The origin of multiple superconducting gaps in MgB2

Microwave Kinetic Inductance Detector Made of Molecular Beam Epitaxy (MBE)-Grown MgB2 Film

We present a MgB2-based Microwave Kinetic Inductance Detector (MKID) featuring a quality factor Qi ~ 105 and noise equivalent power NEP ~ 10-14 W/Hz at 2 K. In comparison to YBCO-based MKIDs, the MgB2 detector shows greater sensitivity to both temperature and magnetic field, a result of its two-gap nature and relatively low critical Hc2 field. Our data indicate that MgB2 is more advantageous for MKID applications at temperatures lower than 3 K.

Bulk MgB2 Superconducting Materials: Technology, Properties, and Applications

The intensive development of hydrogen technologies has made very promising applications of one of the cheapest and easily produced bulk MgB2-based superconductors. These materials are capable of operating effectively at liquid hydrogen temperatures (around 20 K) and are used as elements in various devices, such as magnets, magnetic bearings, fault current limiters, electrical motors, and generators. These applications require mechanically and chemically stable materials with high superconducting characteristics. This review considers the results of superconducting and structural property studies of MgB2-based bulk materials prepared under different pressure-temperature conditions using different promising methods: hot pressing (30 MPa), spark plasma sintering (16-96 MPa), and high quasi-hydrostatic pressures (2 GPa). Much attention has been paid to the study of the correlation between the manufacturing pressure-temperature conditions and superconducting characteristics. The influence of the amount and distribution of oxygen impurity and an excess of boron on superconducting characteristics is analyzed. The dependence of superconducting characteristics on the various additions and changes in material structure caused by these additions are discussed. It is shown that different production conditions and additions improve the superconducting MgB2 bulk properties for various ranges of temperature and magnetic fields, and the optimal technology may be selected according to the application requirements. We briefly discuss the possible applications of MgB2 superconductors in devices, such as fault current limiters and electric machines.

Two-gap topological superconductor LaB2 with high Tc = 30 K

Since two gap superconductivity was discovered in MgB2, research on multigap superconductors has attracted increasing attention because of its intriguing fundamental physics. In MgB2, the Mg atom donates two electrons to the borophene layer, resulting in a stronger gap from the σ band and a weaker gap from the π bond. First-principles calculations demonstrate that the two gap anisotropic superconductivity strongly enhances the transition temperature of MgB2 in comparison with that given by the isotropic model. In this work, we report a three-band (B-σ, B-π, and La-d) two-gap superconductor LaB2 with very high Tc = 30 K by solving the fully anisotropic Migdal-Eliashberg equation. Because of the σ and π-d hybridization on the Fermi surface, the electron-phonon coupling constant λ = 1.5 is significantly larger than the λ = 0.7 of MgB2. Our work paves a new route to enhance the electron-phonon coupling strength of multigap superconductors with d orbitals. On the other hand, our analysis reveals that LaB2 belongs to the weak topological semimetal category, leading to a possible topological superconductor with the highest Tc to date. Moreover, upon applying pressure and/or doping, the topology is tunable between weak and strong with Tc varying from 15 to 30 K, opening up a flexible platform for manipulating topological superconductors.

Phonon-mediated superconductivity in [Formula: see text] compounds: a crystal prediction via cluster expansion and particle-swarm optimization

Investigating superconductivity represents one of the most significant phenomena in the field of condensed matter physics. Our simulations aim to elucidate the structures in the metallic state of Mg1-xMoxB2, which is essential for predicting their superconducting properties. By employing a first-principle cluster expansion and particle-swarm optimization, we have predicted the structures of Mg1-xMoxB2 ternary alloys, including Mg0.667Mo0.333B2, Mg0.5Mo0.5B2, and Mg0.333Mo0.667B2, and have determined their thermodynamically stable configurations under both atmospheric and high-pressure conditions. To investigate the potential for superconductivity in these structures, we have conducted a detailed examination of electronic properties that are pertinent to determining the superconducting state. Regarding superconducting properties, Mg0.333Mo0.667B2 exhibits superconductivity with a critical temperature (Tc) of 7.4 K at ambient pressure. These findings suggest that the theoretically predicted structures in Mg/Mo-substituted metal borides could play a significant role in synthesis and offer valuable insights into superconducting materials.

Possible Eliashberg-Type Superconductivity Enhancement Effects in a Two-Band Superconductor MgB_{2} Driven by Narrow-Band THz Pulses

We study THz-driven condensate dynamics in epitaxial thin films of MgB_{2}, a prototype two-band superconductor (SC) with weak interband coupling. The temperature and excitation density dependent dynamics follow the behavior predicted by the phenomenological bottleneck model for the single-gap SC, implying adiabatic coupling between the two condensates on the ps timescale. The amplitude of the THz-driven suppression of condensate density reveals an unexpected decrease in pair-breaking efficiency with increasing temperature-unlike in the case of optical excitation. The reduced pair-breaking efficiency of narrow-band THz pulses, displaying minimum near ≈0.7  T_{c}, is attributed to THz-driven, long-lived, nonthermal quasiparticle distribution, resulting in Eliashberg-type enhancement of superconductivity, competing with pair breaking.

Non-homogeneous pairing in disordered two-orbital s-wave superconductors

We investigate the effects of non-magnetic disorder in a hybridized two-dimensional two-orbital s-wave superconductor (SC) model. The situation in which electronic orbitals overlap such that the hybridizationVi,jamong them is antisymmetric, under inversion symmetry, was taken into account. The on-site disorder is given by a random impurity potentialW. We find that while the random disorder acts to the detriment of superconductivity, hybridization proceeds to favor it. Accordingly, hybridization plays an important role in two-orbital models of superconductivity, in order to hold the long-range order against the increase of disorder. This makes the present model eligible to describe real materials, since the hybridization may be induced by pressure or doping. In addition, the regime from moderate to strong disorder reveals that the system is broken into SC islands with correlated local order parameters. These correlations persist to distances of several order lattice spacing which corresponds to the size of the SC-Islands.

Discovery of a Superconductor Bi5 O4 S3 Cl Containing the Unique BiS3 Layer

The BiS2 -based layered superconductors with structures similar to those of cuprates and iron-based superconductors have stimulated much research interest. Here, a new quaternary compound is reported, Bi5 O4 S3 Cl, which crystalizes in a tetragonal structure with P4/mmm (No. 123) space group having alternately stacking unique BiS3 layers and Bi2 O2 layers along the c-axis with a Cl atom located at the center of the unit cell. A superconducting transition above 3 K is observed for both electrical transport and magnetic measurements. Hall resistivity measurements show its multiband character with a conduction dominated by electron-like charge carriers. The first-principles calculations exhibit that the semiconducting parent phase Bi5 O4 S3 Cl becomes metallic when sulfur vacancies are introduced, which hints the origin of superconductivity in Bi5 O4 S3 Cl. The findings will inspire the exploration of new BiS-based superconductors.

Surface Superconductivity with High Transition Temperatures in Layered CanBn+1Cn+1 Films

Proposed by Ginzberg nearly 60 years ago, surface superconductivity refers to the emergent phenomenon that the electrons on or near the surface of a material becomes superconducting despite its bulk is nonsuperconducting. Here, based on first-principles calculations within density functional theory, we predict that the superconducting transition temperature T_c at the surfaces of Ca_nB_n+1C_n+1 (n = 1, 2, 3, ...) films can be drastically enhanced to ∼90 K from 8 K for bulk CaBC. Our detailed analyses reveal that structural symmetry reduction at surfaces induces pronounced carrier self-doping into the surface B-C layer of the films and shifts the σ-bonding states toward the Fermi level; furthermore, the in-plane stretching modes of the surface layers experience significant softening. These two effects work collaboratively to strongly enhance the electron-phonon coupling, which in turn results in much higher T_c values than the McMillian limit. These findings point to new material platforms for realizing unusually high-T_c surface superconductivity.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

Carbon-Coating Layers on Boron Generated High Critical Current Density in MgB2 Superconductor

Boron particles with a homogeneous carbon-coating layer were employed as the precursor to fabricate MgB₂ superconductors to generate artificial two-dimensional (2D) flux-pinning centers. Systematic microstructure investigation reveals that the carbon layers are well-distributed in the MgB₂ matrix without agglomeration. The thickness of the carbon layers is smaller than the MgB₂ coherent length, which makes them transparent to supercurrent. The critical current density is increased because of the strong flux-pinning effects of the 2D carbon layers in the superconductor as highly efficient flux-pinning centers and the increased irreversibility field due to the carbon-doping effects.

Relation between Crystal Structure and Transition Temperature of Superconducting Metals and Alloys

Using the Roeser–Huber equation, which was originally developed for high temperature superconductors (HTSc) (H. Roeser et al., Acta Astronautica 62 (2008) 733), we present a calculation of the superconducting transition temperatures, T c , of some elements with fcc unit cells (Pb, Al), some elements with bcc unit cells (Nb, V), Sn with a tetragonal unit cell and several simple metallic alloys (NbN, NbTi, the A15 compounds and MgB 2 ). All calculations used only the crystallographic information and available data of the electronic configuration of the constituents. The model itself is based on viewing superconductivity as a resonance effect, and the superconducting charge carriers moving through the crystal interact with a typical crystal distance, x. It is found that all calculated T c -data fall within a narrow error margin on a straight line when plotting ( 2 x ) 2 vs. 1 / T c like in the case for HTSc. Furthermore, we discuss the problems when obtaining data for T c from the literature or from experiments, which are needed for comparison with the calculated data. The T c -data presented here agree reasonably well with the literature data.

Extrinsic Two-Dimensional Flux Pinning Centers in MgB2 Superconductors Induced by Graphene-Coated Boron

Extrinsic two-dimensional flux pinning centers, via graphene-encapsulated boron powder as precursors, have been introduced into MgB₂ superconductors by means of in situ and diffusion sintering methods. Uniform graphene encapsulation of the boron powders was achieved by the hydrothermal method with highly dispersed graphene oxide as the precursor. The graphene coating layers induce remaining graphene layers and other defects acting as flux pinning centers in the matrix as well as improved connectivity in between grains. The increased critical current density ( J_c) is attributed to the enhanced flux pinning force and improved connectivity. Two-dimensional flux pinning centers provided by thin graphene layers and grain boundaries in MgB₂ possess high flux pinning efficiency without suppressing the connectivity of the MgB₂ superconductor.

Observation of Bogoliubov Band Hybridization in the Optimally Doped Trilayer Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ}

Using a laser-excited angle-resolved photoemission spectroscopy capable of bulk sensitive and high-energy resolution measurements, we reveal a new phenomenon of superconductors in the optimally doped trilayer Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ}. We observe a hybridization of the Bogoliubov bands derived from the inner and outer CuO_{2} planes with different magnitudes of energy gaps. Our data clearly exhibit the splitting of coherent peaks and the consequent enhancement of spectral gaps. These features are reproduced by model calculations, which indicate that the gap enhancement extends over a wide range of Fermi surface up to the antinode. The significant modulation of electron pairing uncovered here might be a crucial factor to achieve the highest critical temperature in the trilayer cuprates.

Free surfaces recast superconductivity in few-monolayer MgB2: Combined first-principles and ARPES demonstration

Two-dimensional materials are known to harbour properties very different from those of their bulk counterparts. Recent years have seen the rise of atomically thin superconductors, with a caveat that superconductivity is strongly depleted unless enhanced by specific substrates, intercalants or adatoms. Surprisingly, the role in superconductivity of electronic states originating from simple free surfaces of two-dimensional materials has remained elusive to date. Here, based on first-principles calculations, anisotropic Eliashberg theory, and angle-resolved photoemission spectroscopy (ARPES), we show that surface states in few-monolayer MgB2 make a major contribution to the superconducting gap spectrum and density of states, clearly distinct from the widely known, bulk-like σ- and π-gaps. As a proof of principle, we predict and measure the gap opening on the magnesium-based surface band up to a critical temperature as high as ~30 K for merely six monolayers thick MgB2. These findings establish free surfaces as an unavoidable ingredient in understanding and further tailoring of superconductivity in atomically thin materials.

Anisotropic resonance modes emerging in an antiferromagnetic superconducting state

Two strong arguments in favor of magnetically driven unconventional superconductivity arise from the coexistence and closeness of superconducting and magnetically ordered phases on the one hand, and from the emergence of magnetic spin-resonance modes at the superconducting transition on the other hand. Combining these two arguments one may ask about the nature of superconducting spin-resonance modes occurring in an antiferromagnetic state. This problem can be studied in underdoped BaFe₂ As₂, for which the local coexistence of large moment antiferromagnetism and superconductivity is well established by local probes. However, polarized neutron scattering experiments are required to identify the nature of the resonance modes. In the normal state of Co underdoped BaFe₂ As₂ the antiferromagnetic order results in broad magnetic gaps opening in all three spin directions that are reminiscent of the magnetic response in the parent compound. In the superconducting state two distinct anisotropic resonance excitations emerge, but in contrast to numerous studies on optimum and over-doped BaFe₂ As₂ there is no isotropic resonance excitation. The two anisotropic resonance modes appearing within the antiferromagnetic phase are attributed to a band selective superconducting state, in which longitudinal magnetic excitations are gapped by antiferromagnetic order with sizable moment.

Real-Time Observation of Phonon-Mediated σ-π Interband Scattering in MgB_{2}

In systems having an anisotropic electronic structure, such as the layered materials graphite, graphene, and cuprates, impulsive light excitation can coherently stimulate specific bosonic modes, with exotic consequences for the emergent electronic properties. Here we show that the population of E_{2g} phonons in the multiband superconductor MgB_{2} can be selectively enhanced by femtosecond laser pulses, leading to a transient control of the number of carriers in the σ-electronic subsystem. The nonequilibrium evolution of the material optical constants is followed in the spectral region sensitive to both the a- and c-axis plasma frequencies and modeled theoretically, revealing the details of the σ-π interband scattering mechanism in MgB_{2}.

Ground state, collective mode, phase soliton and vortex in multiband superconductors

This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these bands. The discovery of prominent multiband superconductors MgB2 and later iron-based superconductors, has triggered enormous interest in multiband superconductors. The most recently discovered superconductors exhibit multiband features. The multiband superconductors possess novel properties that are not shared with their single-band counterpart. Examples include: the time-reversal symmetry broken state in multiband superconductors with frustrated interband couplings; the collective oscillation of number of Cooper pairs between different bands, known as the Leggett mode; and the phase soliton and fractional vortex, which are the main focus of this review. This review presents a survey of a wide range of theoretical exploratory and experimental investigations of novel physics in multiband superconductors. A vast amount of information derived from these studies is shown to highlight unusual and unique properties of multiband superconductors and to reveal the challenges and opportunities in the research on the multiband superconductivity.

Size and symmetry of the superconducting gap in the f.c.c. Cs3C60 polymorph close to the metal-Mott insulator boundary

The alkali fullerides, A(3)C(60) (A = alkali metal) are molecular superconductors that undergo a transition to a magnetic Mott-insulating state at large lattice parameters. However, although the size and the symmetry of the superconducting gap, Δ, are both crucial for the understanding of the pairing mechanism, they are currently unknown for superconducting fullerides close to the correlation-driven magnetic insulator. Here we report a comprehensive nuclear magnetic resonance (NMR) study of face-centred-cubic (f.c.c.) Cs(3)C(60) polymorph, which can be tuned continuously through the bandwidth-controlled Mott insulator-metal/superconductor transition by pressure. When superconductivity emerges from the insulating state at large interfullerene separations upon compression, we observe an isotropic (s-wave) Δ with a large gap-to-superconducting transition temperature ratio, 2Δ0/k(B)T(c) = 5.3(2) [Δ0 = Δ(0 K)]. 2Δ0/k(B)T(c) decreases continuously upon pressurization until it approaches a value of ~3.5, characteristic of weak-coupling BCS theory of superconductivity despite the dome-shaped dependence of Tc on interfullerene separation. The results indicate the importance of the electronic correlations for the pairing interaction as the metal/superconductor-insulator boundary is approached.

Ginzburg-Landau theory of dirty two band s(+/-) superconductors

In this Letter, we study the effect of nonmagnetic impurities on two-band superconductors by deriving the corresponding Ginzburg-Landau equation. Depending on the strength of (impurity-induced) interband scattering, we find that there are two distinctive regions where the superconductors behave very differently. In the strong impurity-induced interband scattering regime T(c) << tau(t)(-1), where tau(t) approximately mean lifetime an electron stays in one band, the two-band superconductor behaves as an effective one-band dirty superconductor. In the other limit T(c) > or = tau(t)(-1), the dirty two-band superconductor is described by a network of frustrated two-band superconductor grains connected by Josephson tunneling junctions, and the Anderson theorem breaks down.

Type-1.5 superconductivity

We demonstrate the existence of a novel superconducting state in high quality two-component MgB2 single crystalline superconductors where a unique combination of both type-1 (lambda{1}/xi{1}<1/sqrt[2]) and type-2 (lambda{2}/xi{2}>1/sqrt[2]) superconductor conditions is realized for the two components of the order parameter. This condition leads to a vortex-vortex interaction attractive at long distances and repulsive at short distances, which stabilizes unconventional stripe- and gossamerlike vortex patterns that we have visualized in this type-1.5 superconductor using Bitter decoration and also reproduced in numerical simulations.

A versatile system for ultrahigh resolution, low temperature, and polarization dependent laser-angle-resolved photoemission spectroscopy

We have developed a low temperature ultrahigh resolution system for polarization dependent angle-resolved photoemission spectroscopy (ARPES) using a vacuum ultraviolet (vuv) laser (hnu=6.994 eV) as a photon source. With the aim of addressing low energy physics, we show the system performance with angle-integrated PES at the highest energy resolution of 360 mueV and the lowest temperature of 2.9 K. We describe the importance of a multiple-thermal-shield design for achieving the low temperature, which allows a clear measurement of the superconducting gap of tantalum metal with a T(c)=4.5 K. The unique specifications and quality of the laser source (narrow linewidth of 260 mueV, high photon flux), combined with a half-wave plate, facilitates ultrahigh energy and momentum resolution polarization dependent ARPES. We demonstrate the use of s- and p-polarized laser-ARPESs in studying the superconducting gap on bilayer-split bands of a high T(c) cuprate. The unique features of the quasi-continuous-wave vuv laser and low temperature enables ultrahigh-energy and -momentum resolution studies of the spectral function of a solid with large escape depth. We hope the present work helps in defining polarization dependent laser excited angle-resolved photoemission spectroscopy as a frontier tool for the study of electronic structure and properties of materials at the sub-meV energy scale.

Observation of Leggett's collective mode in a multiband MgB2 superconductor

We report observation of Leggett's collective mode in a multiband MgB2 superconductor with Tc=39 K arising from the fluctuations in the relative phase between two superconducting condensates. The novel mode is observed by Raman spectroscopy at 9.4 meV in the fully symmetric scattering channel. The observed mode frequency is consistent with theoretical considerations based on first-principles computations.

Analysis of H(c2)(θ,T) for Mg(B(1-x)C(x))(2) single crystals by using the dirty two-gap model

To understand the effect of carbon doping on the superconductivity in MgB(2), we obtained the angle- and temperature-dependent upper critical fields [H(c2)(θ) and H(c2)(T)] for Mg(B(1-x)C(x))(2) single crystals (x = 0.06 and 0.1) from resistivity measurements while varying the temperature, the field, and the direction of the field. The detailed values of the diffusivity for two different directions for each σ-band and π-band were obtained to explain both the temperature- and the angle-dependent H(c2) by using the dirty-limit two-gap model. The induced impurity scattering of the σ-band and the π-band for both the ab-plane and the c-direction is studied.

Anisotropic drude response and the effect of anisotropic C substitution in

The in-plane and the out-of-plane optical spectra of small single crystals of Mg(B1-xCx)2 were directly determined by a microscope spectroscopy technique. Contrary to previous reports, the estimated plasma frequencies for both directions are quite consistent with the band calculation. A multi-Drude picture corresponding to a multiband system is necessary to explain the whole spectral profile. The spectral changes with the carbon substitution indicate a decrease of carrier concentration as well as an increase of scattering rate, particularly, in the sigma bands.

Enhancement of the superconducting transition temperature of MgB2 by a strain-induced bond-stretching mode softening

We report a systematic increase of the superconducting transition temperature T(c) with a biaxial tensile strain in MgB2 films to well beyond the bulk value. The tensile strain increases with the MgB2 film thickness, caused primarily by the coalescence of initially nucleated discrete islands (the Volmer-Weber growth mode.) The T(c) increase was observed in epitaxial films on SiC and sapphire substrates, although the T(c) values were different for the two substrates due to different lattice parameters and thermal expansion coefficients. We identified, by first-principles calculations, the underlying mechanism for the T(c) increase to be the softening of the bond-stretching E(2g) phonon mode, and we confirmed this conclusion by Raman scattering measurements. The result suggests that the E(2g) phonon softening is a possible avenue to achieve even higher T(c) in MgB2-related material systems.

Mechanism of gap opening in a triple-band Peierls system: in atomic wires on Si

One dimensional (1D) metals are unstable at low temperature undergoing a metal-insulator transition coupled with a periodic lattice distortion, a Peierls transition. Angle-resolved photoemission study for the 1D metallic chains of In on Si(111), featuring a metal-insulator transition and triple metallic bands, clarifies in detail how the multiple band gaps are formed at low temperature. In addition to the gap opening for a half-filled ideal 1D band with a proper Fermi surface nesting, two other quasi-1D metallic bands are found to merge into a single band, opening a unique but k-dependent energy gap through an interband charge transfer. This result introduces a novel gap-opening mechanism for a multiband Peierls system where the interband interaction is important.

Pair-breaking and superconducting state recovery dynamics in MgB2

We present studies of the photoexcited quasiparticle dynamics in MgB2 where, using femtosecond optical techniques, Cooper pair-breaking dynamics (PBD) have been temporally resolved for the first time. The PBD are strongly temperature and photoexcitation intensity dependent. Analysis of the PBD using the Rothwarf-Taylor equations suggests that the anomalous PBD arises from the fact that in MgB2 photoexcitation is initially followed by energy relaxation to high frequency phonons instead of, as commonly assumed, e-e thermalization. Furthermore, the bare quasiparticle recombination rate and the probability for pair breaking by phonons have been determined.

Mott transitions in multiorbital systems

Using the dynamical mean field theory it is shown that interorbital Coulomb interactions in nonisotropic multiorbital materials give rise to a single Mott transition. Nevertheless, narrow and wide subbands exhibit different excitation spectra in the metallic and insulating phases. The close analogy between "multigap" insulating behavior and multigap superconductivity is pointed out.

Anomalous coherence peak in the microwave conductivity of c-axis oriented MgB2 thin films

The temperature dependence of the real part of the microwave complex conductivity at 17.9 GHz obtained from surface impedance measurements of two c-axis oriented MgB2 thin films reveals a pronounced maximum at a temperature around 0.6 times the critical temperature. Calculations in the frame of a two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that this maximum corresponds to an anomalous coherence peak resembling the two-gap nature of MgB2. Our model assumes there is no interband impurity scattering and a weak interband pairing interaction, as suggested by band structure calculations. In addition, the observation of a coherence peak indicates that the pi band is in the dirty limit and dominates the total conductivity of our films.