surface states, which is another contributor to the ultra-high modulation depth.

Manifestation of a Second Dirac Surface State and Bulk Bands in THz Radiation from Topological Insulators

Topological insulators (TIs) are interesting quantum matters that have a narrow bandgap for bulk and a Dirac-cone-like conducting surface state (SS). The recent discovered second Dirac surface state (SS) and bulk bands (BBs) located ~1.5 eV above the first SS are important for optical coupling in TIs. Here, we report on the time-domain measurements of THz radiation generated from TIs n-type Cu(0.02)Bi2Se3 and p-type Bi2Te3 single crystals by ultrafast optical pulse excitation. The observed polarity-reversal of the THz pulse originated from transient current is unusual, and cannot be reconciled with the photo-Dember effect. The second SS and BBs are found to be indispensable for the explanation of the unusual phenomenon. Thanks to the existence of the second SS and BBs, TIs manifest an effective wide band gap in THz generation. The present study demonstrates that time-domain THz spectroscopy provide rich information of the optical coupling and the electronic structure of TIs.

Ultrafast electron dynamics at the Dirac node of the topological insulator Sb2Te3

Topological insulators (TIs) are a new quantum state of matter. Their surfaces and interfaces act as a topological boundary to generate massless Dirac fermions with spin-helical textures. Investigation of fermion dynamics near the Dirac point (DP) is crucial for the future development of spintronic devices incorporating topological insulators. However, research so far has been unsatisfactory because of a substantial overlap with the bulk valence band and a lack of a completely unoccupied DP. Here, we explore the surface Dirac fermion dynamics in the TI Sb2Te3 by time- and angle-resolved photoemission spectroscopy (TrARPES). Sb2Te3 has an in-gap DP located completely above the Fermi energy (EF). The excited electrons in the upper Dirac cone stay longer than those below the DP to form an inverted population. This was attributed to a reduced density of states (DOS) near the DP.

Effect of Surface States on Terahertz Emission from the Bi2Se3 Surface

Three-dimensional topological insulators are materials that behave as an insulator in the interior, but as a metal on the surface with Dirac surface states protected by the topological properties of the bulk wavefunctions. The newly discovered second surface state, located about 1.5 eV above the conduction band in Bi2Se3 allows direct photoexcitation of the surface electrons in n-doped samples with a Ti:sapphire femtosecond laser. We have observed efficient THz generation from the Bi2Se3 basal plane upon femtosecond optical excitation. By performing polarization-resolved studies on the emitted THz spectrum, two emission mechanisms have been identified, namely, emission generated from the transient photocurrent under the influence of the surface depletion field and from nonlinear optical rectification. The two types of emission are governed by distinct selection rules. And while the former is characterized by a narrow-band spectrum, the latter, involving almost instantaneous optical transitions, has a broad bandwidth and is enhanced by the presence of resonant transitions. These two emission mechanisms are further separated by their distinct doping dependence upon exposure to ambient air. With surface selectivity, THz emission spectroscopy thus provides a valuable spectroscopic tool for studies of the optical conductivity and dynamics of the surface state in centrosymmetric Bi2Se3.

Use of ultrafast time-resolved spectroscopy to demonstrate the effect of annealing on the performance of P3HT:PCBM solar cells

The organic solar cells of heterojunction system, ITO/PEDOT:PSS/P3HT:PCBM/Al, with a thermal annealing after deposition of Al exhibit better performance than those with an annealing process before deposition of Al. In this study, ultrafast time-resolved spectroscopy is employed to reveal the underlying mechanism of annealing effects on the performance of P3HT:PCBM solar cell devices. The analyses of all decomposed relaxation processes show that the postannealed devices exhibit an increase in charge transfer, in the number of separated polarons and a reduction in the amount of recombination between excited carriers. Moreover, the longer lifetime for the excited carriers in postannealed devices indicates it is more likely to be dissociated into photocarriers and result in a larger value for photocurrent, which demonstrates the physical mechanism for increased device performance.

Triplet superconductivity in 3D Dirac semi-metal due to exchange interaction

Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi-metal. Investigation of the order parameters and energies of these states at zero temperature in a wide range of values of chemical potential μ, the effective electron-electron coupling constant λ and Debye energy TD demonstrates that when the exchange interaction is neglected the singlet always prevails, however, in significant portions of the (μ, λ, TD) parameter space the energy difference is very small. This means that interactions that are small, but discriminate between the spin singlet and the spin triplet, are important in order to determine the nature of the superconducting order there. The best candidate for such an interaction in the materials under consideration is the exchange (the Stoner term) characterized by constant λex. We show that at values of λex, much smaller than ones creating Stoner instability to ferromagnetism λex ∼ 1, the triplet pairing becomes energetically favored over the singlet ones. The 3D quantum critical point at μ = 0 is considered in detail. This can be realized experimentally in optically trapped cold atom systems.

Dirac fermion relaxation and energy loss rate near the Fermi surface in monolayer and multilayer graphene

Ultrafast dynamics of Dirac fermions near the Fermi surface in monolayer and multilayer graphene are revealed using optical pump mid-infrared probe spectroscopy. The energy loss rate of Dirac fermions is also determined via energy-resolved transient transmissivity spectra, which is significantly suppressed as the number of layers in graphene increases.