arXiv subjects

J. P. Carbotte

Publications and source records attributed to J. P. Carbotte.

At least 37 records · Page 2Linked to original sources

arXiv2016

Optical and Transport Properties in 3D Dirac and Weyl Semimetals

Within a Kubo formalism, we study dc transport and ac optical properties of 3D Dirac and Weyl semimetals. Emphasis is placed on the approach to charge neutrality and on the differences between Dirac and Weyl materials. At charge neutrality, the zero-temperature limit of the dc conductivity is not universal and also depends on the residual scattering model employed. However, the Lorenz number L retains its usual value L_0. With increasing temperature, the Wiedemann-Franz law is violated. At high temperatures, L exhibits a new plateau at a value dependent on the details of the scattering rate. Such details can also appear in the optical conductivity, both in the Drude response and interband background. In the clean limit, the interband background is linear in photon energy and always extrapolates to the origin. This background can be shifted to the right through the introduction of a massless gap. In this case, the extrapolation can cut the axis at a finite photon energy as is observed in some experiments. It is also of interest to differentiate between the two types of Weyl semimetals: those with broken time-reversal symmetry and those with broken spatial-inversion symmetry. We show that, while the former will follow the same behaviour as the 3D Dirac semimetals, for the zero magnetic field properties discussed here, the latter type will show a double step in the optical conductivity at finite doping and a single absorption edge at charge neutrality. The Drude conductivity is always finite in this case, even at charge neutrality.

cond-mat.mes-hall↗

arXiv2016

Hall quantization and optical conductivity evolution with variable Berry phase in $α$-$T_3$ model

The $α$-$T_3$ model is characterized by a variable Berry phase that changes continuously from $π$ to $0$. We take advantage of this property to highlight the effects of this underlying geometrical phase on a number of physical quantities. The Hall quantization of the two limiting cases is dramatically different - a relativistic series is associated with a Berry phase of $π$ and a non-relativistic series is associated with the other limit. We study the quantization of the Hall plateaux as they continuously evolve from a relativistic to a non-relativistic regime. Additionally, we describe two physical quantities that retain knowledge of the Berry phase, in the absence of a motion-inducing magnetic field. The variable Berry phase of the $α$-$T_3$ model allows us to explicitly describe the Berry phase dependence of the dynamical longitudinal optical conductivity and of the angular scattering probability.

cond-mat.mes-hall↗

arXiv2015

Anomalous Behaviour in the Magneto-Optics of a Gapped Topological Insulator

The Dirac fermions at the surface of a topological insulator can be gapped by introducing magnetic dopants. Alternatively, in an ultra-thin slab with thickness on the order of the extent of the surface states, both the top and bottom surface states acquire a common gap value ($Δ$) but with opposite sign. In a topological insulator, the dominant piece of the Hamiltonian ($\hat{H}$) is of a relativistic nature. A subdominant non-relativistic piece is also present and in an external magnetic field ($B$) applied perpendicular to the surface, the $N=0$ Landau level is no longer at zero energy but is shifted to positive energy by the Schr{ö}dinger magnetic energy. When a gap is present, it further shifts this level down by $-Δ$ for positive $Δ$ and up by $|Δ|$ for a negative gap. This has important consequences for the magneto-optical properties of such systems. In particular, at charge neutrality, the lowest energy transition displays anomalous non-monotonic behaviour as a function of $B$ in both its position in energy and its optical spectral weight. The gap can also have a profound impact on the spectral weight of the interband lines and on corresponding structures in the real part of the dynamical Hall conductivity. Conversely, the interband background in zero field remains unchanged by the non-relativistic term in $\hat{H}$ (although its onset frequency is modified).

cond-mat.mes-hall↗

arXiv2015

Cyclotron Resonance in Topological Insulators: Non-Relativistic Effects

The low-energy Hamiltonian used to describe the dynamics of the helical Dirac fermions on the surface of a topological insulator contains a subdominant non-relativistic (Schrödinger) contribution. This term can have an important effect on some properties while having no effect on others. The Hall plateaus retain the same relativistic quantization as the pure Dirac case. The height of the universal interband background conductivity is unaltered, but its onset is changed. However, the non-relativistic term leads directly to particle-hole asymmetry. It also splits the interband magneto-optical lines into doublets. Here, we find that, while the shape of the semiclassical cyclotron resonance line is unaltered, the cyclotron frequency and its optical spectral weight are changed. There are significant differences in both of these quantities for a fixed value of chemical potential or fixed doping away from charge neutrality depending on whether the Fermi energy lies in the valence or conduction band.

cond-mat.mes-hall↗

arXiv2015

Comparison of pressurized sulfur hydride with conventional superconductors

A recent report that sulfur hydride under pressure is an electron-phonon superconductor with a Tc of 190 K has been met with much excitement although it is yet to be confirmed. Based on several electron-phonon spectral density functions already available from density functional theory, we find that the electron-phonon spectrum is near optimum for Tc with a particularly large value of its characteristic phonon energy omega_ln which is due to the small hydrogen mass. We find that the thermodynamic universal BCS ratios are near those for Pb and Nb3Sn. We suggest that optical measurements could be a useful tool to establish the existence and nature of the superconductivity in this system. Conventional superconductors are in the impurity-dominated dirty limit. By contrast sulfur hydride will be in the clean limit because of its large energy gap scale. The AC optical conductivity will display distinct and separate signatures of the superconducting gap in the low-energy impurity-dominated range of the optical spectrum and additional phonon structures at higher energies where the clean limit applies.

cond-mat.supr-con↗

arXiv2015

Particle-Hole Asymmetry in Gapped Topological Insulator Surface States

We consider the combined effect of a gap and a Zeeman interaction on the helical Dirac fermions which exist on the surface of a topological insulator. Magneto-optical properties, the magnetization, Hall effect and the density of states are considered with emphasis on the particle-hole asymmetry which arises when a subdominant Schrödinger piece is included along with the dominant Dirac part of the Hamiltonian. When appropriate, we compare our results with those of a single valley gapped graphene system for which Zeeman splitting behaves differently. We provide a derivation of the phase offset in the magnetic oscillations brought about by the combined effect of the gap and Schrödinger term without requiring the semiclassical Onsager quantization condition. Our results agree with previous discussions based on semiclassical arguments.

cond-mat.mes-hall↗

arXiv2015

Isotope Effect of Underdoped Cuprates in the Yang-Rice-Zhang Model

The underdoped region of the cuprate's phase diagram displays many novel electronic phenomena both in the normal and the superconducting state. Many of these anomalous properties have found a natural explanation within the resonating valence bond spin liquid phenomenological model of Yang-Rice-Zhang (YRZ) which includes the rise of a pseudogap. This leads to Fermi surface reconstruction and profoundly changes the electronic structure. Here we extend previous work to consider the shift in critical temperature on $^{16}$O to $^{18}$O substitution, The isotope effect has been found experimentally to be very small at optimal doping yet to rapidly increase to very large values with underdoping. The YRZ model provides a natural explanation of this behavior and supports the idea of a pairing mechanism which is mainly spin fluctuations with a subdominant $(\sim 10\%)$ phonon contribution.

cond-mat.supr-con↗

arXiv2015

Optical spectral weight: comparison of weak and strong spin-orbit coupling

The Fermi velocity ($v_{F}$) associated with the spin-orbit coupling is two orders of magnitude smaller for spintronic semiconductors than it is for topological insulators. Both families can be treated with the same Hamiltonian which contains a relativistic (Dirac) linear in momentum term proportional to $v_{F}$ and a non-relativistic quadratic contribution with Schrödinger mass (m). We find that the AC dynamic longitudinal and transverse (Hall) magneto-conductivities are strongly dependent on the size of $v_{F}$. When the Dirac fermi velocity is small, the absorption background provided by the interband optical transitions is finite only over a very limited range of photon energies as compared with topological insulators. Its onset depends on the value of the chemical potential ($μ$) and on the magnetic field (B), as does its upper cut off. Within this limited range its magnitude is however constant and has the same magnitude of $e^{2}π/(8h)$ as is found in topological insulators and also in graphene noting a difference in degeneracy factor. The total optical spectral weight under the universal interband background is $e^{2}π/(8h)4mv_{F}^{2}$. In contrast to the known result for graphene no strict conservation law applies to the spectral weight transfers between inter and intra band transition brought about by variations in the magnitude of the chemical potential when a non-relativistic contribution is present in the Hamiltonian whatever size it may have.

cond-mat.mes-hall↗

arXiv2015

Electron-phonon correlations on spin texture of gapped helical Dirac Fermions

The metallic surface states of a topological insulator support helical Dirac fermions protected by topology with their spin locked perpendicular to their momentum. They can acquire mass through magnetic doping or through hybridization of states on opposite faces of a thin sample. In this case there can be a component of electron spin oriented perpendicular to the surface plane. The electron-phonon interaction renormalizes the dynamics of the charge carriers through their spectral density. It also modifies the gap channel and a second spectral function enters which, not only determines the out of plane spin component, but also comes into in-plane properties. While the out of plane spin component is decreased below the Fermi momentum ($k_F$), the in plane component increases. There are also correlation tails extending well beyond $k_F$. The angular resolved photo-emission line shapes aquire Holstein side bands. The effective gap in the density of states is reduced and the optical conductivity aquires distinct measurable phonon structure even for modest value of the electron-phonon coupling.

cond-mat.mes-hall↗

arXiv2015

Magnetic Properties of Dirac Fermions in a Buckled Honeycomb Lattice

We calculate the magnetic response of a buckled honeycomb lattice with intrinsic spin-orbit coupling (such as silicene) which supports valley-spin polarized energy bands when subjected to a perpendicular electric field $E_z$. By changing the magnitude of the external electric field, the size of the two band gaps involved can be tuned, and a transition from a topological insulator (TI) to a trivial band insulator (BI) is induced as one of the gaps becomes zero, and the system enters a valley-spin polarized metallic state (VSPM). In an external magnetic field ($B$), a distinct signature of the transition is seen in the derivative of the magnetization with respect to chemical potential ($μ$) which gives the quantization of the Hall plateaus through the Streda relation. When plotted as a function of the external electric field, the magnetization has an abrupt change in slope at its minimum which signals the VSPM state. The magnetic susceptibility ($χ$) shows jumps as a function of $μ$ when a band gap is crossed which provides a measure of the gaps' variation as a function of external electric field. Alternatively, at fixed $μ$, the susceptibility displays an increasingly large diamagnetic response as the electric field approaches the critical value of the VSPM phase. In the VSPM state, magnetic oscillations exist for any value of chemical potential while for the TI, and BI state, $μ$ must be larger than the minimum gap in the system. When $μ$ is larger than both gaps, there are two fundamental cyclotron frequencies (which can also be tuned by $E_z$) involved in the de-Haas van-Alphen oscillations which are close in magnitude. This causes a prominent beating pattern to emerge.

cond-mat.mes-hall↗

arXiv2014

Electron-boson spectral density of LiFeAs obtained from optical data

We analyze existing optical data in the superconducting state of LiFeAs at $T =$ 4 K, to recover its electron-boson spectral density. A maximum entropy technique is employed to extract the spectral density $I^2χ(ω)$ from the optical scattering rate. Care is taken to properly account for elastic impurity scattering which can importantly affect the optics in an $s$-wave superconductor, but does not eliminate the boson structure. We find a robust peak in $I^2χ(ω)$ centered about $Ω_R \cong$ 8.0 meV or 5.3 $k_B T_c$ (with $T_c =$ 17.6 K). Its position in energy agrees well with a similar structure seen in scanning tunneling spectroscopy (STS). There is also a peak in the inelastic neutron scattering (INS) data at this same energy. This peak is found to persist in the normal state at $T =$ 23 K. There is evidence that the superconducting gap is anisotropic as was also found in low temperature angular resolved photoemission (ARPES) data.

cond-mat.supr-con↗

arXiv2014

Magnetization of the Metallic Surface States in Topological Insulators

We calculate the magnetization of the helical metallic surface states of a topological insulator. We account for the presence of a small sub-dominant Schr{ö}dinger piece in the Hamiltonian in addition to the dominant Dirac contribution. This breaks particle-hole symmetry. The cross-section of the upper Dirac cone narrows while that of the lower cone broadens. The sawtooth pattern seen in the magnetization of the pure Dirac limit as a function of chemical potential ($μ$) is shifted; but, the quantization of the Hall plateaus remains half integral. This is verified by taking the derivative of the magnetization with respect to $μ$. We compare our results with those when the non-relativistic piece dominates over the relativistic contribution and the quantization is integral. Analytic results for the magnetic oscillations are obtained where we include a first order correction in the ratio of non-relativistic to relativistic magnetic energy scales. Our fully quantum mechanical derivations confirm the expectation of semiclassical theory except for a small correction to the expected phase. There is a change in the overall amplitude of the magnetic oscillations. The Dingle and temperature factors are modified.

cond-mat.mes-hall↗

arXiv2014

Chiral anomaly and optical absorption in Weyl semimetals

Weyl semimetals are a three-dimensional topological phase of matter with isolated band touchings in the Brillouin Zone. These points have an associated chirality, and many of the proposals to detect the Weyl semimetal state rely on the chiral anomaly. A consequence of the chiral anomaly is that under the application of an $\vec{E}\cdot\vec{B}$ field, charge is transferred between points of opposite chirality. In this paper we propose an optical absorption experiment that provides evidence for the chiral anomaly. We use the Kubo formula, and find that an applied $\vec{E}\cdot\vec{B}$ induces the formation of step-like features at finite frequency in the interband optical conductivity. We study the effect of scattering, and finite temperatures on this feature and find that it should be observable at low temperatures in pure samples. Finally we discuss how the application of an $\vec{E}\cdot\vec{B}$ field can be used to map out the frequency dependence of the scattering rate.

cond-mat.mes-hall↗

arXiv2014

Hexagonal warping on spin texture, Hall conductivity and circular dichroism of Topological Insulator

The topological protected electronic states on the surface of a topological insulator can progressively change their Fermi cross-section from circular to a snowflake shape as the chemical potential is increased above the Dirac point because of an hexagonal warping term in the Hamiltonian. Another effect of warping is to change the spin texture which exists when a finite gap is included by magnetic doping, although the in-plane spin component remains locked perpendicular to momentum. It also changes the orbital magnetic moment, the matrix element for optical absorption and the circular dichroism. We find that the Fermi surface average of z-component of spin is closely related to the value of the Berry phase. This holds even when the Hamiltonian includes a subdominant non-relativistic quadratic in momentum term (which provides particle-hole asymmetry) in addition to the dominant relativistic Dirac term. There is also a qualitative correlation between $\left\langle S_z \right\rangle$ and the dichroism. For the case when the chemical potential falls inside the gap between valence and conduction band, the Hall conductivity remains quantized and unaffected in value by the hexagonal warping term.

cond-mat.mes-hall↗

arXiv2014

Electron-Phonon Spectral Density of MgB2 from Optical Data, through Maximum Entropy

We use maximum entropy techniques to extract an electron-phonon density from optical data in the normal state at T = 45 K in MgB2. Limiting the analysis to a range of phonon energies below 110 meV which is sufficient to capture all phonon structures we find a spectral function which is in good agreement with that calculated for the quasi two-dimensional sigma-band. Extending the analysis to higher energies up to 160 meV we find no evidence for any additional contributions to the fluctuation spectrum but find that the data can only be understood if the density of states is taken to decrease with increasing energy.

cond-mat.str-el↗

arXiv2014

High energy fluctuation spectra in cuprates from infrared optical spectroscopy

Coupling of the charge carriers in the high temperature superconducting oxides to bosonic modes has been widely reported using a variety of experimental probes. These include angular resolved photoemission (ARPES), scanning tunnelling spectroscopy (STS), Raman scattering (RS) and infrared optical spectroscopy (IRS). The energy scale investigated has been mostly limited to a relatively small range up to 300 meV or so. Although some ARPES experiments report boson structure up to 800 meV in the dressed electron dispersion curves the data are not analyzed to recover the spectral density of the fluctuation spectrum. We have extended to higher energies up to 2.2 eV the usual maximum entropy technique used to invert optical data so as to obtain an electron-boson spectral density. This has required that we include in our inversions, the calculated (LDA) particle-hole symmetrized energy dependent electronic density of states (DOS). Our analysis reveals that significant spectral weight remains in the fluctuation spectra up to 2.2 eV in the Bi-2212 family and to 1.2 eV in Bi-2201 for all doping levels considered.

cond-mat.supr-con↗

arXiv2014

Theory of magnetic oscillations in Weyl semimetals

Weyl semimetals are a new class of Dirac material that posses bulk energy nodes in three dimensions. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We derive expressions for the density of states, electronic specific heat, and the quantum oscillations of the magnetization, DC conductivity, and thermal conductivity. We find phase shifts in the quantum oscillations that distinguish the Weyl semimetal from conventional three dimensional Schrödinger Fermions.

cond-mat.str-el↗

arXiv2014

Particle-hole asymmetry on Hall conductivity of a topological insulator

The helical Dirac states on the surface of a topological insulator are protected by topology and display significant particle-hole asymmetry. This asymmetry arises from a subdominant Schrödinger type contribution to the Hamiltonian which provides a small perturbation to a dominant Dirac contribution. This changes the Landau levels energies in an external magnetic field ($B$) and provides modifications to the usual relativistic optical matrix elements. Nevertheless we find that the relativistic quantization of the Hall plateaux remains even when the ratio of the Schrödinger ($E_0$) to Dirac ($E_1$) magnetic energy scale increases either through an increase in $B$, a decrease in the Schrödinger mass or of the Dirac fermi velocity. First corrections to the optical matrix elements(OME) in the relativistic case drop out at least to order $(E_0/E_1)^3$. In the opposite limit $E_1$ small, the quantization remains classical but there is a split into two series. The first corrections to the OME in this case, cancel out at least to order $(E_1/E_0)^4$.

cond-mat.mes-hall↗